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Unit specification
Aims
This module aims to engage students with a circle of
algorithmic techniques and concrete problems arising
in elementary number theory and graph theory.
Brief description
Modern Discrete Mathematics is broad subject bearing
on everything from logic to logistics. Roughly speaking, it
is a part of mathematics that touches on those subjects that
Calculus and Algebra can't: problems where there is no sensible notion
continuity or smoothness and little algebraic structure. The subject,
which is typically concerned
with finite or at the most countable sets of objects,
abounds with interesting, concrete problems and entertaining examples.
Throughout, we will be interested in developing and analysing
algorithms: explicit recipes to solve problems and
prove theorems.
Intended learning outcomes
Students should develop the ability to think and argue algorithmically,
mainly by studying examples in elementary number theory, graph theory and
combinatorics. | 677.169 | 1 |
Synopsis
A guide to the theory behind bond math formulas | 677.169 | 1 |
The focus of the study was to identify secondary school students' difficulties with aspects of linearity and linear functions, and to assess their teachers' understanding of the nature of the difficulties experienced by their students. A cross-sectional study with 1561 Grades 8–10 students enrolled in mathematics courses from Pre-Algebra to Algebra II, and their 26 mathematics teachers was employed. All participants completed the Mini-Diagnostic Test (MDT) on aspects of linearity and linear functions, ranked the MDT problems by perceived difficulty, and commented on the nature of the difficulties. Interviews were conducted with 40 students and 20 teachers. A cluster analysis revealed the existence of two groups of students, Group 0 enrolled in courses below or at their grade level, and Group 1 enrolled in courses above their grade level. A factor analysis confirmed the importance of slope and the Cartesian connection for student understanding of linearity and linear functions. There was little variation in student performance on the MDT across grades. Student performance on the MDT increased with more advanced courses, mainly due to Group 1 student performance. The most difficult problems were those requiring identification of slope from the graph of a line. That difficulty persisted across grades, mathematics courses, and performance groups (Group 0, and 1). A comparison of student ranking of MDT problems by difficulty and their performance on the MDT, showed that students correctly identified the problems with the highest MDT mean scores as being least difficult for them. Only Group 1 students could identify some of the problems with lower MDT mean scores as being difficult. Teachers did not identify MDT problems that posed the greatest difficulty for their students. Student interviews confirmed difficulties with slope and the Cartesian connection. Teachers' descriptions of problem difficulty identified factors such as lack of familiarity with problem content or context, problem format and length. Teachers did not identify student difficulties with slope in a geometric | 677.169 | 1 |
Online Number Theory Tutoring
for All Grades
Our Online Number Theory Tutoring program is designed to help you get the desired grade by mastering the subject.
Number and Operations are an essential part of the study of Mathematics. A number is a quantity that is used in counting and measuring. The definition of the term number includes such numbers as zero, negative numbers, rational numbers and complex numbers. The study of Number and Operations involves understanding representations, relationships and number systems.
Rational Numbers
Irrational Numbers
Significant Figures
Sets
Indices
Polynomials
Imaginary Number
Complex Number
Matrices
Matrices and Determinants
Sequences and Series
Mathematical Induction
Binomial Theorem
Ratio and Proportion
Whether you need Number Theory help or some quick assistance in understanding Number Theory questions before a test or an exam, our Number Theory tutors can help. Our tutors provide you with instant help, homework help and help with assignments in Number Theory.
We have Number Theory tutors who are experts in Number Theory across K-12 and beyond. Whatever your requirements are, the rigor and discipline of our tutor certification program will ensure that you get all that you want and more in your Number Theory tutor. Our tutors are familiar with the National and various State Standards required across grades in the US and other countries.
With our Online Number Theory Tutoring and Number Theory Homework help programs, studying the subject becomes easy and fun for students. Under the expert guidance of our tutors, students excel in Number Theory.
Click on your grade below to get a sample list of topics covered in that Grade for Number Theory. Please note that all tutoring programs will be customized for the individual. | 677.169 | 1 |
Engineering Math (ODE) Homework by pjmarron
Im taking an engineering course named Ordinary Differential Equations, and basically I don't understand any of the examples therefore not being able to do any of the problems in the textbook. So i have… (Budget: $30-$250 USD, Jobs: Mathematics) | 677.169 | 1 |
Intermediate Algebra Graphs and Models
9780321416162
ISBN:
0321416163
Edition: 3 Pub Date: 2007 Publisher: Prentice Hall
Summary: The Third Edition of the Bittinger Graphs and Models series helps readers succeed in algebra by emphasizing a visual understanding of concepts. This latest edition incorporates a new Visualizing for Success feature that helps readers make intuitive connections between graphs and functions without the aid of a graphing calculator. In addition, readers learn problem-solving skills from the Bittinger hallmark five-step ...problem-solving process coupled with Connecting the Concepts and Aha! Exercises. As you have come to expect with any Bittinger text, we bring you a complete supplements package including MyMathLabtrade; and the New Instructor and Adjunct Support Manual. KEY TOPICS: Basics of Algebra and Graphing; Functions, Linear Equations, and Models; Systems of Linear Equations and Problem Solving; More Equations and Inequalities; Polynomials and Polynomial Functions; Rational Expressions, Equations, and Functions; Exponents and Radicals; Quadratic Functions and Equations; Exponential and Logarithmic Functions; Conic Sections; Sequences, Series, and the Binomial Theorem. MARKET: For all readers interested in Algebra321416162-3-0-3 Orders ship the same or next business day... [more] | 677.169 | 1 |
Summary: 95 Statistics is all around us, and Triola helps students understand how this course will impact their lives beyondthe classroomndash;as consumers, citizens, and profes...show moresionals.Elementary Statistics Using the TI-83/84 Plus Calculator, Third Edition provides extensive instruction for using the TI-83 and TI-84 Plus (and Silver Edition) calculators for statistics, with information on calculator functions, images of screen displays, and projects designed exclusively for the graphing calculator. Drawn from Triola's Elementary Statistics, Eleventh Edition, this text provides the same student-friendly approach with material presented in a real-world context.The Third Edition contains more than 2,000 exercises, 87% are new, and 82% use real data. It also contains hundreds of examples; 86% are new and 94% use real data. By analyzing real data, students are able to connect abstract concepts to the world at large, learning to think statistically and apply conceptual understanding using the same methods that professional statisticians employ.Datasets and other resources (where applicable) for this book are available here . ...show less
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N/a Boston, MA 2011 Hard Cover Third Edition Fair 4to-over 9?"-12" tall. Text book has rough tears on top and bottom edges of cover. Corners are bumped. Includes CD. 865 pages. There is highlighting...show more throughout entire book. Some writing on a couple of the pages. Used sticker on spine and back cover. This includes the TI-84 calculator. ...show less
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Love Is the Answer Washington, DC
Access code for this book is sold separately and is NOT included. Hardcover w/unopened CD. Very clean; strong binding, no marks or highlighting | 677.169 | 1 |
Actually, I think it is rewarding to look some things up, even if you use Google and Co.. For a student it is also a psychological effect to find solutions on the Internet. Namely, if you have some problem in symplectic geometry courses, these problems are normally rather specific, so you will have trouble finding solutions on the web easily. However, when using Google books, you can easily find parts of books which may contain relevant information for your proof or even give a good starting point for a proof. If someone simply uses the Internet to copy a proof then he/she will have problems to really understand mathematics. But, admittedly, there are proofs that I haven't understood or, this more often the case, wouldn't be able to reproduce offhand. In this case, the internet proves to be very useful, especially if you also have students that try to autodidactically learn some further topics in mathematics.
Personally, I would design problem sheets as follows:
-Make 3 to 4 easy problems which simply consist of getting familiar with the definitions and the rules in the respective field.
-Then make one problem that is rather technical and requires the student to make some longer steps in proving the statement. These calculations shouldn't be too complicated as otherwise the student will probably lose patience and simply look the solution up.
-Then design 2-3 problems that are more far-leading and require using calculation rules, and a bit creativity. Still, they shouldn't be too complicated.
Why am i always telling you about the complexity of the problems? Well, at least in Germany, we have only 30% of the students obtaining a degree in mathematics. I don't know how things are handles in the U.S. or elsewhere, but most of our students are frustrated becuase they simply don't find a starting point for the exercises. And this shouldn't happen.
I think, most of the students have the will to solve problems on their own. Especially mathematics and physics are subjects you study because you're passionate about them. Biological research has shown indeed that motivated apes are more thankful and curious then demotivated apes. I think this applies to students as well (and to us as well). The typical student involved in a biologically complicates process. The post-adolesence. The years 15-30 are the years where you are requires to pass a lot of tests. And for doing so you have to be motivated and self-confident. At least in Germany, for a lot of students, this is a problem (But I don't think it's much different elsewhere, at least I hope so, because otherwise, we're doing something wrong here).
Most cheating can be avoided if questions are motivating and asked in sch a manner that the first ones are easy to answer, and the following ones increase slightly in diffculty.
This is my opinion. I talk to a lot of students in physics which suffer from depressions because they believe they won't get anything. This belief is apparenbtly that deep that they simply copy homework or use Google. Mostly, when these students continue their studies they are very succesful later on. But a lot of them simply stops studying math and physics. A lot of potential is wasted here.
All I've written may sound a bit offtopic, but I think that there is the real problem. If you motivate students to think on their own, they will rejoice in proofs and all that. This was also my (personal) experience. | 677.169 | 1 |
Mathematics is crucial to all aspects of engineering and technology. Understanding key mathematical concepts and applying them successfully to solve problems are vital skills every engineering student must acquire. This text teaches, applies and nurtures those skills. Mathematics for Engineers is informal, accessible and practically oriented. The material is structured so students build up their knowledge and understanding gradually. The interactive examples have been carefully designed to encourage students to engage fully in the problem-solving process. MyMathLab(r) is a series of text-specific, easily customizable online courses for Prentice Hall textbooks in mathematics and statistics. Powered by CourseCompass (Pearson Education's online teaching and learning environment) and MathXL(r) (our online homework, tutorial, and assessment system), MyMathLab gives you the tools you need to deliver all or a portion of your course online, whether your students are in a lab setting or working from home. | 677.169 | 1 |
Today's
students have a critical need to learn and understand math
vocabulary. It no longer passes the test to just memorize
functions and do calculations, but not be able to explain how the
work was done. | 677.169 | 1 |
This textbook is suitable for graduate students in engineering and also for use in a senior-level course. Some knowledge of the use of ordinary and partial differential equations to describe problems related to engineering analysis is assumed, as is a rudimentary knowledge of matrix algebra. The book is divided into twelve chapters, each being devoted to some mathematical problems, and four appendices are included to describe reference material. The author starts with an elementary example of the deflection of a tightly stretched wire under a distributed load. This example is sufficient to: (a) refresh the reader on some aspects of differential equations that will prove important for understanding approximate solutions, (b) introduce the concept of approximate solutions, and (c) actually define and illustrate the finite element method (FEM). The next chapters are devoted to linear second order ordinary differential equations, a finite element function for two dimensions, Poisson's equation (FEM approximation, applications). One chapter is devoted to higher-order elements difficulties arising in maintaining continuity of the approximating function between elements. Chapter 9 presents a FEM program for two-dimensional boundary value problems. All codes are written in MATLAB script, which can be run on the student version of MATLAB. Also, a number of applications related to various fields of engineering is provided. In the exercises at the end of most chapters, there is a section on "Numerical experiments and code development" with problems that encourage students to test the codes. All codes, example data files, and auxiliary codes are available for download on the website for this book.
Reviewer:
Pavol Chocholatý (Bratislava) | 677.169 | 1 |
In this differentiation instructional activity, students select from a list of differentiation rules which one they have to use to find the derivative of the given equation. They evaluate one integral exactly.
Directions are written to solve a related rate problem step by step. There are five example problems to practice solving for related rates. Use of the Chain Rule and/or implicit differentiation is one of the key steps to solving these word problems.
Students review vocabulary words for calculus. In this calculus lesson, a list of vocabulary words is provided for students to review. Students may use this list as a review of important terms to know for calculus.
Young scholars calculate the velocity of object as they land or take off. In this calculus lesson, students are taught how to find the velocity based on the derivative. They graph a picture the represent the scenario and solve for the velocity. | 677.169 | 1 |
Resources for math teachers
Resources for Algebra 1 and Algebra 2
Using the internet as a teaching tool
Algebra 1
Algebra 2
General HELP
1-
HOTMATH will help you with many step-by-step solutions to the odd problems of almost every textbook
2-
PURPLE MATH Offers a variety of complete lessons with quizzes and extra tutorials. These are just some
topics your students can use. There are many more topics.
3- Fee is required
4-
5- Search for the lesson that you want. Copy the hyperlink and then import that
video to your computer by using a free software from
For the first time only:
a- Go to
b- Download the Free Ipod Video Converter 2.92
c- Install or run the program and create an icon on your
desktop (Just to find it)
d- Open the Free IPOD converter
e-
f- Click on the Youtube icon
g- Paste the link of the video that you want to show your
students
h- Click that you want to automatically convert your video to
an Ipod format (mp4)
i- Make sure to select the folder for your file (Go to
parameters)
j- Click download now
k-
6- Use your textbook websites
7- Test for Juniors and Seniors: KEMPT. To get there type or go to | 677.169 | 1 |
Chapter 1: Introduction to Spreadsheet Models for Optimization
Chapter 1
Introduction to Spreadsheet Models for Optimization
This is a book about optimization with an emphasis on building models and using spreadsheets. Each facet of this theme—models, spreadsheets, and optimization— has a role in defining the emphasis of our coverage.
A model is a simplified representation of a situation or problem. Models attempt to capture the essential features of a complicated situation so that it can be studied and understood more completely. In the worlds of business, engineering, and science, models aim to improve our understanding of practical situations. Models can be built with tangible materials, or words, or mathematical symbols and expressions. A mathematical model is a model that is constructed—and also analyzed—using mathematics. In this book, we focus on mathematical models. Moreover, we work with decision models, or models that contain representations of decisions. The term also refers to models that support decision-making activities. | 677.169 | 1 |
Easy Input Tool
Entering your math problem has never been easier. Use the keyboard to enter common math symbols or insert special symbols and expressions using the toolbar. Filter by subject to find the symbols most relevant to you.
Problems are recognized and then formatted as they appear in your math textbook.
Select Your Topic
Complex problems mean that you could have many different answers. Use the dropdown topic selection menu to select the topic that most closely matches what you are looking for.
Step-by-step answers. Instantly.
Math Instant answers returns your answer plus step-by-step solutions to even the most complex problems. Roll over unfamiliar terms in each of the steps to get an explanation of what they mean.
Want to see a graph? Instant math allows you to graph your solutions too. | 677.169 | 1 |
Algebra, says Devlin, is a language, a very precise language written in symbols, and it's everywhere: in nearly all electronic devices, every statistic and each Internet search engine - and, indeed, in every train leaving Boston.
"You can store information using it. You can communicate information using it," Devlin said. "Google has made billions capitalizing on algebra."
Yet our schools don't always do a very good job teaching it, Devlin said. Instead of showing students the possibilities and beauty algebra offers, they ultimately steer frustrated and bored students away from math and the 21st century careers that use it - the opposite of the intended result.
...
Algebra, by the dictionary's definition, is essentially abstract arithmetic, letters and symbols representing relationships between groups, sets, matrices or fields. It's a way to find a piece to a puzzle using the pieces you already have in place.
It comes in very handy for engineers, financial analysts and sociologists, not to mention World of Warcraft video game players, some of whom use algebraic formulas to decide which weapon is more effective under certain circumstances - perhaps another hook to lure unsuspecting teens into seeing the useful side of algebra.
...
Laptop computer. The computer is just an implementation in electrical circuits of a special form of algebra (called Boolean algebra) invented in the 19th century. Ordinary algebra is used to design and manufacture computers, and is at the heart of how to program them.
Cell phone. A cell phone is a particular kind of computer. An important feature of cell phones is that your phone receives all the signals sent to every cell phone in the region, but only responds to signals sent to your phone. This is achieved by using signal coding systems built on algebra.
Parking cop. Today's parking enforcement officers may carry equipment connecting them directly to a central vehicle database that registers your parking fine before you get back to the car and see the ticket on the windshield. Without algebra, such a system could not exist.
Hybrid car. Modern cars often come equipped with GPS, a highly sophisticated system that is designed using enormous amounts of mathematics that builds on algebra.
Delivery truck. Large retail chains use mathematical methods to determine the routing and scheduling of their delivery trucks; algebra is fundamental to those methods.
Stoplight. These days, stoplights are centrally controlled by computers, so there is even algebra involved in turning the light from red to green.
IPod. This is a math device in your hand. The iPod stores music using sophisticated mathematics built on algebra. And the iPod shuffle mechanism uses regular school algebra to order your songs randomly.
...
Even though it is a very pro-algebra article, my favorite quote was by an unknown source:
"Algebra ... the intensive study of the last three letters of the alphabet."
Share this:
I had to solve two problems for myself today. I am posting my solutions here, mainly for my own reference but maybe somebody out there might have the same issues to be solved.
The first problem I faced was installing a network printer so that it would be available to all users on that machine. This is probably a minor problem for seasoned IT pros, but since I am not one, it took some investigating. I learned that local printers are installed automatically for all users, while network printers are associated with user profiles. This means that when you install a network printer it is only available to the user profile that you used when installing.
The solution is to install the network printer as a local printer. In other words, go to Control Panel .. Printers. Click "Add a printer". Select that you want to install a local printer. At this point you will create a new port, using a Standard TCP/IP port. You'll need to have the IP address of the printer to do this and you'll also want to have the drivers handy.
Since it is installed as a local printer it will now be available to all users when they log in. The bug I still haven't worked out, though some of you may have an idea, is that even though I have selected it to be the default printer in my profile, it is not necessarily the default printer for other users. If is the first printer installed, no problem, but otherwise it is not the default for other users. | 677.169 | 1 |
This website is housed at the School of Mathematics and Statistics, University of St. Andrews, Scotland. There is a biographies index, which has biographical information, arranged alphabetically by the person's last name or arranged by time periods, beginning with pre-500 A.D. Each biography is signed by the article's author, and a list of References is also provided for further research. There is also a History Topics index, with topics broken down into math in various cultures and math topics--i.e., algebra, mathematical physics, etc.
This website includes historical biographies of women in mathematics, a list of links to professional societies in mathematics, K-12 teaching materials, the full text to proceedings from the International Conference on Technology in Collegiate Mathematics (1994-2003), and a indexed page of links to other websites on various math topics search website "Math Archives" is the home to the Electronic Proceedings of the International Conference on Technology in Collegiate Mathematics. This is an annual conference, and the Math Archives has full text of the papers from 1994 to 2003. There is both an author and subject indexUSA.gov is the U.S. government web portal to all federal, state, tribal, and local government web resources and services. USA.gov is intended to help people navigate government information, procedures, and policies.
A to Z of Mathematics: A Basic Guide Print Location: Ref QA93 .S49 2002
Using the language of a general reader, this book discusses the basic skills required for understanding math. A number of examples show not only how to work a math problem but also why the problems are solved that way.Facts on File Calculus Handbook Print Location: Ref QA303.2 M36 2003
Intended use is for middle school, high school and college students taking single-variable calculus. It's a comfortingly slim book. There are included a number of well-known calculus theoremsAn international non-profit organization dedicated to advancing science around the world by serving as an educator, leader, spokesperson and professional association. In addition to organizing membership activities, AAAS publishes the journal Science (earlier issues online), as well as many scientific newsletters, books and reports, and supports programs that raise the bar of understanding for science worldwide. AAAS also provides some career reosources that are of general interest.
American Mathematical Society
Founded in 1888 to further mathematical research and scholarship, the American Mathematical Society fulfills its mission through programs and services that promote mathematical research and its uses, strengthen mathematical education, and foster awareness and appreciation of mathematics and its connections to other disciplines and to everyday life.
Aim is to advance the participation of girls and women in the sciences, from biomedicine to mathematics and the social sciences, in engineering, and in the technologies, in all areas and at all levels.
Organized in 1920, the National Council of Teachers of Mathematics is now the world's largest group of its kind. You can find content standards for teaching mathematics here, as well as weekly problems and games for you to try with students of all agesQuotations
Dictionary of Quotations in Mathematics Print Location: Ref QA99 .D53 2002
A book of quotes on mathematics, divided into topical chapters. The goal of the book is to make students aware that there is a higher reason for doing mathematics than simply solving a problemInstitute of Mathematical Statistics
Worldwide organization whose purpose is to spread awareness on the applications and developments of statistics and probability. Student membership is free. You can also get full text on many of the articles found within the recent issues of four IMS publications: Annals of Applied Probability, Annals of Probability, Annals of Statistics, and Statistical ScienceMathGuide
The MathGuide is an Internet-based subject gateway to scholarly relevant information in mathematics, located at the Lower Saxony State- and University Library, Göttingen (Germany).AI | 677.169 | 1 |
Precalculus is a preparatory course for calculus and covers the following topics: algebraic, exponential, logarithmic, trigonometric equations and inverse trigonometric identities. Prerequisite: Grade of b or higher in MATH 150, or a score of 24 or above on the math portion of the ACT or 540 or above SAT score or a passing score on the Columbia College math placement exam. G.E.
Prerequisite(s) / Corequisite(s):
Grade of B or higher in MATH 150, or a score of 24 or above on the math portion of the ACT or 540 or above SAT score or a passing score on the Columbia College math placement exam.
Course Rotation for Day Program:
Offered Fall and Spring.
Text(s):
Most current editions of the following:
Most current editions of the following:
Trigonometry
By Stewart, Redlin, & Watson (Brooks-Cole) Recommended
Precalculus
By Blitzer, R. (Prentice Hall) Recommended
Course Objectives
To demonstrate fundamental technical skills and clear understanding of the basic concepts of algebraic and transcendental functions.
To solve real-world problems using algebraic and transcendental functions.
To identify connections between mathematics and other disciplines.
To use appropriate technology to enhance their mathematical understanding and to solve real-world problems.
Measurable Learning Outcomes:
• Determine if a relation is a function. • Identify the domain and range of a function. • Use the graph of a function to identify characteristics of the function such as symmetry and intervals of increasing, decreasing, and constant behavior. • Recognize graphs of common functions and graph transformations of these common functions. • Combine functions arithmetically and through composition and identify the domain of the resulting functions. • Describe and explain the fundamental concepts associated with inverse functions, including the definition of one-to-one functions and the graphical interpretation of inverses. • Define, evaluate and graph trigonometric functions • Define, evaluate and graph inverse trigonometric functions. • Solve rational and polynomial equations including those with complex numbers. *Solve simple problems using the Law of Sine and the Law of Cosines to compute angle measures and side lengths of triangles. *Know the basic trigonometric identities, addition formulas, double- angle formulas, and half-angle formulas for the sine and cosine functions. *Solve basic trigonometric equations. *Simplify exponential and logarithmic expressions and solve exponential and logarithmic equations. *Solve applied problems using exponential and logarithmic functions | 677.169 | 1 |
A First Course in Complex Analysis With Second Edition of A First Course in Complex Analysis with Applications is a truly accessible introduction to the fundamental principles and applications of complex analysis. Designed for the undergraduate student with a calculus background but no prior experience with complex variables, this text discusses theory of the most relevant mathematical topics in a student-friendly manor. With Zill's clear and straightforward writing style, concepts are introduced through numerous examples and clear illustrations. Students are guided and su... MOREpported through numerous proofs providing them with a higher level of mathematical insight and maturity. Each chapter contains a separate section on the applications of complex variables, providing students with the opportunity to develop a practical and clear understanding of complex analysis. Previous Edition 9780763746582 | 677.169 | 1 |
As atudents progress in thier educational pathway, more knowledge and skills will be required. This course will foster a development and understanding of mathematics in the real world. Students will acquire skills in adding, subtracting, multiplyuing and diving signed numbers which will include integers. Students will solve multi-step equations involving the real number system and algebraic thinking. Problems solving in this course includes applications of ratios, proportion, fractions, and percents. It continues to develop other important mathematics topics including patterns, functions, gemoetry, measurement, probability, and statistics. It provides hands-on, visuals for students who are below grade level as well as renrichment for advanced students.
Algebra I is intended to build a foundation for all higher math classes. It is the brige from the concrete to the abstract study of mathematics. This course will review algebraic expressions, integers, and mathematical proporties that will lead into working with variables and linear equations. There will be an in-depth study of graphing, polynomials, quadratic equations, data analysis, and systems of equations through direct class instruction, group work, homework, and Fuse (I-pads). | 677.169 | 1 |
Tag Info
At least for me, starting by trying to solve the homework questions, even if I hadn't fully grasped some proofs (or even full grasped the concepts involved) usually worked out better than trying to understand everything first and only then starting with the homework problems.
As long as I found a solution (where found means found it myself, though. I tried ...
I will second Serge Lang's book "Basic Mathematics". It is definitely challenging though for those used to traditional high-school textbooks.
But as originally asked, AOPS has something called the "Alcumus" which you might find useful.
As mentioned on the website :
Art of Problem Solving's Alcumus offers students a ...
I don't know anything about programming but you mentioned "3D" and to me that screams Linear Algebra. However, you only mention doing Gr.7 level math so you have lots of work to do. When growing up I learned a lot from the site Purple Math. It seems to have a lot more topics now then when I used to use it but I remember it being quite good.
Recently I have ...
If you've enjoyed the Khan Academy for coding, then check out it offerings with respect to math! That's my "starting point" recommendation. (Math:...that's where Sal Khan got going, before branching off into other areas.)
See also Paul's Notes: Click on course notes: you'll see a drop down menu: Algebra, Calculus I, II, III, Linear Algebra, etc. Many ...
The obvious answer is the math section of Khan Academy!
More advanced courses can be found here and here, a couple of nice ones on analysis and functional analysis by Joel Feinstein here and some brilliant ones on linear algebra/systems/optimisation by Stephen Boyd here.
It is also worthwhile to check for courses here and (in the future) here.
See also ...
I find this interesting myself as I also have messy writing.
For me I always try to keep equal signs aligned and leave equal spacing. I also prefer using paper landscape as opposed to portrait but this is all just personal preference.
As for speed vs. neatness, I think it really is just about finding a fine line between them, neatness is important but you ...
It may just be my fanatical opinion, but I think that clarity is one of the most important attributes of performing mathematics, regardless of level.
For your purposes, let me present an example: Regardless of what course I am teaching, whether it be first year calculus or fourth year topology, I always have students who submit messy, poorly structured, ...
My handwriting is pretty bad, I love $\LaTeX$, I've lectured on chalkboards/blackboards a couple of times, and given computerized presentations.
My general feeling is that you should make the general direction of everything you write in exams crystal clear, and keep letters/symbols distinct, but otherwise don't waste too much time on lovely handwriting. ...
I.M Gelfand's books
on trigonometry,algebra,functions and graphs and calculus of variations(and much more) are comparable to Feynman Lectures. He has even stated his effort to write a book like feynman's in the book's preface. I strongly recommend the books. You can search the books in amazon for user reviews.
Search by web for how to understand mathematics. Read for instance:
- many topics of mathematics
- this is about Serge Lang
Good Luck!
I posted this first in a comment, but it is really worth status as an answer.:
A middle school teacher gifted me an old book: "How to Lie with Statistics" by Darrell Huff:
"Darrell Huff runs the gamut of every popularly used type of statistic, probes such things as the sample study, the tabulation method, the interview technique, or the way results are ...
It is a common misconception in regard to math, but this kind of misconception is common everywhere.
It's caused by the recursive properties of knowledge. The more you learn, the more you realize how little you know.; i.e:
Since it is known that less informed individuals see fields as more finite than informed individuals; While laymen may relate to the ...
Probability with dice and coin tosses seems like a standard starting point. Discussion of normal distributions (percentiles, standard deviation) also is pretty fundamental.
The great thing about both of those is that they're easy to illustrate. Probability is great to discuss in terms of games of chance (and while talking about dice and coin tosses is great ...
Maybe you can look into:
Share My Lesson
High School Statistics Resources
Statistics and Probability
Books
Activities and Projects for High School Statistics Courses by Ron Millard, John C. Turner
See this list of books on Google
Teaching Stats in High School
Search out other such books and resources
You might also want to try some of the ...
The number looks small enough to be brute-forced on a computer. Just try every possible factor, starting with 2, 3, 4, ... and keep dividing them out as long as the division comes out even. Then continue looking for factors of the quotient. You don't even need to explicitly restrict to primes, because any composite number you try simply won't divide the ...
The thing with Project Euler is that there is usually an obvious brute-force method to do the problem, which will take just about forever. As the questions become more difficult, you will need to implement clever solutions.
One way you can solve this problem is to use a loop that always finds the smallest (positive integer) factor of a number. When the ...
Project Euler problems (at least the ones that I have done) tend to deal with a lot of number theory topics. So, reading an introductory number theory book could be helpful.
With regards to your particular situation, I suggest finding primes first, then testing the primes for divisibility. That is, to find prime factors of $25$, don't test $1, 2, 3, 4, 5, ...
The important aspect in these kinds of permutations and combinations questioins is the direction with which you are approaching the problem.
For some questions, starting from the left most digit and then moving towards right may be a good strategy. Ex-- How many numbers are greater than 500 or less than 800 kind of questions, where hundred's digit has a lot ...
On the wiki page I noticed this appeared:
Lisa Glendenning (May 2005). Mastering Quoridor (B.Sc. thesis). University of New Mexico.
The link to it does not work, but if you can get to it, it probably at least contains references to published work done on the game.
I agree with the author of the question that inferring the domain from the definition of the function is backward. There are a couple of points that I think would be worth adding to the previous answers.
Firstly, it is not quite clear to me that the one right setup in which all of mathematics is happening is $\mathbb{R}$. There seems to be no particular ...
We have a museum at our university, with an installation of morenaments, an application I wrote myself. We find visitors of all ages spending hours drawing wallpaper ornaments with these. For iOS devices like the iPad, there is a newer development called iOrnament. These applications can be great to use an aesthetic faszination and turn it into curiosity ...
My two cents: if you are not sure about where exactly in mathematics you want to go, then vector calculus is a pretty good way to make more paths viable. If you do any sort of analysis, chances are you'll need to know vector calculus forwards and backwards; this is especially true if you want to work in PDEs. If you want to do anything on manifolds ...
Yes. "Studying math is as much about specific examples as it is about general theorems." My teacher Mike Artin used to expound on this concept (and then assign ridiculous and tedious homework assignments) and I would not get what he was saying. But the more I read math, the more I've come to realize that understanding specific examples is what allows you ...
The answer depends on your interests, and on the place you continue your education. In some areas in the world, PhD's are very specialized so any course that is not directly related to the subject matter is not necessary. One could complete a pure math PhD and not know vector or multivariate calculus.
However, this is increasingly rare; more and more PhD ...
I second the notion of Intuiton and Instincts, though in a different context. Many hard research problems are hard simply because there is no cookie cutter method for solving them. After trudging though core curriculum like Calculus, Algebra, Analysis, PDE's, etc, you acquire a vast array of problem solving techniques albeit for specific classes of problems. ...
A controversial and easy answer is "intuition". I know you don't like it, but sadly it is true. All that we know about Calculus started with Newton and Leibnitz's intuition about limits,continuity and derivatives and integrals. And for many decades Calculus stuck to be an "intuitively correct" idea, and along came Augustin-Louis Cauchy who defined it ...
Note first that the derivative of the quadratic in the denominator is $-2x+2$. It would be great if the numerator were $4x-4$, because then we could set $u=3+2x-x^2$, $du=(-2x+2)dx$, and write the indefinite integral as
$$\int\frac{-2}{\sqrt u}du=-2\int u^{-1/2}du\;.$$
Unfortunately, the numerator is actually $4x-5=-2(-2x+2)-1$. The trick is to split the ...
My first think of infinity was square diagonal vs. orthogonal stepping. Start with route (0,0) -- (0,1) -- (1,1), then take (0,0) -- (0,½) -- (½,½) -- (1,½) -- (1,1) and so on. Form of later will come closer to diagonal, but lenght will not.
I have been going back to review my calculus and differential equations for myself. I was using Lyx and LaTex for a while but it is slow and tedious to learn(for me). I will say that if you are willing use Microsoft OneNote install the math plugin which you can download from MS(free) also install the Microsoft Graphing Calculator software (also free) where ...
If you're writing a children's book on mathematics, please start by reading some excellent children's books dealing with mathematics. Here are some books I have fond memories of:
The Man Who Counted
The Phantom Tollbooth
Flatland
Alice in Wonderland / Through the Looking Glass
Everything by Martin Gardner
Godel, Escher, Bach: An Eternal Golden Thread
For me it was Monty Hall problem: ...
The fact that you can't divide by zero always amazed me. I once read the following analogy:
Imagine you go to a shop with 100 dollars in your pocket, and imagine
that everything in the shop costs 1 dollar. How many things can you
buy? 100. What if instead of 1 dollar, each thing costed $0.5? How
many things can you buy? 200. Now imagine that ...
Rosenlicht's Intro to Analsysis was an awesome read, but the real learning took place in the excersises. It was cheap, and just as rigorous as the introductory analysis course I took the following semester!
To be able to solve the problem I think a student would need to know
basic algebra
some trigonometry
some geometry, including the concept of circles, triangles, and equidistance
At what education level...
Education level is a strange concept, but I think a bright student in an advanced secondary mathematics class should be able to solve this. It's ...
I might be being silly but it appears to me that the question is not written very well and it is mathematically inaccurate.
My main issue is that Dana might not be able to stand anywhere. How do we know that there is a place that is one rod away from both Bob and Carl? They might be at a distance of more than two rods away from each other, in which case ...
By the way, just to give a much simpler answer (which indeed does not really explain the issue but might help if you're not studying calculus yet):
The problem here is that, in reality, $\infty$ is not a number. It is used to represent an unimaginably big number, but you obviously can't tell which. Therefore, infinity itself is not a defined number.
That's ...
When your teacher talks about $0/0$ or $\infty/\infty$ or $1^\infty$ he/she's not talking about numbers, but about functions, more precisely about limits of functions.
It's just a convenient expression, but it should not be confused with computations on simple numbers (which $\infty$ isn't, by the way).
When $1^\infty$ is referred to, it is to mean the ...
What $1^\infty$ is, or is not, is merely a matter of definition. Normally, one would only define $a^b$ for some specific class of pairs of $a,b$ - say $b$ - positive integer, $a$ - real number.
When extending the definition of exponentiation to more general pairs, the key thing people keep in mind is that various nice properties are preserved. For ...
The Sieve of Eratosthenes code on Wikipedia is intended to generate a list of all primes up to $n$. Suppose $k\le n$ is not prime, so we have two factors $a,b$. We can't have $a,b$ both larger than $\sqrt{n}$, as then $k=ab$ would be larger than $n$. Thus in order to show that $k$ is prime, we only need to check that it is not divisible by a number up to ...
I was always good at maths as a child, and took to reading extension maths books for fun (other kids thought I was weird). When I was about 10 I was completely hooked when I saw Euclid's proof for an infinity of primes. I had been given it as a question in one of the books I was reading. I spent about an hour desperately trying to prove it . . . then I ...
As a high-school student, who studies Euclidean Geometry for the purpose of Mathematics Olymnpiads, I would recommend the following, not as high-powered as Coxeter, books.
The Geometry of the Triangle - Gerry Leversha
Plane Euclidean Geometry - AD Gardiner and CJ Bradley
Introduction to Geometry (2 book set) - Richard Rusczyk
These are all fairly basic, ...
I'm not sure I like the subspace topology for this.
I think the torus bit is good, though; perhaps expand that to flipping over two cards, one for the space and one for the topology, where the space is given by an identification diagram, which would yield the cylinder, moebius strip, torus, klein bottle, sphere, and the real projective space on R2 (that I ...
To add my 2 cents-part of what's hindering and scaring a lot of people who have to teach "college geometry" these days is the utter collapse of the American high school system. As a result,it's no longer a given that your students are comfortable with what used to be "high school" geometry-something that used to be a given for any student at any university. ...
I was hooked on math by a small side note in a kid's book of mathematics about perfect numbers, numbers that are twice the sum of their factors. For example, 6 is the smallest perfect number because 1 + 2 + 3 + 6 = 2 × 6 and 28 is the next one because 1 + 2 + 4 + 7 + 14 + 28 = 2 × 28. The next perfect numbers are 496, 8,128, 33,550,336, and 8,589,869,056.
I ...
I have my students play almost exactly this game at the start of a course in College Geometry, through GeoGebra. Of course, it lacks the video game style interface you're describing (and which, I agree, would be awesome), so I would be excited to see something like this polished up nicely.
I'll tell you briefly what I do in class and a little about how ... | 677.169 | 1 |
Courses
120. Appreciation of Mathematics An exploration of topics which illustrate the power and beauty of mathematics, with a focus on the role mathematics has played in the development of Western culture. Topics differ by instructor but may include: Fibonacci numbers, mathematical logic, credit card security, or the butterfly effect. This course is designed for students who are not required to take statistics or calculus as part of their studies.
140. Statistics
An introduction to statistical thinking and the analysis of data using such methods as graphical descriptions, correlation and regression, estimation, hypothesis testing, and statistical models. A graphing calculator is required.
160. Calculus for the Social Sciences A graphical, numerical and symbolic introduction to the theory and applications of derivatives and integrals of algebraic, exponential, and logarithmic functions, with an emphasis on applications in the social sciences. A student may not receive credit for both Mathematics 160 and 181.
181. Calculus I
A graphical, numerical, and symbolic study of the theory and application of the derivative of algebraic, trigonometric, exponential, and logarithmic functions, and an introduction to the theory and applications of the integral. Suitable for students of both the natural and the social sciences. A graphing calculator is required. A student may not receive credit for both Mathematics 160 and 181.
182. Calculus II
A graphical, numerical, and symbolic study of the theory, techniques, and applications of integration, and an introduction to infinite series and/or differential equations. A graphing calculator is required. Prerequisite: Mathematics 181 or the equivalent.
201. Modeling and Simulation for the Sciences A course in scientific programming, part of the interdisciplinary field of computational science. Large, open-ended, scientific problems often require the algorithms and techniques of discrete and continuous computational modeling and Monte Carlo simulation. Students learn fundamental concepts and implementation of algorithms in various scientific programming environments. Throughout, applications in the sciences are emphasized. Cross-listed as Computer Science 201. Prerequisite: Mathematics 181.
210. Multivariable Calculus
A study of the geometry of three-dimensional space and the calculus of functions of several variables. Prerequisite: Mathematics 182.
212. Vector Calculus A study of vectors and the calculus of vector fields, highlighting applications relevant to engineering such as fluid dynamics and electrostatics. Prerequisite: MATH 182.
220. Linear Algebra
The theoretical and numerical aspects of finite dimensional vector spaces, linear transformations, and matrices, with applications to such problems as systems of linear equations, difference and differential equations, and linear regression. A graphing calculator is required. Prerequisite: Mathematics 182.
235. Discrete Mathematical Models
An introduction to some of the important models, techniques, and modes of reasoning of non-calculus mathematics. Emphasis on graph theory and combinatorics. Applications to computing, statistics, operations research, and the physical and behavioral sciences.
240. Differential Equations
The theory and application of first- and second-order differential equations including both analytical and numerical techniques. Prerequisite: Mathematics 182.
250. Introduction to Technical Writing An introduction to technical writing in mathematics and the sciences with the markup language LaTeX, which is used to typeset mathematical and scientific papers, especially those with significant symbolic content.
260. Introduction to Mathematical Proof
An introduction to rigorous mathematical argument with an emphasis on the writing of clear, concise mathematical proofs. Topics will include logic, sets, relations, functions, and mathematical induction. Additional topics may be chosen by the instructor. Prerequisite: Math 182
280. Selected Topics in Mathematics
Selected topics in mathematics at the introductory or intermediate level.
310. History of Mathematics A survey of the history and development of mathematics from antiquity to the twentieth century. Prerequisite: Math 260.
410. Geometry
A study of the foundations of Euclidean geometry with emphasis on the role of the parallel postulate. An introduction to non-Euclidean (hyperbolic) geometry and its intellectual implications. Prerequisite: Mathematics 260
421 - 422. Probability and Statistics
A study of probability models, random variables, estimation, hypothesis testing, and linear models, with applications to problems in the physical and social sciences. Prerequisite: Mathematics 210 and 260.
435. Cryptology An introduction to cryptology and modern applications. Students will study various historical and modern ciphers and implement select schemes using mathematical software. Cross-listed with COSC 435. Prerequisites: MATH 220 and either MATH 235 or 260.
439. Elementary Number Theory A study of the oldest branch of mathematics, this course focuses on mathematical properties of the integers and prime numbers. Topics include divisibility, congruences, diophantine equations, arithmetic functions, primitive roots, and quadratic residues. Prerequisite: MATH 260.
441 - 442. Mathematical Analysis
A rigorous study of the fundamental concepts of analysis, including limits, continuity, the derivative, the Riemann integral, and sequences and series. Prerequisites: Mathematics 210 and 260.
445. Advanced Differential Equations This course is a continuation of a first course on differential equations. It will extend previous concepts to higher dimensions and include a geometric perspective. Topics will include linear systems of equations, bifurcations, chaos theory, and partial differential equations. Prerequisite: Math 240.
448. Functions of a Complex Variable An introduction to the analysis of functions of a complex variable. Topics will include differentiation, contour integration, power series, Laurent series, and applications. Prerequisite: MATH 260. | 677.169 | 1 |
College Mathematics CLEP test Ebook
College Mathematics CLEP test
The College Mathematics CLEP test is a great review of basic math. Most of you will already know the main concepts. We will give you detailed examples and exercises to teach and test your skills. You don't need a separate textbook with this or any other CLEP study guide we offer. This ebook will teach you everything you need to know to pass this test!
Here's what you'll learn:
What Your Score Means Venn Diagrams The Pythagorean Theorem Test Taking Strategies Sets Sample Questions Real Number System Probability and Statistics Perimeter and Area of Plane Figures Parallel and Perpendicular Lines Open and Closed Intervals Logic Logarithms and Exponents Functions and Their Graphs Factors and Divisibility Example of Determination of Necessary and Sufficient Conditions Basic Properties of Numbers Answer Key Algebraic Inequalities Algebraic Equations Additional Topics From Algebra And Geometry Absolute Value and Order | 677.169 | 1 |
The physics of hot plasmas is of great importance for describing many phenomena in the Universe and is fundamental for the prospect of future fusion energy production on Earth. Non-trivial results of nonlinear electromagnetic effects in plasmas include the self-organization an self-formation in the plasma of structures compact in time and space. These... more...
This book is a text on mathematical analysis suitable for graduate students and advanced undergraduates. It provides an extensive introduction to proof and to rigorous mathematical thinking. It contains many remarks and examples and 500 exercises designed to provide motivation, test understanding, help practice mathematical writing and explore additional... more...
Covering the main fields of mathematics, this handbook focuses on the methods used for obtaining solutions of various classes of mathematical equations that underlie the mathematical modeling of numerous phenomena and processes in science and technology. The authors describe formulas, methods, equations, and solutions that are frequently used in scientific... more...
The International Mathematical Olympiad (IMO) is a prestigious competition for high-school students interested in mathematics. It offers high school students a chance to measure up with students from the rest of the world. This book contains problems and solutions that appeared on the IMO over the years. It presents a grand total of 1900 problems. more...
Most colleges and universities now require their non-science majors to take a one- or two-semester course in mathematics. Taken by 300,000 students annually, finite mathematics is the most popular. Updated and revised to match the structures and syllabuses of contemporary course offerings, Schaum's Outline of Beginning Finite Mathematics provides a... more...
A renowned mathematician who considers himself both applied and theoretical in his approach, the author has spent most of his professional career at NYU, making significant contributions to both mathematics and computing. He has written several published works and has received numerous honors. more... | 677.169 | 1 |
Thinkwell s Calculus with Edward Burger lays the foundation for success because, unlike a traditional textbook, students actually like using it. Thinkwell works with the learning styles of students who have found that traditional textbooks are not effective. Watch one Thinkwell video lecture and you ll understand why Thinkwell works better. | 677.169 | 1 |
Combinations & Permut lesson was written for a Pre-Calculus class to review combinations and permutations that were learned in Algebra 2. It was also as a review of the two concepts for my Algebra 2 classes after they had worked individual lessons on combinations and permutations.
Presentation (Powerpoint) File
Be sure that you have an application to open this file type before downloading and/or purchasing.
860 | 677.169 | 1 |
Course Descriptions
Algebra 1 starts with a continuation of concepts studied in Pre-Algebra. Students will study and demonstrate knowledge of how to evaluate and simplify expressions; write and solve linear and quadratic equations, functions, and formulas; and write and solve systems of linear equations and inequalities. Students will also learn and show knowledge of how to represent and analyze relationships using tables, equations and graphs; apply basic operations on polynomials; use basic operations on rational and irrational numbers; communicate mathematically; and demonstrate the appropriate use of tools and technology. Algebra 1 is the first of three college-preparatory courses (Algebra 1, Geometry, Algebra 2).
Algebra 2 starts with a continuation of concepts studied in Algebra 1. Students will be involved in communicating information mathematically, solving problems from a real world context and justifying the solutions to problems. Furthermore, they will be challenged by new mathematical ideas that require function analysis, graphing skill, solving higher order equations, investigating complex number systems, and working with matrices, conic sections, logarithms, data analysis and probability. It is a course for students who wish to prepare for further mathematics such as Pre-Calculus or Statistics and who are planning to continue with mathematics in college.
Ancient World History is a survey course intended to introduce students to studying history at the high school level. Beginning with pre-historic times and moving through to the Industrial Revolution, students will examine geography, religion, economics, politics, social and cultural structures and the role these factors played in the growth of human civilization.
AP Biology begins at the molecular level, then moves up to the cell, then the organism, and ends at the level of the ecosystem, thus giving the student an integrated overview of life and its processes. A minimum of one hour's preparation per night is needed to succeed in this course. There is more experimental work than in regular Biology, and most of this will be done after school. Students are immersed in the subject, and will consequently gain knowledge and skills at a much higher rate than you would in a regular course. Additionally, by virtue of the workload, the course can be instrumental in preparing you for studying at university level. And last, Biology is fun!
Students taking this course are expected to have a willingness to work hard since they will be given homework assignments in each and every calculus class. It is most important that students complete their homework each day since much of calculus depends on an understanding of a concept taught in a previous lesson. The use of a graphing calculator is required on the AP Calculus examination, thus you will need one, and will be using this technology on a regular basis so that you become skilled at it. You will also have experience with the basic paper-and-pencil techniques of calculus and be able to apply them when you are not allowed to use your calculator.
Prerequisites: Successful completion of Chemistry with a minimum 'B' grade; consult with your Chemistry teacher. It is also preferred that students will have successfully completed Physics and higher level math.
This course is designed to be the equivalent of the general chemistry course usually taken during the first college year. For some students, this course enables them to undertake, in their first year, second-year work in the chemistry sequence at their institution or to register in courses in other fields where general chemistry is a prerequisite. For other students, the AP Chemistry course fulfills the laboratory science requirement and frees time for other courses. Students in AP Chemistry attain a depth of understanding of fundamentals and a reasonable competence in dealing with chemical problems. The course contributes to the development of the students' abilities to think clearly and to express their ideas, orally and in writing, with clarity and logic. Broad topic areas covered include looking at the structure and states of matter, chemical reactions and some descriptive chemistry. There is also a focus and emphasis on the laboratory experience.
This course is designed to be comparable to fourth semester (or the equivalent) college/university courses in Mandarin Chinese. The AP course prepares students to demonstrate their level of Chinese proficiency across the three communicative modes (Interpersonal, Interpretive, and Presentational) and the five goal areas (Communication, Cultures, Connections, Comparisons, and Communities) as outlined in the Standards for Foreign Language Learning in the 21st Century. Its aim is to provide students with ongoing and varied opportunities to further develop their proficiencies across the full range of language skills within a cultural frame of reference reflective of the richness of Chinese language and culture.
This course is actually two separate classes, Advanced Placement Microeconomics and Advanced Placement Macroeconomics. At the end of the year students will be prepared to sit for two different AP exams and can earn credit for both.
In it's essence, economics is a social science that looks at the production, distribution, and consumption of good and services. It can look at these things from the prospective of a society as a whole or examine the interactions of different societies; this is the field of macroeconomics. It also examines how individuals and/or businesses interact to make and sell good and services; this is the field of microeconomics. Much of the work done in economics deals with idealized situations, where we assume certain motivations (or what economists call incentives) will always hold true. Over the course of the year we will examine these incentives, and the behaviors they are thought to inspire, and then discuss where and when these relationships work and where they break down.
AP English Language is a rigorous exam offered as an alternative to Grade 11 English. The purpose of this course is to examine and practice the tools writers use to craft argument. Course readings include selections from political, historical and social science writings, along with current events and non-fiction prose. Students learn to analyze writing, to develop sound reasoning and argumentation, and to examine the power of language.
The exam is divided into three strands: rhetorical analysis, argument and synthesis. Students develop their ability to analyze text for rhetorical style, argue a point of view and incorporate evidence successfully into an argument. Plenty of opportunity is also given to develop different forms of writing: analytical, expository and persuasive. Emphasis is placed on crafting a written response within a given time period.
As a college level course, AP English Literature and Composition involves a rigorous and challenging approach to English. AP English Literature and Composition engages students in the careful reading and critical analysis of literature through selected works of merit from the 16th Century to modern times. By reading in this manner, students deepen their understanding of how writers use language to give a reader both meaning and pleasure. Students will learn to approach a text critically, analyzing it for the author's meaning(s), and evaluating it artistically and for its historical/social context. By reading, students will explore the development of literature throughout history in its various traditions, styles, and uses of language, the universal themes of literature, how literature reflects life, and the historical, social, and cultural values of a work of literature at any given period.
Writing is a fundamental and essential part of this AP course. Writing assignments will focus on the critical analysis of literature that will include expository, analytical, and argumentative essays. Instruction will include careful attention to developing and organizing ideas in clear, coherent, and persuasive language. It will also include study of the elements of style. By writing, students will develop the writing process, writing as a tool to express ideas clearly and confidently, effective and diverse vocabulary and syntax, different forms of writing (expository, analytic argumentative, creative), and understand the narrative devices used by writers to achieve their purpose.
The AP French Language and Culture and French 4 course is a two year revolving course syllabi designed with reference to the AP French Course Description (see the College Board website for more information) to help you integrate the four language skills through the use of authentic sources and documents. The AP French Language and Culture exam that addresses six groups of learning objectives: spoken and written interpersonal communication, audio, visual, and written interpretative communication, and spoken and written presentational communication. These learning objectives will be addressed through the study of six themes: Global Challenges, Science and Technology, Contemporary Life, Personal and Public Identities, Families and Communication, Beauty and Aesthetics. Students will continue to develop vocabulary and refine their grammar skills while focusing on communication. The study of French and French speaking culture will be interwoven throughout the course. This will be accomplished through a variety of methods involving films, music, texts, listening exercises, speaking exercises, discussions (on French culture, daily life, current events, etc.), and other communicative activities. This class is taught completely in French. Students are expected to leave English and all other languages at the door; all activities will be conducted purely in French. A supplemental grammar and vocabulary book provide for a comprehensive grammar and vocabulary review.
This course is designed to provide a systematic development of the main principles of physics, emphasizing problem solving as well as continuing to develop a deep understanding of physics concepts. It is assumed that the student is familiar with algebra and trigonometry; calculus is seldom used, although some theoretical developments may use basic concepts of calculus. In most colleges, this is a one-year terminal course including a laboratory component and is not the usual preparation for more advanced physics and engineering courses; however, Physics does provide a foundation in physics for students in the life sciences, pre-medicine, and some applied sciences, as well as other fields not directly related to science.
In this course we will concentrate on problem solving, practical applications of physics, career opportunities related to what we are studying, current questions, and future trends. Labs will primarily entail open-ended problem solving which will require you to design experimental methods and analyze your results.
This course is a college-level course for high school students, designed to introduce students to the systematic and scientific study of the behaviors and mental processes of human beings and other animals. Students are exposed to the psychological facts, principles, and phenomena associated with each of the major subfields within psychology. They also learn about the ethics and methods psychologists use in their science and practice.
This is an accelerated studio-focused art class for students who want to refine their technical skills and clarify an artistic direction with intent. The year-long class will be a combination of prescribed and self-directed study based on the guidelines set forth by the National Advanced Placement College Board (AP). This course is for highly motivated students who are seriously interested in the study of art; the program demands significant commitment, students will need to work outside of class at least 5-10 hours a week. Two types of portfolios may be submitted in separate years.
The AP US History course is designed to provide students with the analytical skills and enduring understandings necessary to deal critically with the problems and materials in US history. It will examine events and issues from the Pre-Columbian era and continue right up to the present age. This AP US History course should teach students to assess historical materials and develop the skills necessary to arrive at conclusions on the basis of an informed judgment and to present reasons and evidence clearly and persuasively in an essay format. The course imposes a heavy reading and writing load throughout the year and the demands placed upon students are equivalent to those made by full-year introductory college courses.
The goal of AP World History is to provide students with a solid foundation of skills to help them understand the forces that shape the world in which they live. This course is designed for the exceptionally studious high school student who wishes to earn college credit in high school through a rigorous academic program. Students will use documents and other primary sources, and recognize and discuss different interpretations and historical frameworks. Students will be encouraged to build empathy and understanding of the human condition, understanding historical and geographical context, and make comparisons across cultures. Students will develop skills of research, analysis, discussion, and writing about historical events and multiple perspectives and construct analytical and interpretive essays which address issues of change, continuity, and comparison.
Biology is a fascinating course in which students use scientific methods to find out about the living world. There is a strong practical emphasis and students will be expected to continue to develop their laboratory skills to plan and carry out scientific investigations. Students will learn how to relate biological form to function by observation of living organisms. Other major themes include the chemistry of life, cell theory, and the origins of life on Earth. The curriculum is designed to make the most of the natural environment here in Thailand through fieldwork and the study of local living organisms.
This course examines the composition of various substances and the changes they can go through. It also demonstrates how chemistry touches our lives every day, almost everywhere—in medicine, the clothes we wear, the games we play, as well as the industries that make the things we use. The periodic table and simple compounds are covered, as well as the basics of Chemistry.
Open to any level of singer, from beginner to advanced. Learning proper technique, presentation, and some music theory will be combined with preparing to sing at public performances. Traditional style as well as contemporary and show-choir will be taught. Attending the several public performances to be scheduled will be required.
Open to musicians at all levels of wind instruments and percussion(drums), and to string instruments above beginner level. Students will be able to advance their skill level through playing in the ensemble, and will learn some music theory along the way. This is a performance-based class, there will be several opportunities provided to perform in public, and these will be required activities.
Prerequisites: There is no prerequisite for this class. However if a student has previously shown a lack of commitment to a chosen dance course, it may prove more difficult to be accepted into this course.
The class decide upon a range of dance styles in which they would like to choreograph. Students then choose the style of dance they wish to be involved in and get into choreography groups from there. Each choreography groups teaches the rest of the class their dance. Each group needs to have a different style. Students choose the music and any costumes or props they wish to use. Students research their chosen style through the internet, videos and literature. Students need to stay true to the chosen style as much as possible in a 'creative fashion.' Students are responsible for their own work schedule within the designated lessons and out of class time. We will have after school practices to prepare for a performance at the end of the year.
Creative Writing is a year-long course aimed at developing writing skills relevant to both poetry and fiction. Starting with poetry, it hones students' abilities to create patterns in language, to use imagery, rhyme and rhythm, and to choose diction that evokes meaning.
The elements of short stories are explored and students learn to develop their own short stories, together with the skills involved in drafting and editing. In the final semester, students investigate the processes involved in writing a novel and produce the first 10,000 words of their own work.
The course also includes a component on 'How to Publish' and covers areas such as internet-publishing, self-publishing, magazine publications, literary agents and publishing houses.
Students learn a dance choreographed by the teacher, to introduce and explore the basic movements and elements of dance. Students apply this knowledge and understanding to choreograph a section of the dance, working in small groups. Each group teaches their choreographed section to the class with the help of the teacher. Students further develop their knowledge, understanding and skills by choreographing a group dance. (Project) Students are responsible for choosing their music, structuring the dance, deciding upon a theme and/or style and developing the movement to portray their theme. Students perform the teacher's dance, their projects and any Level 2 dance pieces. Students evaluate the process and product to demonstrate their knowledge, understanding and skill. Students have a final practical assessment in the form of a performance and/or a motif development task. Students take one written exam at the end of the semester to demonstrate their knowledge and understanding of the theory.
Educational Dance Level 2 is designed to further develop students' knowledge, understanding and skills in the choreographic process, the teaching and the performance of Dance. Students learn the 'Teacher' dance to reinforce concepts from Level 1, and to experience different ideas. Students evaluate their work to demonstrate their progress and improvement. Students choreograph a dance alone or in pairs, depending on how many Level 2 students are in the class. Students are responsible for researching ideas, choosing their music accompaniment, structuring the dance, deciding upon a theme and/or style. Students are expected to explore more complex movements and use more challenging choreographic devices to develop the movement, and to portray their chosen theme and /or style. Students teach the class their dance, with limited teacher intervention. Students may perform in their own dance and will evaluate the process and product to demonstrate their deeper knowledge, understanding and skill. Students write a paper to detail their experience, illustrating their points with referral to their knowledge of the theory.
Desktop Publishing/Journalism can be used to satisfy computer credit requirements for graduation and is open to students in Grades 10-12 meeting the prerequisites.
This course teaches the fundamentals of using a desktop publishing program to create flyers and newsletters as well as large projects like a yearbook. Students will also learn how to match writing styles and techniques to different types of media by creating articles for the school's newsletter, yearbook, and website. They will also create flyers to help promote/advertise various school activities.
Teaches the fundamentals of how to design and create 2D graphics and animation to meet a specific purpose. Students will learn to use software tools and the design processes necessary to produce products that can stand alone or be used in various end use applications like websites, newsletters, flyers, or logos. Students will also learn the basics of editing digital photographs.
The fundamentals of drawing are taught through various media encounters, such as Graphite, Pastel, Marker, India Ink, Scratchboard, Charcoal, Oil Pastels, & Colored Pencils. Students will be introduced to the basics of drawing by learning simple techniques and exercises. They will investigate the elements and principles of art (line, form, value, color, composition, etc.) as they refine their use of various media. Students will refer to works by great masters as well as contemporary and cross-cultural exemplars for further inspiration and clarity. Requirements include: (a) keeping a portfolio of sketches, exercises, and finished work; (b) self-evaluations and group critiques; (c) an oral presentation; (d) keeping a sketchbook; (e) projects; and (f) final exam.
English 10 is a communication arts class focusing on analyzing literature for themes, style, structure and characterization; the writing process; effective oral communication; as well as listening skills. Through close study of two novels, two plays (one by Shakespeare), various poems and short stories, and a unit focused on film, students will gain key skills that will enable them to successfully communicate their ideas and opinions in a variety of ways.
English 11 is a compulsory subject taken in Grade 11, unless a student is enrolled in AP English Language. Its exploration of literary texts runs parallel to a honing of literary skills, enabling students over the course of the year to develop vocabulary, writing style and analysis. A weekly writing workshop not only give students SAT practice, but also enables them to make progress with various forms of writing: creative, expository, analytical and persuasive.
Together with an indepth study of one of Shakespeare's plays, students are also introduced to a selection of 19th and 20th century texts with an emphasis on prose analysis. There is in addition an ongoing focus on poetry, its patterns of diction, rhythm and imagery, as well as its historical context. Beginning with Beowulf, students are given an overview of the development of English poetry from its earliest beginnings to the present day.
Grade 12 English is a year-long course aimed at exposing students to a wide variety of poetry, prose, and drama from Chaucer and Shakespeare to the present day works of British and American authors. Throughout the course, students will engage in the close reading of literature and in written responses to these works, gaining knowledge of the world of literature and the world in general through the themes literature addresses. Reading will develop the ability to analyze a written work for meaning and artistic quality, as well as study the craft of writing. Writing assignments will develop the ability to offer critical analysis of literature that will include expository, analytical, and argumentative essays, writing styles that can be applied to other academic areas and to university studies. Instruction will include careful attention to developing and organizing ideas in clear, coherent, and persuasive language. It will also include study of the elements of style. By the end of the course, students will be prepared for university study of literature and possess the necessary writing skills for academic success.
English 9 is a compulsory subject taken in Grade 9. The main focus of the course is to create strong foundations in reading and writing. Over the course of the year, students are also introduced to literary concepts and are given an opportunity to develop their vocabulary. They are taught how to read and write analytically. Weekly writing workshops give students an opportunity to make progress with various forms of writing: creative, expository, analytical and persuasive.
Together with an indepth study of one of Shakespeare's plays, students also study a selection of 20th century texts with an emphasis on prose analysis. There is in addition an ongoing focus on poetry, its patterns of diction, rhythm and imagery, as well as its historical context. Students are given an introductory course in poetry in the first quarter. This is followed up by a close look at the development of modern poetry from its roots in World War II.
Environmental Science is a course designed to give students a basis for further study in this field, and to help instill a sense of environmental awareness beyond what they may already have. The class begins with basic ecology and familiarization with the biosphere, and proceeds to examine the ways in which we affect the ecosystems in which we live. Students are encouraged to develop and live out their own environmental ethic.
French 1 is an introduction to the French language and the French-speaking world. The four language skills (reading, writing, speaking, and listening) will be developed in an integrated way through in-class activities (skits, dialogues, etc.) films, music, internet activities, and games. Students will learn vocabulary to describe themselves, their family, and everyday life, as well as the vocabulary needed to travel around the Francophone world. By the end of the course, students will be able to express themselves in present, future, and the two basic past tenses (passé composé and imparfait).
French 2 is a course that is centered around a fictitious apartment building. During the year, students will continue to develop their language skills through exploration of French-speaking cultures around the world and continue to develop their communication skills in the present, future, and two basic past tenses (passé composé and imparfait) through many interactive projects, films, music, and other communicative activities.
French 3 has a fairly intense cultural component. Students will explore the French-speaking world, first through different regions of France, then through French-speaking countries of the world from Europe to Africa, Asia and the Americas. Other cultural activities include cultural discussions, cooking, field trips, and films. Students will also read two short story collections (Le Petit Nicolas and traditional African folktales), a play (an African comedy), and different poems (representative of different cultures and/or literary movements). All four language skills will be integrated into our cultural and reading studies and you will be introduced to remaining essential grammar concepts (the futur, conditionnel, subjonctif, and pronouns), and communication skills.
This course is designed for students who have successfully completed Algebra 1. The course helps students develop logical thinking patterns, and also helps them become aware of the geometrical patterns in their environment. This is accomplished by working proofs and problems with the help of postulate, theorems, and axioms. The topics covered include: angles, polygons, circles, lines, points, arcs, triangles, and some basic trigonometry.
This course is designed to promote the concept that a positive, healthy lifestyle can enhance your quality of life. It will focus on preparing the student for making responsible decisions about their life necessary for personal control. The course will be divided into two units of work: sport first aid, and drugs and sex education.
The sport first aid course will demonstrate strategies for the assessment, management, and prevention of injuries in sport first aid settings and enable the student to form opinions about health-promoting actions, and draw conclusions about health and physical activity concepts.
The drug and sex education course is to clearly identify the consequences associated with the use and abuse of drugs and premarital sexual activity. It will enable the student to understand the value of healthy behaviors.
In this course the students will learn the basics of computer programming using the Python programming language. Basic programming concepts are covered including variables, data types, mathematical operations, input/output, iteration, conditional execution, functions, error handling, and object oriented programming. The course has a very large problem solving component and requires a very high level of precision and attention to detail.
Open to musicians on any instrument above the level of beginner, and a simple audition may be required. The course will provide opportunity to learn the theory and then apply it to playing different styles, with a focus on improvising, and will not be confined to jazz but will also explore Blues, Rock, Funk, and other pop styles. A performance-based class, and opportunities to perform in public several times each semester will be scheduled, and will be required activities.
Mandarin 1 is a high school class. If taken in Grade 7 or 8, this class does not count towards the foreign language requirements for graduation.
This is a course in standard Mandarin Chinese, the official language of the People's Republic of China. It is designed for complete beginners who have no prior knowledge of Mandarin Chinese. The aim of the course is to provide students with a grasp of basic structures and the ability to carry out simple conversations in Chinese, as well as the knowledge required to recognize and read approximately four hundred basic Chinese characters.
Mandarin 2 is a high school class. If taken in Grade 7 or 8, this class does not count towards the foreign language requirements for graduation.
This course is designed for students who have already completed Mandarin 1 Chinese, or who can demonstrate that they have acquired knowledge of the language to the required level. After revision of the structures, vocabulary and characters covered in Mandarin 1, the course continues to develop students' ability in reading, speaking, writing and aural comprehension, building upon the structures already acquired during Mandarin 1. This course is open to students from Grades 7–12.
This class is for the intermediate students to continue to develop their language skills and their study of Pinyin as well as Chinese characters. Other cultural activities include relevant cultural discussions, cooking, field trips, and watching many different films.
This course contains a very significant reading component – throughout the year, you will read two graded reader series (level one) (Chinese breeze: Cuo, Cuo, Cuo and Liang Ge Xiang Shang Tian De Hai Zi), a play, and different poems. All four language skills will be integrated into our cultural and reading studies and you will continue to improve in your comprehension and communication skills.
Throughout the course, students will engage in conversations, provide and obtain information, express feelings and emotions, and exchange opinions mostly in Chinese. Students will demonstrate an understanding of the relationship between the practices and perspectives of the aspects of Chinese culture studied in class. Students will reinforce and further their knowledge of other disciplines through the Chinese language and its cultures. Students will demonstrate understanding of the nature of language through comparisons of the Chinese language and their own. Students will be able to use the Chinese language both within and beyond the school setting.
Textbook: Easy Steps to Chinese 3
The main goal of this course is for students to learn to better understand the complexities of the world that surrounds them. By studying geography, they will discover and explore the relationships between people and the environment, and links between people, places, and culture.
The course will focus primarily on human geography, especially in the political and economic realms. Students will be asked to apply their knowledge of world history to understand the factors that have shaped the modern development of nations and peoples, as well as the situations being faced by countries in real time (i.e. current events). Students will be challenged to think critically about, and actively reflect on, problems facing the earth globally and locally, with the first semester focusing on Europe and the Americas and the second semester focusing on Asia and the Middle East.
With a better understanding of these issues, students will be better equipped to find positive ways to interact with the earth and those who inhabit it. Students will also build on their geography skills while learning about different places on earth and explore the issues they face living on this planet here and now.
The fundamentals of painting are taught through various media encounters, such as acrylic, watercolor, gouache, oil and batik painting. Students learn technical skills with an emphasis on studio production. This course is designed to develop higher-level thinking, through the use of historical reference and exploration of different modes of painting such as, realistic, abstract, and non-objective, students are encouraged to develop their own styles of painting. Emphasis is on individual expression, composition, and technique. Requirements include: (a) keeping a sketchbook of ideas, notes and vocabulary; (b) critiques; (c) an oral presentation, (d) projects; (e) final exam.
Student will work from still life, landscape, portraiture, the figure, and creativity-based subjects.
Those students who have completed Painting and wish to become further involved with advanced techniques and concepts may proceed to Studio Art.
Successful completion of this semester course will earn certification. Students wishing to coach or officiate in the school's sports program will need to complete this course. This course consists of 6 basic components: Practical; Rules; Mechanics; Performance understanding; Students will prepare a short Personal Exercise Program (PEP). Students will complete a minimum of 10 hours in the after school sports program which does not include playing sports.
Team Sports is an elective with emphasis placed on refining fundamental skills, introducing game strategies and effectively utilizing available human resources. Challenge initiatives are used to reinforce collaboration skills with written and performance assessments used to determine mastery. Students have an in depth opportunity to learn basic skills and vocabulary about activities that will be played as they move through high school. Students are taught new skills as well as given the chance to increase some skills formerly taught in other classes through participating in activities such as basketball, soccer, volleyball. Students will also have the opportunity to learn and accomplish higher sport specific skills through a variety of team and large group activities.
Students will further develop their practical skills, gain a deeper understanding and knowledge of rules, techniques and terminology and continue to work on their social development, including cooperation, teamwork and responsibility. Through these different activities the following components will be emphasized and assessed: Practical performance and improvement; knowledge of rules, techniques and terminology; attendance and punctuality to lessons, wearing PE uniform; the ability to demonstrate a proper warm up and cool down routine; general enthusiasm for the topic and active involvement.
Students will participate in activities which illustrate the different focuses of Health Related Fitness. Students will gain an understanding of the meaning of exercise as a form of physical activity, and its relationships to fitness. Students will assess and monitor their physical fitness levels and physical activity patterns, and will develop their own physical fitness program. Students will be expected to demonstrate and apply their knowledge and understanding of the information learned through out the year.
Physical Science is a required full-year required course that explores introductory physics during the first semester, and introductory chemistry during the second semester. The main goal of this course is to continue to develop the student's ability to do science. Students will learn many different science process skills, and will learn how to use their skills in studying and solving problems. The class will involve a great deal of inquiry-based lab work. The students will often work in teams using cooperative learning. During the first semester, the students will work on and finish the Technology Project and the Rube Goldberg Project. Many different resources will be explored in order to enhance their ability to do science.
Physics is a full-year course that primarily explores the areas of Mechanics (first semester) and Electromagnetics (second semester). Physics is a prerequisite for AP Physics B, which is a full-year course that explores all areas of physics.
A major goal of this course is to continue to develop your ability to do science. You will use inquiry-based lab work and longer-term projects to help sharpen your science process and critical-thinking skills. There is an abundance of on-line tutorials, labs, and other websites that we will be making use of throughout the course. The following websites are linked with your textbook: go.hrw.com and
There will be at least one lab session during each unit and there will be a test at the end of each unit.
Students who choose Precalculus should have previously demonstrated a mastery of Algebra 1, Geometry, and Algebra 2. It is important that students do their homework every day since much of this math course depends on understanding concepts taught in a previous lessons. The use of a graphing calculator is required for some sections in Precalculus. Students will be doing Functions and their Graphs, Polynomial and Rational Functions, Trigonometry, Sequences, Series, Probability, Analytic Geometry, and Limits in this course.
Students will be encouraged to integrate art into their ever day lives. They will be given opportunity to grow in their appreciation of art and skill, as well as recognize art terms and create works of art while striving for their best.
In this course students will learn the advanced concepts and techniques of drawing. They will have choice of concentration, with deadlines to meet. Students will focus on drawing skills using a variety of media such as pencil, colored pastels, markers, charcoal and pen. They will be challenged and encouraged to grow in their skills.
This course aims to develop the kind of adults the world needs: thoughtful, responsible, reflective, articulate, and independent world citizens. The studies of this class will be varied and flexible, however there are several key components: students will reflect on their twelve years of education to produce meaningful comments on their learning; students will anticipate issues that may arise their first few years of university and prepare to meet the challenges of life in a new place; students will practice professional communications and interactions; and students will interact regularly with the guidance and career counselor to discuss a wide range of topics.
Spanish 1 is a high school class. If taken in Grade 7 or 8, this class does not count towards the foreign language requirements for graduation.
In Spanish 1, students will study Spanish using a holistic approach that focuses on the acquisition of skills in six core areas: listening, speaking, reading, writing, grammar, and vocabulary. Along with language acquisition, students will strive to gain an authentic and extensive understanding of the varied cultures and customs of the Spanish-speaking world. The first level course will focus on the building of a strong foundation of the basic concepts inherent in the language.
Spanish 2 is a high school class. If taken in Grade 7 or 8, this class does not count towards the foreign language requirements for graduation.
In Spanish 2, we will continue our study of Spanish by building upon, strengthening, and reinforcing the skills in the six core areas: listening, speaking, reading, writing, grammar, and vocabulary. We will continue to seek out an authentic and extensive understanding of the varied cultures and customs of the Spanish-speaking world. The second level course will continue to focus on the building of a strong foundation of the basic concepts inherent in the language, and will provide students with opportunities to deepen their practical understanding of the language through individual and group projects. Some topics of study in this course will include: stem-changing verbs, simple conditional verb tenses, simple future and past verb tenses, adjective agreement, and vocabulary acquisition.
The Spanish 3 course will continue to build upon, strengthen, and reinforce the students' skills in the six core areas: listening, speaking, reading, writing, grammar, and vocabulary. In this course, a strong emphasis will be placed on the strengthening of the students' skills and knowledge with regards to the practical, everyday use of the language. We will strive to deepen our understanding of how the language works as a tool for communication through a wide range of projects and activities specially geared toward providing as authentic a cultural and linguistic experience as possible. Some topics of study in this course will include: reflexive verbs and pronouns, the imperfect verb tense, making comparisons, asking for and giving advice, and the environment.
The Spanish 4 course will continue to build upon, strengthen, and reinforce the students' skills in the six core areas: listening, speaking, reading, writing, grammar, and vocabulary. Along with focusing on these core skill areas, a strong emphasis will be placed on fluency and pronunciation in Spanish. The majority of instructions and communications will be in Spanish and students will be strongly encouraged to communicate in the target language as much as possible. Through a wide range of projects and activities geared toward providing as authentic a cultural and linguistic experience as possible, the students will deepen their understanding of how the language works as a tool for communication Some topics of study in this course will include: compound tenses, discussing past and future events, the subjunctive tense, legends and folklore, means of communication, and the world we live in.
Students can let their imaginations soar, allow them to explore their creativity and learn the tools they need to express their thoughts and ideas.
The Speech and Drama course will focus primarily on developing on-going confidence, self-esteem and strengthen verbal communication skills.
The curriculum will provide unique opportunities for students to develop clear speech, fluent delivery and pleasing social skills. This will be done through participation in a wide range of creative activities including speech, drama, movement, improvisation and poetry reading within a supportive environment.
Occasional dress up, along with the use of props and make-up will add to the excitement of the lessons.
The program will also encompass work on movement – to build an awareness and confidence in his / her own body; the spoken word – to cultivate good and expressive speech; and finally drama – to perform confidently before an audience.
These classes will each conclude with a presentation, with the emphasis on the process, and not final product, as students are encouraged to continually develop their abilities and keep exploring their creativity.
Lessons will include:
Exercises in relaxation, breathing and articulation
Movement, drama and poetry reading
Short script performance
To summarize, the skills gained through Speech and Drama are as follows:
Statistics is a mathematical discipline that helps us use numbers to tell a story. The purpose of this course is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. By the end of this course students will be able to formulate a hypothesis; design an experiment, survey, or simulation; execute the design, collecting appropriate data; select the appropriate statistical techniques to analyze the data; and develop and evaluate inferences based on the data. In addition, the student will develop their skills to interpret and critique the day-to-day statistics that they encounter. Throughout the course students will be using resources on the web as well as computers and computer software. Students will be expected to master the appropriate technology needed to enhance understanding and to accomplish specific goals.
The fundamentals of art are taught through various media encounters. Students learn technical skills in their choice of drawing, painting, sculpting, printmaking, collage and other media. Individual solutions to assignments are encouraged. Emphasis is on individual expression, composition, and technique. This course cannot be repeated.
This course is open to students in Grades 11-12 and can be taken at the same time as Studio Art I.
Studio Art II is similar to Studio Art I, but focuses more on individual approaches in content as well as technical skills. Assignments are more challenging than Studio Art I. More emphasis is placed on individual expression than in Studio Art I. Studio Art cannot be repeated.
Study hall is a period for students to actively participate in their academics. This can take the form of reviewing classroom notes, finishing homework, studying for a test/quiz, and/or completing a group project. It can also be used to work on an independent study course or an on-line program. Community service hours can be completed during this time by being a teacher's assistant (TA), tutoring/mentoring in the elementary classes, or working with a non-government agency (NGO) or missionary within the community. Used wisely this time can be an addition to a student's educational resume.
This course will introduce the student to a basic understanding of principles of scenic design, lighting design, and other technical aspects of the theater. Technical Theater is also offered in the second semester to allow collaboration on the end of year theater production. The class will involve a brief introduction and lessons on the following Areas of Study: History of Stage Scenery; Types of Scenery; Script Analysis; Set Design; Lighting Design; Sound Design; Careers in Technical Theater.
Thai FL is offered to students in Grades 9-12 who wish to start or to continue with studies of Thai language. The language level offered is based on student ability and fluency in Thai. This is not a course for Thai nationals.
Thai GL is a course for students who carry a Thai passport or have Thai nationality. It can also be taken by foreign students who have the ability to understand, speak, read, and write Thai. This course covers the areas of Thai social studies, culture, history, geography, literature, and language. In this class, students will have the opportunity to participate in activities both inside and outside the classroom, not only during school hours, but also on holidays, weekends, and after school. Students will learn from textbooks, from the community, from reputable people, from field trips, and so on. This method of learning will help students to learn tolerance, responsibility for themselves and others, leadership, and teamwork. The course will involve work in small groups within the class, and in larger groups with the other Thai GL classes.
Students will develop a strong grasp of the most important areas of contemporary theater making while learning effective use of the voice and body, texts, spaces and objects. Looking closely at the design and construction of dramatic literature, environments and spaces within which performance can occur. Students will research and develop ideas for use on the three main types of stages as community settings and experimental projects in non-traditional spaces. The course culminates with a performance of a full length theatrical performance.
Teaches the fundamentals of how to use authoring tools, HTML tags, and styles to build websites/pages. Students will also learn to use color and good design principles to create websites/pages that effectively meet specific end use requirements.
The purpose of this course is to offer students focused time in which to hone and develop their writing skills. This workshop course offers independent and one-on-one practice under the guidance of the instructor. The specific intention is to increase the effectiveness of the student's writing in the following areas: proper English mechanics and grammar usage, communicating a clear message, developing a theme, and writing for a specific audience and purpose. This course may be taken as a single semester, or for the entire year, dependent upon the instructor's recommendation. | 677.169 | 1 |
Prealgebra - 4th edition
Summary: Tussy and Gustafson's fully integrated learning process is designed to expand students' reasoning abilities and teach them how to read, write, and think mathematically. In this thorough review of arithmetic and geometry, the authors also introduce the fundamental algebraic concepts needed by students who intend to take an introductory algebra course. Tussy and Gustafson build the strong mathematical foundation necessary to give students confidence to apply their newl...show morey acquired skills in further mathematics courses, at home, or on the job. ...show less
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many teaching aspects and experiences to her work with an engineering degree,
tutoring since 1989, homeschooling since 1997, and classroom experience.
This Study Guide provides a thorough treatment of expectations as outlined in the "Numbers and Numeration" and the
"Measurement" strands of the curriculum, including topics such as, integers, fractions, decimals, expanded form, percentages,
ratios, decimals, sales tax, discount, simple interest, rates, circles, right prisms, and cylinders.
Please note that this is Book 1, and Book 2 is needed to complete the course of studies for Grade 8.
Retail Price $25.95
many teaching aspects and experiences to her work with an engineering
degree, tutoring since 1989, homeschooling since 1997, and classroom
experience.
Math
8 Workbook 1 is a companion to Study Guide 1This Workbook provides a
thorough treatment of expectations as outlined in the "Numbers
and Numeration" and the "Measurement" strands of the curriculum,
including topics such as, integers, fractions, decimals, expanded
form, percentages, ratios, decimals, sales tax, discount, simple
interest, rates, circles, right prisms, and cylinders.
Please
note that this is Book 1, and Book 2 is needed to complete the
course of studies for Grade 8. It is recommended that the Workbooks
are used on a daily basis to build skills in a consistent manner,
and to enhance classroom learning.
Math
8 Workbook 2 is a companion to Study Guide 2In
Ontario, the overall expectations outlined by the Ministry of
Education are very similar for both Math 9 Applied
and Math 9 Academic courses, so this book can
be used for either course. While the overall stress of this study
guide is towards helping the Applied student succeed,
we have also included some multi-step questions and calculations
of prisms and cylinders to comply with all of the specific expectations
of the Academic Program of Studies. Throughout the book are helpful
hints to jog your memory, methods to make learning concepts much
easier, and a series of exercises, pop quizzes and final exams.
This means you will become increasingly confident and prepared
when it comes to school tests. Supplementary exercises are included
for students who want extra reinforcement. This book was recently
revised by a 39 year Ontario math professional teacher as an added
benefit to students of his many years of teaching experience including
the new Ontario math curriculum. All of these supplementary exercises
compliment the present Math 9 Text Ontario edition of
Addison-Wesley Mathematics 9 (ISBN 0-201-614737- 5).
Exercises
in the Math 9 Workbook compliment the Math 9by both a retired professional math teacher and an honours mathematics
graduate who is also involved in tutoring students in the new
Ontario Math curriculum. Once again, this will give you an excellent
overview of any type of question you may be tested on during your
school year. The drill and practice questions in this workbook
were derived from a combination of questions received from a number
of Ontario schools and from those created by both authors. Students
receive a great insight into the variety of questions and exercises
presently used by teachers in Ontario. We recommend that you use
the EZ Learning Solutions workbooks on a daily basis to build
skills and enhance your classroom learning.
Exercises
in the Math 9 Workbook 2, Fermi Math Problem Solving, follow new
recommendations from the Ministry of Education for Math 9 in Ontario
schools. The Fermi Math 9 problem solving workbook provides unique
step by step problem solving procedures that combine math and
science calculations. Teachers, students, and parents will appreciate
not only following the scientific methodology but the ability
to integrate many disciplines in real life applications following
the Enrico Fermi method of estimation used to develop strong analytical
and problem solving skills. Fermi incredible estimation skills
included activities like estimating the number of pianos in Chicago
or the number of grains of sand on the beaches of the world. These
labs were designed by a retired professional math who has taught
in Ontario Schools for over 38 years and presented by your favourite
author of EZ Learning Solutions study guides and workbooks.
The directions for these labs recommend the TIPS (Targeted Implementation
& Planning) Think/Pair/Share format on how to complete these
mathematical problem-solving labs. TIPS activities are designed
to include the subjects of math, science, geography, business
and probability while making observations and calculations with
decimals, integers, fractions, percents, rations, algebra and
formulas.
This is not a high-tech solution but a "back to basics",
student-oriented method of directed learning designed to enable
students to meet the requirements of the difficult new curriculum.
Our approach is "Get to the point and get on with the lesson".
This guide covers concepts taught in the Ontario Math Academic Curriculum
such as quadratic functions, linear systems, multi-step problems,
geometric figures, trigonometry, and factoring. It contains helpful
hints to jog your memory, methods to make learning concepts much
easier, and a series of exercises, quizzes and final exams. The
"Chalk Talk" areas provide the student with useful memory
aids and a helpful overview of what was just learned. This all means
that students will be more confident and better prepared at exam
time. Supplementary exercises are included for students who want
extra practice. All of these supplementary exercises compliment
the present Ontario edition of Nelson Mathematics 10 (ISBN
017-615704-2)and Principles of Mathematics 10 by Addison
Wesley (ISBN 0-201-71122-2).
Exercises
in the Math 10 Workbook compliment the Math 10to give you an excellent overview of any type of question you
may be tested on during your school year. The drill and practice
questions in this workbook were derived from a combination of
questions received from a number of Ontario schools to those created
by an Ontario Professional Teacher with 39 years of experience.
Never again will you get such an insight into the variety of questions
and exercises presently used by teachers in Ontario. We recommend
that you use the EZ Learning Solutions workbooks on a daily basis
to build skills and enhance your classroom learning.
Exercises
in the Math 10 Workbook 2 complete the second half of the school
year following the Math 10 Academic Workbook 1. All EZ Learning
workbooks follow the Math 10 Study Guide and the program of studies
providing both much needed summative questions as well as many
classic drill and practice questions. Once again you not only
have a great variety of questions but also complete solutions
to give you that extra edge to excel beyond the average student.
The questions were designed to give you an excellent overview
of any type of question you may be tested on during your school
year. The drill and practice questions in this workbook were derived
from a combination of questions received from a number of Ontario
schools to those created by an Ontario Professional Teacher with
39 years of experience. Never again will you get such an insight
into the variety of questions and exercises presently used by
teachers in Ontario. We recommend that you use the EZ Learning
Solutions workbooks on a daily basis to build skills and enhance
your classroom learning.
The
unique aspect of this book is that it was written by both a professional
teacher who has continually chosen to work with students having
the greatest difficulty with the new Ontario math curriculum and
by a teacher who was working with an ADD child. This is not a
high-tech solution but a "back to basics", student-oriented
method of directed learning designed to enable students to be
successful with the requirements of this difficult new curriculum.
Our approach is "Get to the point and get on with the lesson".
This study guide covers concepts taught in the new Ontario Math
Applied Curriculum including proportional reasoning: ratios/rates/percent,
introduction to Trigonometry, linear functions and linear systems,
and quadratic functions and factoring. It contains helpful hints
to jog your memory, methods to make learning concepts much easier,
and a series of exercises and quizzes, and a final exam for home
and school students. The "Chalk Talk" areas provide
the student with useful memory aids and a helpful overview of
what was just learned. This all means that students will be confident
and better prepared at exam time. Supplementary exercises are
included for students who want extra practice. All of these supplementary
exercises compliment the present Ontario edition of Mathematics,
Applying the Concepts by McGraw-Hill Ryerson (ISBN 0-07-086490-X)
and Foundations of Mathematics 10 by Addison Wesley (ISBN 0-201-68484-5).
In
this book you will find a very thorough review of grade 9, 10,
and 11 academic mathematics to help the University/College and
University student with the fundamentals in a straightforward
style. Both professionals felt
a great need to provide a spiral learning situation building on
past skills due to the length of time between semesters and the
need to strengthen these past skills in order to master the new
Ontario Math 11 curriculum.This study guide covers all key concepts
taught in the new Ontario Math University/College and University
Curriculum including a review of essential skills, rational expressions
and complex numbers, reciprocal functions, trigonometric ratios,
modeling periodic functions, trigonometric functions and radians,
and trigonometric graphs and transformations. Please note that
this is only the first book of the University/College and University
program of studies and you will need Book 2 to complete these
courses. The order of the topics covered in this book are in the
usual order that most Math professionals teach these courses in
Ontario schoolsThis
is Book 2 of the complete Math 11 University/College and University
high school programs. In this book you will find a very thorough
review of grade 9, 10, and 11 academic mathematics to help the
University/College and University level student with the fundamentals
in a straightforward style completing the second half of this
course but with that academic edge
with university ready skills. Both professionals felt a great
need to provide a spiral learning situation building on past skills
due to the length of time between semesters and the need to strengthen
these past skills in order to master the new Ontario Math 11 curriculum.
This study guide covers all key concepts taught in both the new
Ontario University/College and University Math 11 Curriculum including
solving trigonometric equations, trigonometric identities, and
solving quadratic trigonometric equations, Sequences and Series,
and ConicsMath
12 Advanced Functions and Introductory Calculus, University Preparation Book 1 - Available September 30th, 2005
Following
the Ontario program of studies this study guide builds on students
past abilities using functions then introduces the basic concepts
and skills of calculus. In this book you will find a very thorough
step by step understanding to help the University preparation
student with the fundamentals of Calculus after investigating
and applying the properties of polynomials and exponential and
logarithmic functions in a straightforward style. This book was
written by Bruce Mullens, after 40 years of teaching Mathematics
in Ontario and stands as a testament to his ability to understand
the type of problems that constantly evolve throughout this difficult
course. Bruce consulted with many colleagues and review tests,
quizzes, and final exams reflect the level of understanding taught
in Ontario schools and required to have success in University.
The first half of the school term covered in Book 1 thoroughly
completes all required expectations by presenting lessons in the
following: investigating the graphs of Polynomial functions, manipulating
algebraic expressions, understanding the nature of exponential
growth and decay, applying logarithmic functions, understanding
rates of change, understanding the graphical definition of the
derivative and connecting derivatives and graphs.
Please note that this is only the first book of the University
program of studies and you will need Book 2 to complete this course.
The order of the topics covered in this book are in the usual
order that most Math professionals teach these courses in Ontario
schools
Math
12 Advanced Functions and Introductory Calculus, University Preparation
Book 2 - Available February 15, 2006
Following
the Ontario program of studies this study guide builds on students past abilities using functions then
introduces the basic concepts and skills of calculus. In this book you will find a very thorough step by step
understanding to help the University preparation student with the fundamentals of Calculus after investigating
and applying the properties of polynomials and exponential and logarithmic functions in a straightforward style.
This book was written by Bruce Mullen, after 40 years of teaching Mathematics in Ontario and stands as a testament
to his ability to understand the type of problems that constantly evolve throughout this difficult course.
Bruce consulted with many colleagues and review tests, quizzes, and final exams reflect the level of understanding
taught in Ontario schools and required to have success in University.
The second half of the school term covered in Book 2 thoroughly completes all required expectations by presenting lessons
in the following: understanding the first-principles definition of the derivative, determining derivatives, determining
the derivatives of exponential and logarithmic functions, using differential calculus to solve problems, sketching the
graphs of polynomial, rational, and exponential functions, and using calculus techniques to analyse models of functions.
Please note that this is only the second book of the University program of studies and you will need Book 1 to complete
the first half of this course. The order of the topics covered in this book are in the usual order that most Math professionals
teach these courses in Ontario schools | 677.169 | 1 |
NMTA Mathematics 14 eBook
Get the guide that gets results! This digital study guide from XAMonline is available for immediate download and formatted for onscreen reading. It provides an overview of the main competencies and skills assessed on the NMTA Mathematics test. Aligned specifically to current state standards, the NMTA Mathematics study guide covers the sub-areas of Mathematical Processes, Methods, Number Concepts, and Their Historical Development; Geometry and Measurement; Data Analysis, Statistics, Probability, and Discrete Mathematics; and Patterns, Algebraic Relationships, and Functions. Turn your knowledge into practice with 80 sample test questions and comprehensive answer rationales provided to enhance your study.
XAMonline eBooks are viewed exclusively using FREE Adobe Digital Editions software. You can only use this eBook on devices that support Adobe Digital Editions software | 677.169 | 1 |
Functions, Statistics, and Trigonometry
Main goal: The goal of Functions, Statistics, and Trigonometry is to present topics from these three areas in a unified way to help students prepare for everyday live and future courses in mathematics. Spreadsheet, graphing and CAS technology are employed to enable students to explore and investigate, and to deal with complicated functions and data.
Main theme I: This text extends student knowledge of linear, quadratic, exponential, logarithm, polynomial and trigonometric equations and functions, with a new focus on statistical modeling with these functions.
Main theme II: Statistics are introduced in this text in the ways that people who work in a variety of different disciplines use them. Major topics include the selection of statistical displays, the differences between population and sample statistics, statistical distributions with emphasis on binomial and normal distributions, and statistical inference in addition to the statistical modeling mentioned above.
Main theme III: Trigonometry is explored. Trigonometric functions are used in their two main roles: as functions that enable lengths of segments and measures of angles of figures to be determined, and as functions that model periodic phenomena. The work with trigonometry includes strong connections with the geometry, matrices, and complex numbers that students encountered in previous courses.
Binomial Probability Applet
Main theme IV: The themes of statistics and trigonometry are integrated. By viewing statistical distributions as functions, properties of one idea can be applied to the other. A typical example is the transformation of graphs and its conceptual relative, the standardization of data. Modeling data by functions enables an examination of the distinguishing characteristics of the various types of functions that make them important.
Comparison between this and earlier editions: The statistical work has been rewritten with more emphasis on decision-making. The work with functions and trigonometry remains about the same as in previous editions.
Some distinctive lessons: Using statistics to solve a mystery: The Federalist papers (1-8); From New York to New Delhi (5-10); Designing simulations (6-7); Polynomial models (7-2); How much does a loan cost? (8-6); Is that coin fair? (10-8); The geometry of complex numbers (13-5). | 677.169 | 1 |
Synopsis
Written in a rigorous yet logical and easy to use style, spanning a range of disciplines, including business, mathematics, finance and economics, this comprehensive textbook offers a systematic, self-sufficient yet concise presentation of the main topics and related parts of stochastic analysis and statistical finance that are covered in the majority of university programmes.
Providing all explanations of basic concepts and results with proofs and numerous examples and problems, it includes:
an introduction to probability theory
a detailed study of discrete and continuous time market models
a comprehensive review of Ito calculus and statistical methods as a basis for statistical estimation of models for pricing
a detailed discussion of options and their pricing, including American options in a continuous time setting.
An excellent introduction to the topic, this textbook is an essential resource for all students on undergraduate and postgraduate courses and advanced degree programs in econometrics, finance, applied mathematics and mathematical modelling as well as academics and practitioners | 677.169 | 1 |
DIVE Math-Instruction CDs
We carry the DIVE Math CDs after numerous requests from
our customers. Those who used the DIVE CDs say good things about them and want
to continue with the program. That says a lot to us--our children use them now.
They tell us that Dr. Shormann explains the lessons in an easy to understand
fashion. If you want to save on a bundle purchase.
The DIVE Into Math series teaches every lesson in each Saxon Math textbook from Saxon Math 54 and up. See How DIVE Into Math Works for an overview of how the CDs work, system requirements, and notes on choosing the correct edition.
The Dive Calculus CD lesson lectures are ten to twenty minutes long. Then Dr. Shormann gives practice problems for the students to work. They can replay the lesson and practice problems as needed to master the material.
CLEP Professor for CLEP and AP Calculus is now provided FREE in DIVE Calculus 2nd Edition.
Students see and hear everything the instructor is writing and saying on a whiteboard on their computer screen. It is just like being in a real classroom, except there is no teacher in the way. Students learn by working practice problems that are similar, but not identical to the practice problems in the text. Lessons are 10-20 minutes long (doesn't count the time it takes to work practice problems). If students need more practice, they can work the problems in the text in addition to the DIVE problems explained on the CD. Easily re-wind, fast-forward, and pause with the click of a mouse. Each lesson is stored as an individual file. It is easy to choose the proper lecture.
"All DIVE CDs are taught from a Christian perspective, with an emphasis on mathematics as a tool for studying God's creation. Dr. Shormann's Christian testimony is on every CD and many lessons start with an encouraging Bible verse.
System Requirements
On each DIVE CDs is printed "Win/Mac Version For Macintosh or Windows 98 and Higher."
Why Use DIVE into Math CDs?
DIVE Syllabus Index Science Syllabi are on the lower half of this page. Use this to coordinate with popular high school science textbooks.
Why Use DIVE Into Math? Watch a YouTube video about DIVE Math from the publisher. (This link will open a new window.)
Very Important Notes about DIVE Exchange
Before you purchase, please be sure you have chosen the correct edition
for your textbook. If you aren't sure which edition to choose, please check
this link to see the
DIVE Syllabus Index (This opens a new window at the publisher's website.)
We do not accept returns on opened software. If you chose the wrong edition and have not opened it, we will exchange it (within 15 days--ok, call us and let us know it is coming and what you want in exchange) for the correct edition with a $4.95
for S&H.
All said, get the book you are using and check the edition before you order! If you aren't sure, get the book in hand and give us a call! | 677.169 | 1 |
Chapter 7. GMAT Quantitative
"Go down deep enough into anything and you will find mathematics."
—Dean Schlicter
The Graduate Management Admission Test (GMAT) Quantitative section is designed to test your ability to reason mathematically, to understand basic math terminology, and to recall basic mathematic formulae and principles. You should be able to solve problems and apply relevant mathematics concepts in arithmetic, algebra, geometry, and data analysis. | 677.169 | 1 |
Algebra at Cool math .com Hundreds of free Algebra 1, Algebra 2 and Precalcus Algebra lessons. Great to share with students and serve as extra information. Some contain some great animation related to the topics presented. Bored with Algebra? Confused by Algebra? Hate Algebra? We can fix that. Coolmath Algebra has hundreds of really easy to follow lessons and examples. Algebra 1, Algebra 2 and Precalculus Algebra. with system:unfiledby 2 users
Homework Help StudyBuddy StudyBuddy.com is an education Web site and homework help destination for students in grades K-12. It features an easy-to-use search engine with dependable results, reference tools, fun activities, games and more. You can find better answers faster and easier with StudyBuddy. StudyBuddy can provide all the homework help you need. Enter a question in StudyBuddy search and you'll get the answers buddyhelphomeworkmathpaperssciencestudywithwriting with system:unfiledby 2 users
Algebrator A software program to help students learning Algebra. A student must purchase to use. with algebrator
Any Time Tutor AnytimeTutor offers Math and Sciences tutoring for students from Grade 4 through college. All you need is access to the internet to connect to any of our qualified tutors. Stuck with math we can help!,Help with calculus, algebra, geometry and statistic help,Are you having difficulty understanding English Grammar,Don't worry about your computer science projects algebracalculusgeometryhelphomeworkmathstatisticworksheet with system:unfiled
Math Foundation Math Foundation is an award-winning program which features interactive e-learning tools to help you master the concepts of mathematics quickly and easily. The courseware is highly effective for adult learners, homeschool and traditional students. with foundationhomelearningmathtutorial | 677.169 | 1 |
Specific course objectives
Learn how to work in the complex framework, evaluate integrals of olomorphic functions, manipulate power and Fourier series, adopt the point of view of signal theory, calculate and operate with Fourier and Laplace transforms, solve simple ordinary differential equations with constant coefficients, understand convolutions.
Course programme
The language of signals
Continuous and discrete signals.
Basic operations on signals: sum and linear combinations of signals, traslation and rescalings. | 677.169 | 1 |
MATLAB Student Version
04/01/03
Students in engineering, math or science have a new technical computing resource designed for their needs. The MathWorks' MATLAB Student Version includes full-featured versions of MATLAB and Simulink, the software products used by engineers, scientists and mathematicians at leading universities, research labs, technology companies and government labs. MATLAB integrates computation, data analysis, visualization and programming in one environment. Simulink is one of the leading interactive environments for modeling, simulating and analyzing dynamic systems. In addition, there is no difference between the student and professional versions of the program, which, according to the company, is important because students are learning skills with the same tools they may use in a professional arena. The program also comes with MATLAB and Simulink books to help students get started. This product has a special student price of $99. The MathWorks, (508) 647-7000 | 677.169 | 1 |
Contents:
Overview
Mathematical Word Processing
With Scientific WorkPlace, Scientific Word, and Scientific Notebook you can enter mathematics easily with the mouse or, as you gain confidence and familiarity, with keyboard shortcuts.
LaTeX Typesetting
In Scientific WorkPlace and Scientific Word you can choose to typeset complex technical documents with LaTeX, the industry standard for mathematics typesetting. Because of its precision and quality, publishers and writers of scientific material use LaTeX extensively. When you typeset, LaTeX automatically generates footnotes, indexes, bibliographies, tables of contents, and cross-references. This typesetting power comes without you having to learn LaTeX. Scientific WorkPlace and Word automatically saves your documents as LaTeX files.
Computer Algebra
A computer algebra system, or CAS, is a mathematics engine that performs the symbolic computations fundamental to algebra, trigonometry, and calculus. Recent versions of Scientific WorkPlace and Scientific Notebook include the kernel to the computer algebra system MuPAD®. With MuPAD, you can evaluate, factor, combine, expand, and simplify terms and expressions that contain integers, fractions, and real and complex numbers, as required in simple arithmetic and algebra. You can also evaluate integrals and derivatives, perform matrix and vector operations, find standard deviations, and perform many other more complex computations involved in calculus, linear algebra, differential equations, and statistics. Additionally, you can create 2D and 3D plots of polynomials, trigonometric functions, and exponentials, and you can create animated 2D and 3D plots and explore them with the MuPAD VCAM window. | 677.169 | 1 |
High School Mathematics
Mathematics is indispensable for understanding our world. In addition to providing the tools of arithmetic, algebra, geometry and statistics, it offers a way of thinking about patterns and relationships of quantity and space and the connections among them. Mathematical reasoning allows us to devise and evaluate methods for solving problems, make and test conjectures about properties and relationships, and model the world around us.
Standards and Grade Level Expectations
1. Number Sense, Properties, and Operations
1
The complex number system includes real numbers and imaginary numbers
2
Quantitative reasoning is used to make sense of quantities and their relationships in problem situations
3
Art and design have purpose and function
2. Patterns, Functions, and Algebraic Structures
1
Functions model situations where one quantity determines another and can be represented algebraically, graphically, and using tables
2
Quantitative relationships in the real world can be modeled and solved using functions
3
Expressions can be represented in multiple, equivalent forms
4
Solutions to equations, inequalities and systems of equations are found using a variety of tools | 677.169 | 1 |
Once you have studied the lessons and learned the necessary background material, please attempt the exercises. If you get stuck, you will then be able to reply with a clear listing of your steps and reasoning so far. | 677.169 | 1 |
maple1
Course: MATH 291, Fall 2009 School: Rutgers Rating:
Word Count: 1154
Document Preview ask you to hit the "enter" key (new line) with the request RET. Now, please, log in to eden and get a prompt in an x-window. Then type xmaple & RET The system should respond with a Maple screen on your display. There are standard ways for you to move or resize the screen, and various Maple-specific command possibilities. Maple is a huge program with a great many capabilities. We'll just explore a few of them. Right now I'd like you to move your mouse into the Maple window. You should see this, which is the command line: >| The symbol for your cursor is | and it is currently at an input line, indicated by the > sign. Please type 3+2 RET Maple did nothing with your input you only get another input line, and a complaint message from Maple! Move your cursor back (with the arrow keys or the mouse) to the first input line, and then move the cursor to the the end of the line. The input line should look like > 3 + 2| Then continue your typing with a semicolon followed by a return: ; RET Something should happen. You should get 5 and a new input line. You can move your cursor up and down. Now move your cursor back to your new input line. Type 17*3; RET and see what the result is. At the next input line type %+5; RET and explain the result. What do you think the meaning of the symbol % is? Now type the following to learn what ^ means. 2^3; RET But . . . I made a mistake! I wanted you to calculate the 300th power of 2. Please do the following: move your cursor back to the input line with 2^3 and position it in the following place: > 2^3|; and now type 00 and immediately hit RET. What happened? Please compute 3300 in the same fashion by moving your cursor and changing the input line. (Hint: position your cursor after the 2, type backspace, and then type 3.) What are the first 5 and last 5 decimal digits of this number? A little more: please type (look carefully here I'm asking for a colon, not a semicolon!) 5+6: RET You should immediately get another input line. Type (for example) %+7; and deduce what Maple does when an input line ends with a : (that is, a colon). Note that computations might and do occur which have results that are huge and silly to print out if you don't need them -- 2^(2^(2^(2^2))), for example. Try that sometime on your own, please, with ";" rather than a ":" and see what happens (hah!). Onward: please type 20; RET and see the result. Go back with your cursor and put a space between the 2 and the 0 and hit RET. What's the result? Now let's try 2*3+7; RET and observe that Maple follows the usual rules of precedence. Can you put parentheses in so that Maple will compute two times the sum of three plus seven instead? Remember to hit RET after you make the alterations. You should have gotten 20 as your answer, of course. If you did not make an error inserting the parentheses, go back and take one out (create an intentional error!) and then hit RET. What happens? haven't You broken anything. Let's keep exploring. Please get a new input line and try these commands in succession to learn how to do more arithmetic and to explore more features of Maple. OVER
... you can't break the program, so explore!
... you can't break the program, so explore!
... you can't break the program, so explore!
... you can't break the program, so explore!
2/3; RET Maple computes "exactly" and can do some (fourth grade?) arithmetic: %*300; RET Now try sqrt(2); RET and now %^2; RET so Maple knows the "meaning" of fractions and square roots or at least how to manipulate them. And now try (remember, if you mess up with a parenthesis or something else, just go back and do it again nothing is broken!): (sqrt(2)-1)^5; RET This result is puzzling. Sometimes Maple is lazy. Let's urge it to work by writing expand(%); RET That's better. But what if we want or need decimal approximations? Try evalf(sqrt(2)); RET Parentheses need to be matched always a source of anxiety as more and more complex expressions and commands are typed. What if we want more digits of 2? We can coax evalf to do this with more informed use. To see how, type help(evalf); RET Another screen should pop up. When I use Maple I tend to need a lot of help so the help screens accumulate on my display. You can "click" them on and off, and eliminate them entirely (click on the upper left or right corners of the screen to see how). Read the evalf screen until you can figure out how to get the first 100 digits (after the decimal point) of 2. I usually skip down to the examples on any help screen first, because they are usually relevant to my questions! What is the one-hundredth digit after the decimal point? Can you tell me the three-hundredth digit after the decimal point of 171/3 ? Use lots of parentheses, even in exponents, to inform Maple clearly what you want. Now try 1400/24; RET and we learn that Maple knows how to factor integers automatically. Can you get Maple to factor your social security number? How would you find a factoring command in Maple? If the first thing you try with the help command doesn't work, look at the references on the SEE ALSO line and check one of them. We can go on to try some algebra. But notice that you can stop your Maple session at any time in a variety of ways. One way that is polite to the system and also simple for you is to type quit RET and your Maple window will disappear, and you can exit the program by clicking on the File button. Of course all of your work will also have vanished, but at some other time you can explore various possibilities of saving what you've done.
Disclaimer! Non-advertisement!! Important information!!! Symbolic manipulation programs such as Maple are increasingly available. Mathematica and Derive are other programs with the same capability. There are many special purpose programs in science, engineering, and mathematics which have extensive "intelligence" to analyze models. We're considering Maple here because Rutgers has a site license for this program. It is generally available on Rutgers systems. The specific instructions won't be the same from program to program, but many of the same ideas will be present. Students should expect to have a machine do tiresome or elaborate symbolic computations as well as numerical comput you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!640:291:01Part II: playing with algebra on Maple9/15/2002Maple's mos
. you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!640:291:01Part III: playing with calculus on Maple9/15/2002The basic
. you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!640:291:01Part IV: playing with graphs on Maple9/15/2002The graphing
DisclaimerThis site makes available conceptual plans that can be helpful in developing building layouts and selecting equipment for various agricultural applications. These plans do not necessarily represent the most current technology or constructi
UNDER
FACTS AND FIGURES 2000 - 2001Office of Institutional Research and PlanningMichael F. Middaugh, Assistant Vice President for Institutional Research and Planning Dale W. Trusheim, Associate Director of Institutional Research and Planning Karen W. Bau
Coll
Introduction to RDownloadingFor your home/office computer, you can get binaries (ready-to-run) for R by going to http:/ clicking on CRAN and picking one of "mirror" websites to download from, click on Windows, base, R-2.2.1-win32.
Latin square design The Latin square design is for a situation in which there are two extraneous sources of variation. If the rows and columns of a square are thought of as levels of the the two extraneous variables, then in a Latin square each treat
Using SPSS to Perform a Chi-Square Goodness-of-fit Test The data set consists of two variables: one indicates the categories, and the other the counts for each category. First step: Select Data Weight Cases. A box pops up with a list of the input var
reak the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, soNew users may read this side before starting. Please don't read the other side until later. It m
reak the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, so640:192:01Part I: playing with arithmetic on maple9/1/2005What you should type will be in
reak the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, so640:192:01Part II: playing with algebra on maple9/1/2005The most attractive feature of map
reak the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, so640:192:01Part III: playing with calculus on maple9/1/2005The basic calculus commands do d
reak the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, so640:192:01Part IV: playing with graphs on maple9/1/2005The graphing capabilities of maple
This version prepared 6/30/200356 Lecture 14 / : IntermezzoBIRTHDAY TIME!Suppose you have a crowd of people. When will two of them share a birthday?* Probabilistic answer This question is studied in almost every elementary probability text.
This version prepared 6/30/200338Lecture 9: Probably .9.1 Vocabulary A real-world experiment has various outcomes. The collection of all possible outcomes is called the sample space. This vocabulary discussion will be accompanied by two simple e
September 15, 2003ALIENS!Due Thursday, September 18 Background assumptions We imagine an alien language which has only three words: 40% of the words are 1111111. Abbreviate this word with A. It is seven bits long. 30% of the words are 00000. Abb | 677.169 | 1 |
Successful application of mathematical principles to solve a range of challenging problems. Clear integration of knowledge, understanding and skills from different areas. Comprehensive responses containing all necessary detail.
B
Broad knowledge and understanding, although some responses lacked detail or contained minor errors.
Broad knowledge and understanding, although some responses lacked detail or contained minor errors.
Successful application of mathematical principles to solve a variety of problems. Some integration of knowledge, understanding and skills from different areas. Some responses lacked necessary detail or contained minor errors.
C
Satisfactory knowledge and understanding of the syllabus; satisfactory application of mathematical processes in performing routine tasks. Some responses lacked detail; some significant errors.
Satisfactory knowledge and understanding of the syllabus; satisfactory application of mathematical processes in performing routine tasks. Some responses lacked detail; some significant errors.
Satisfactory application of mathematical principles to solve some problems. Satisfactory integration of knowledge, understanding and skills from different areas, when given some direction.
D
Basic knowledge of the syllabus and limited understanding of mathematical principles; attempted to carry out mathematical processes in straightforward contexts, but many significant errors.
Basic knowledge of the syllabus and limited understanding of mathematical principles; attempted to carry out mathematical processes in straightforward contexts, but many significant errors.
Limited application of mathematical principles to solve problems.
E
Very limited knowledge of the syllabus; difficulty carrying out mathematical processes at a basic level.
Very limited knowledge of the syllabus; difficulty carrying out mathematical processes at a basic level.
Limited application of mathematical principles to solve even the most basic problems. | 677.169 | 1 |
Monthly Archives: January 2011
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John Page describes his 'Math Open Reference' project as a free interactive textbook on the web, initially covering Geometry.
The tools include various function explorers. Younger students could explore linear functions for example, whilst older students could use the general Graphical Function Explorer to explore any functions, trigonometric for example. | 677.169 | 1 |
Secondary Mathematics I [2011]
Interpret functions that arise in applications in terms of a context. For F.IF.4 and 5, focus on linear and exponential functions. For F.IF.6, focus on linear functions and intervals for exponential functions whose domain is a subset of the integers. Mathematics II and III will address other function types. N.RN.1 and N.RN.2 will need to be referenced here before discussing exponential models with continuous domains.
F.IF.6
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.*
Distance-Time Graphs
This tutorial is designed to help students understand the concept of slope and how distance-time graphs represent the relationship of collected data.
Function Flyer
The applet on this site allows the students to manipulate the graph of a function by changing the value of exponents, coefficients and constants.
Graphit
With this interactive applet students are able to create graphs of functions and sets of ordered pairs on the same coordinate plane.
Growth Rate
In this lesson from Illuminations, students are given growth charts for the heights of girls and boys in order to approximate rates of change in the height of boys and girls at different ages. Students will use these approximations to plot graphs of the rate of change of height vs. age for boys and girls.
Interpreting Functions Curriculum Guide
The Utah State Office of Education (USOE) and educators around the state of Utah developed these guides for the Secondary Mathematics 1 Cluster "Understand the concept of a function and use function notation." / Standards F.IF.1, F.IF.2, F.IF.3 and Cluster "Interpret functions that arise in applications in terms of a context" / Standards F.IF.4, F.IF.5 and F.IF.6 and Cluster "Analyze functions using different representations" / Standards F.IF.7 and F.IF.9.
Multi-Function Data Flyer
The applet in this lesson allows students to plot ordered pairs and then change the values in order to observe the effects of those changes.
Rate of Change and Slope
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review | 677.169 | 1 |
Synopsis
An accessible guide to developing intuition and skills for solving mathematical problems in the physical sciences and engineering
Equations play a central role in problem solving across various fields of study. Understanding what an equation means is an essential step toward forming an effective strategy to solve it, and it also lays the foundation for a more successful and fulfilling work experience. Thinking About Equations provides an accessible guide to developing an intuitive understanding of mathematical methods and, at the same time, presents a number of practical mathematical tools for successfully solving problems that arise in engineering and the physical sciences.
Equations form the basis for nearly all numerical solutions, and the authors illustrate how a firm understanding of problem solving can lead to improved strategies for computational approaches. Eight succinct chapters provide thorough topical coverage, including:
Approximation and estimation
Isolating important variables
Generalization and special cases
Dimensional analysis and scaling
Pictorial methods and graphical solutions
Symmetry to simplify equations
Each chapter contains a general discussion that is integrated with worked-out problems from various fields of study, including physics, engineering, applied mathematics, and physical chemistry. These examples illustrate the mathematical concepts and techniques that are frequently encountered when solving problems. To accelerate learning, the worked example problems are grouped by the equation-related concepts that they illustrate as opposed to subfields within science and mathematics, as in conventional treatments. In addition, each problem is accompanied by a comprehensive solution, explanation, and commentary, and numerous exercises at the end of each chapter provide an opportunity to test comprehension.
Requiring only a working knowledge of basic calculus and introductory physics, Thinking About Equations is an excellent supplement for courses in engineering and the physical sciences at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers, practitioners, and educators in all branches of engineering, physics, chemistry, biophysics, and other related fields who encounter mathematical problems in their day-to-day | 677.169 | 1 |
Maths
Why Should I Study This Subject?
There are many reasons why people choose to study A Level Mathematics. It might be a requirement for what you want to study at university. Since maths is one of the most traditional subjects a good grade in maths can boost an application for almost every course! Studies have also shown that people with Maths A Level also tend to earn more on average than people without it. Though this itself may or may not be a good enough reason to study maths, the skills it allows you to develop include problem solving, logic and analysing situations. Add in the improvements to your basic numeracy skills and that bit of creativity needed to solve maths problems and you've got yourself a set of skills which would make you more desirable for almost any job! Finally, you might also really like maths - this is as good a reason as any to continue studying it. If you study something you enjoy you are likely to do better at it. With maths there is the excitement of new discoveries you will make. You will see more of the beauty of it and realise just how much everything in the universe is connected to mathematics.
The bottom line is, maths is an amazing subject to have at A Level and provided you have a solid understanding of the GCSE concepts before you start, alongside some perseverance and effort, you should be able to do well.
What Will I Study?
Year 1: Core 1, Core 2 & either Mechanics 1 or Statistics 1 or Decision 1
Year 2: Core 3, Core 4 & either Mechanics 1 or Statistics 1 or Decision 1 or Mechanics 2 or Statistics 2
How Will it be Assessed?
Each of the modules is assessed by an exam only.
Exam Board
Edexcel, for further details:
What Can I do Next?
Many university courses such as physics, psychology, economics, computing, engineering and business studies prefer students to have A Level maths if possible. Having A level maths is a great signal to any employer that you can think logically, work hard and have a great level of numerical skill.
What Grades Will I Need?
8 GCSE grades A*- C. Students are required to have at least an A grade at GCSE to study maths at A Level. | 677.169 | 1 |
Guiding Principles for Development
The authors were guided by the following principles in the development of the Connected Mathematics materials. These statements reflect both research and policy stances in mathematics education about what works to support students' learning of important mathematics.
The "big" or key mathematical ideas around which the curriculum is built are identified.
The underlying concepts, skills, or procedures supporting the development of a key idea are identified and included in an appropriate development sequence.
An effective curriculum has coherence-it builds and connects from investigation to investigation, unit-to-unit, and grade-to-grade.
Mathematical tasks for students in class and in homework are the primary vehicle for student engagement with the mathematical concepts to be learned. The key mathematical goals are elaborated, exemplified, and connected through the problems in an investigation.
Ideas are explored through these tasks in the depth necessary to allow students to make sense of them. Superficial treatment of an idea produces shallow and short-lived understanding and does not support making connections among ideas.
The curriculum helps students grow in their ability to reason effectively with information represented in graphic, numeric, symbolic, and verbal forms and to move flexibly among these representations.
The curriculum reflects the information- processing capabilities of calculators and computers and the fundamental changes such tools are making in the way people learn mathematics and apply their knowledge of problem-solving tasks.
Connected Mathematics is different from many more familiar curricula in that it is problem centered. The following section elaborates what we mean by this and what the value added is for students of such a curriculum.
Student Learning: Rationale for a Problem-Centered Curriculum
Students' perceptions about a discipline come from the tasks or problems with which they are asked to engage. For example, if students in a geometry course are asked to memorize definitions, they think geometry is about memorizing definitions. If students spend a majority of their mathematics time practicing paper-and-pencil computations, they come to believe that mathematics is about calculating answers to arithmetic problems as quickly as possible. They may become faster at performing specific types of computations, but they may not be able to apply these skills to other situations or to recognize problems that call for these skills. Formal mathematics begins with undefined terms, axioms, and definitions and deduces important conclusions logically from those starting points. However, mathematics is produced and used in a much more complex combination of exploration, experience-based intuition, and reflection. If the purpose of studying mathematics is to be able to solve a variety of problems, then students need to spend significant portions of their mathematics time solving problems that require thinking, planning, reasoning, computing, and evaluating.
A growing body of evidence from the cognitive sciences supports the theory that students can make sense of mathematics if the concepts and skills are embedded within a context or problem. If time is spent exploring interesting mathematics situations, reflecting on solution methods, examining why the methods work, comparing methods, and relating methods to those used in previous situations, then students are likely to build more robust understanding of mathematical concepts and related procedures. This method is quite different from the assumption that students learn by observing a teacher as he or she demonstrates how to solve a problem and then practices that method on similar problems.
A problem-centered curriculum not only helps students to make sense of the mathematics, it also helps them to process the mathematics in a retrievable way.
Teachers of CMP report that students in succeeding grades remember and refer to a concept, technique, or problem-solving strategy by the name of the problem in which they encountered the ideas. For example, the Basketball Problem from What Do You Expect? in Grade Seven becomes a trigger for remembering the processes of finding compound probabilities and expected values.
Results from the cognitive sciences also suggest that learning is enhanced if it is connected to prior knowledge and is more likely to be retained and applied to future learning. Critically examining, refining, and extending conjectures and strategies are also important aspects of becoming reflective learners.
In CMP, important mathematical ideas are embedded in the context of interesting problems. As students explore a series of connected problems, they develop understanding of the embedded ideas and, with the aid of the teacher, abstract powerful mathematical ideas, problem- solving strategies, and ways of thinking. They learn mathematics and learn how to learn mathematics.
Characteristics of Good Problems
To be effective, problems must embody critical concepts and skills and have the potential to engage students in making sense of mathematics. And, since students build understanding by reflecting, connecting, and communicating, the problems need to encourage them to use these processes.
Each problem in Connected Mathematics satisfies the following criteria:
The problem must have important, useful mathematics embedded in it.
Investigation of the problem should contribute to students' conceptual development of important mathematical ideas.
Work on the problem should promote skillful use of mathematics and opportunities to practice important skills.
The problem should create opportunities for teachers to assess what students are learning
In addition each problem satisfies some or all of the following criteria:
The problem should engage students and encourage classroom discourse.
The problem should allow various solution strategies or lead to alternative decisions that can be taken and defended.
Solution of the problem should require higher-level thinking and problem solving.
The mathematical content of the problem should connect to other important mathematical ideas.
Practice With Concepts, Related Skills, and Algorithms
Students need to practice mathematical concepts, ideas, and procedures to reach a level of fluency that allows them to "think" with the ideas in new situations. To accomplish this we were guided by the following principles related to skills practice.
Immediate practice should be related to the situations in which the ideas have been developed and learned.
Continued practice should use skills and procedures in situations that connect to ideas that students have already encountered.
Students need opportunities to use the ideas and skills in situations that extend beyond familiar situations. These opportunities allow students to use skills and concepts in new combinations to solve new kinds of problems.
Students need practice distributed over time to allow ideas, concepts and procedures to reach a high level of fluency of use in familiar and unfamiliar situations and to connect to other concepts and procedures.
Students need guidance in reflecting on what they are learning, how the ideas fit together, and how to make judgments about what is helpful in which kinds of situations.
Throughout the Number and Algebra Strands development, students need to learn how to make judgments about what operation or combination of operations or representations is useful in a given
situation, as well as, how to become skilful at carrying out the needed computation(s). Knowing how to, but not when to, is insufficient. Skills
in CMP under Mathematics Content and Algebra in CMP under Mathematics Content.
Rationale for Depth versus Spiraling
The concept of a "spiraling" curriculum is philosophically appealing; but, too often, not enough time is spent initially with a new concept to build on it at the next stage of the spiral. This leads to teachers spending a great deal of time re-teaching the same ideas over and over again. Without a deeper understanding of concepts and how they are connected, students come to view mathematics as a collection of different techniques and algorithms to be memorized.
Problem solving based on such learning becomes a search for the correct algorithm rather than seeking to make sense of the situation, considering the nature and size of a solution, putting together a solution path that makes sense, and examining the solution in light of the original question. Taking time to allow the ideas studied to be more carefully developed means that when these ideas are met in future units, students have a solid foundation on which to build. Rather than being caught in a cycle of relearning the same ideas at a superficial level, which are quickly forgotten, students are able to connect new ideas to previously learned ideas and make substantive advances in knowledge.
With any important mathematical concept, there are many related ideas, procedures, and skills. At each grade level, a small, select set of important mathematical concepts, ideas, and related procedures are studied in depth rather than skimming through a larger set of ideas in a shallow manner. This means that time is allocated to develop understanding of key ideas in contrast to "covering" a book. The Teacher's Guides accompanying CMP materials were developed to support teachers in planning for and teaching a problem-centered curriculum. Practice on related skills and algorithms are provided in a distributed fashion so that students not only practice these skills and algorithms to reach facility in carrying out computations, but they also learn to put their growing body of skills together to solve new problems.
Field Testing
Developing Depth of Understanding and Use
Through the field trials process we were able to develop units that result in student understanding of key ideas in depth. An example is illustrated in the way that Connected Mathematics treats proportional reasoning-a fundamentally important topic for middle school mathematics and beyond. Conventional treatments of this central topic are often limited to a brief expository presentation of the ideas of ratio and proportion, followed by training in techniques for solving proportions. In contrast, the CMP curriculum materials develop core elements of proportional reasoning in a seventh grade unit, Comparing and Scaling, with the groundwork for this unit having been developed in four prior units. Five succeeding units build on and connect to students' understanding of proportional reasoning. These units and their connections are summarized as follows:
Grade 6Bits and Pieces I and II introduce students to fractions and their various meanings and uses. Models for making sense of fraction meanings and of operating with fractions are introduced and used. These early experiences include fractions as ratios. The extensive work with equivalent forms of fractions builds the skills needed to work with ratio and proportion problems. These ideas are developed further in the probability unit How Likely Is It? in which ratio comparisons are informally used to compare probabilities. For example, is the probability of drawing a green block from a bag the same if we have 10 green and 15 red or 20 green and 30 red?
Grade 7Stretching and Shrinking introduces proportionality concepts in the context of geometric problems involving similarity. Students connect visual ideas of enlarging and reducing figures, numerical ideas of scale factors and ratios, and applications of similarity through work with problems focused around the question: "What would it mean to say two figures are similar?"
The next unit in grade seven is the core proportional reasoning unit, Comparing and Scaling, which connects fractions, percents, and ratios through investigation of various situations in which the central question is: "What strategies make sense in describing how much greater one quantity is than another?" Through a series of problem-based investigations, students explore the meaning of ratio comparison and develop, in a progression from intuition to articulate procedures, a variety of techniques for dealing with such questions.
A seventh grade unit that follows, Moving Straight Ahead, is a unit on linear relationships and equations. Proportional thinking is connected and extended to the core ideas of linearity- constant rate of change and slope. Then in the probability unit What Do You Expect?, students again use ratios to make comparisons of probabilities.
Grade 8Thinking With Mathematical Models; Looking For Pythagoras; Growing, Growing, Growing, and Frogs, Fleas, and Painted Cubes extend the understanding of proportional relationships by investigating the contrast between linear relationships and inverse, exponential, and quadratic relationships. Also in Grade Eight, Samples and Populations uses proportional reasoning in comparing data situations and in choosing samples from populations.
These unit descriptions show two things about Connected Mathematics-the in-depth development of fundamental ideas and the connected use of these important ideas throughout the rest of the units.
CMP Instructional Model
Problem-centered teaching opens the mathematics classroom to exploring, conjecturing, reasoning, and communicating. The Connected Mathematics teacher materials are organized around an instructional model that supports this kind of teaching. This model is very different from the "transmission" model in which teachers tell students facts and demonstrate procedures and then students memorize the facts and practice the procedures. The CMP model looks at instruction in three phases: launching, exploring, and summarizing. The following text describes the three instructional phases and provides the general kinds of questions that are asked. Specific notes and questions for each problem are provided in the Teacher's Guides.
Launch
In the first phase, the teacher launches the problem with the whole class. This involves helping students understand the problem setting, the mathematical context, and the challenge. The following questions can help the teacher prepare for the launch:
What are students expected to do?
What do the students need to know to understand the context of the story and the challenge of the problem?
What difficulties can I foresee for students?
How can I keep from giving away too much of the problem solution?
The launch phase is also the time when the teacher introduces new ideas, clarifies definitions, reviews old concepts, and connects the problem to past experiences of the students. It is critical that, while giving students a clear picture of what is expected, the teacher leaves the potential of the task intact. He or she must be careful to not tell too much and consequently lower the challenge of the task to something routine, or to cut off the rich array of strategies that may evolve from a more open launch of the problem.
Explore
The nature of the problem suggests whether students work individually, in pairs, in small groups, or occasionally as a whole class to solve the problem during the explore phase. The Teacher's Guide suggests an appropriate grouping. As students work, they gather data, share ideas, look for patterns, make conjectures, and develop problem-solving strategies.
It is inevitable that students will exhibit variation in their progress. The teacher's role during this phase is to move about the classroom, observing individual performance and encouraging on-task behavior. The teacher helps students persevere in their work by asking appropriate questions and providing confirmation and redirection where needed. For students who are interested in and capable of deeper investigation, the teacher may provide extra questions related to the problem. These questions are called Going Further and are provided in the explore discussion in the Teacher's Guide. Suggestions for helping students who may be struggling are also provided in the Teacher's Guide. The explore part of the instruction is an appropriate place to attend to differentiated learning.
The following questions can help the teacher prepare for the explore phase:
How will I organize the students to explore this problem? (Individuals? Pairs? Groups? Whole class?)
What materials will students need?
How should students record and report their work?
What different strategies can I anticipate they might use?
What questions can I ask to encourage student conversation, thinking, and learning?
What questions can I ask to focus their thinking if they become frustrated or off-task?
What questions can I ask to challenge students if the initial question is "answered"?
As the teacher moves about the classroom during the explore, she or he should attend to the following questions:
What difficulties are students having?
How can I help without giving away the solution?
What strategies are students using? Are they correct?
How will I use these strategies during the summary?
Summarize
It is during the summary that the teacher guides the students to reach the mathematical goals of the problem and to connect their new understanding to prior mathematical goals and problems in the unit. The summarize phase of instruction begins when most students have gathered sufficient data or made sufficient progress toward solving the problem. In this phase, students present and discuss their solutions as well as the strategies they used to approach the problem, organize the data, and find the solution. During the discussion, the teacher helps students enhance their conceptual understanding of the mathematics in the problem and guides them in refining their strategies into efficient, effective, generalizable problem-solving techniques or algorithms.
Although the summary discussion is led by the teacher, students play a significant role. Ideally, they should pose conjectures, question each other, offer alternatives, provide reasons, refine their strategies and conjectures, and make connections. As a result of the discussion, students should become more skillful at using the ideas and techniques that come out of the experience with the problem.
If it is appropriate, the summary can end by posing a problem or two that checks students' understanding of the mathematical goal(s) that have been developed at this point in time. Check For Understanding questions occur occasionally in the summary in the Teacher's Guide. These questions help the teacher to assess the degree to which students are developing their mathematical knowledge. The following questions can help the teacher prepare for the summary:
How can I help the students make sense of and appreciate the variety of methods that may be used?
How can I orchestrate the discussion so that students summarize their thinking about the problem?
What questions can guide the discussion?
What concepts or strategies need to be emphasized?
What ideas do not need closure at this time?
What definitions or strategies do we need to generalize?
What connections and extensions can be made?
What new questions might arise and how do I handle them?
What can I do to follow up, practice, or apply the ideas after the summary?
Support for Classroom Teachers
When mathematical ideas are embedded in problem-based investigations of rich context, the teacher has a critical responsibility for ensuring that students abstract and generalize the important mathematical concepts and procedures from their experiences with the problems. In a problem-centered classroom, teachers take on new roles-moving from always being the one who does the mathematics to being the one who guides, interrogates, and facilitates the learner in doing and making sense of the mathematics.
The Teacher's Guides and Assessment Resources developed for Connected Mathematics provide these kinds of help for the teacher:
The Teacher's Guide for each unit engages teachers in a conversation about what is possible in the classroom around a particular lesson. Goals for each lesson are articulated. Suggestions are made about how to engage the students in the mathematics task, how to promote student thinking and reasoning during the exploration of the problem, and how to summarize with the students the important mathematics embedded in the problem. Support for this Launch-Explore- Summarize sequence occurs for each problem in the CMP curriculum.
An overview and elaboration of the mathematics of the unit is located at the beginning of each Teacher's Guide, along with examples and a rationale for the models and procedures used. This mathematical essay helps a teacher stand above the unit and see the mathematics from a perspective that includes the particular unit, connects to earlier units, and projects to where the mathematics goes in subsequent units and years.
Actual classroom scenarios are included to help stimulate teachers' imaginations about what is possible.
Questions to ask students at all stages of the lesson are included to help teachers support student learning.
Reflection questions are provided at the end of each investigation to help teachers assess what sense students are making of the 'big" ideas and to help students abstract, generalize, and record the mathematical ideas and techniques developed in the Investigation.
Diverse kinds of assessments are included in the student units and the Assessment Resources that mirror classroom practices as well as highlight important concepts, skills, techniques, and problem solving strategies.
Multiple kinds of assessment are included to help teachers see assessment and evaluation as a way to inform students of their progress, apprise parents of students' progress, and guide the decisions a teacher makes about lesson plans and classroom interactions. Components of CMP | 677.169 | 1 |
Mathematics A Discrete Introduction
9780534356385
ISBN:
0534356389
Pub Date: 2000 Publisher: Brooks/Cole
Summary: This book is an introduction to mathematics--in particular, it is an introduction to discrete mathematics. There are two primary goals for this book: students will learn to reading and writing proofs, and students will learn the fundamental concepts of discrete mathematics | 677.169 | 1 |
Math Solver II is a scientific calculator. Math Solver II includes a step-by-step solution for any mathematical expression, to make work/homework more fun and easy. Also includes a Simple Mode, for... more
PANAGEOS .- level: Advanced ; language: English Plane Analytic Geometry Problem Solver, is for the user who already knows the subject and wants to verify his/hers solutions, or for the teacher orChildren can effectively learn math with friendly natural animals and/or worms. The comprehensive game of Space Tour, touring among various planets and the experience to fly over the surface of the... more
Calculate geometry problems with this tool. Geometry Solver 3D will solve analytic geometry problems easily. It will provide tools for calculations in 3D as well as graphic OpenGL demonstrations.... more
Math Mechanixs is an easy to use scientific and engineering FREE math software program. (FREE registration is required after 60 days). The typical tool for solving mathematical problem has been... more
STFMath is a multipurpose math utility, suitable not only for students, but also for engineers, professors, or anyone interested in math: functions (draw, analyze, evaluate), calculators (complex,... more
Children can effectively learn math with friendly natural animals and/or worms.The comprehensive game to rescue the princess frog from Witch's Castle is provided. The witch's dragons multiple to... more
Get into the pilot seat and learn about volume and surface area while blasting away space debris to save your ship! Galactic Geometry is a 3D educational game that offers an engaging environment... more
GEUP 3D is an interactive solid geometry software for math calculation and visualization. It allows to create dynamic and general constructions/applications visually by defining math elements. GEUP... more
Geometry calculates geometric figures such as spheres, triangles, cones, trapezoids, circles and cylinders. Also, it has an application in engineering to calculate the flow and geometry in an open... more
Math for kids of all ages. Also has times tables for kids.When you get the right answer you get a happy face. When it is wrong you get a sad face. Has 3 levels of difficulty to choose from.There... more
Magic Math Space Tour for ages 11-12 is a quiz-oriented CAI that provides an enjoyable environment for children to study math. Friendly animals and worms participate in the animations and introduce... more
Math Composer is a powerful yet easy to use tool for creating all your math documents. It is a simple way for math teachers and instructors to create math worksheets, tests, quizzes, and exams.... more | 677.169 | 1 |
Survey Of Mathematics I –
mth361
(3 credits)
This is the first course of a two-part course sequence presenting a survey of mathematics. This course addresses the conceptual framework for mathematics. The focus of this course is on real number properties, patterns, operations, and algebraic reasoning and problem solving.
Real Numbers and Applications
Standards and Professional Organizations
Describe the standards and principles of mathematics as taught in K-12 schools.
Examine the role of professional mathematics organizations | 677.169 | 1 |
An Introduction to Modern Mathematical Computing
With Mathematica
by Jonathan M. Borwein and Matthew P. Skerritt
Thirty years ago, mathematical computation was difficult to perform and thus used sparingly. However, mathematical computation has become far more accessible due to the emergence of the personal computer, the discovery of fiber-optics and the consequent development of the modern internet, and the creation of Maple, Mathematica, and Matlab.
An Introduction to Modern Mathematical Computing: With Mathematica looks beyond teaching the syntax and semantics of Mathematica and similar programs, and focuses on why they are necessary tools for anyone who engages in mathematics. It is an essential read for mathematicians, mathematics educators, computer scientists, engineers, scientists, and anyone who wishes to expand their knowledge of mathematics. This volume will also explain how to become an experimental mathematician, and will supply useful information about how to create better proofs.
The text covers material in elementary number theory, calculus, multivariable calculus, introductory linear algebra, and visualization and interactive geometric computation. It is intended for upper-undergraduate students, and as a reference guide for anyone who wishes to learn to use the Mathematica program.
Places primary importance on the mathematics, rather than being a 'how to' manual for making computations
Integrates numerous worked examples and introduces all key programming constructions | 677.169 | 1 |
Aliens From the Planet Nomathus
Students will know the derivation of the quadratic formula, and additionally how and why to use it. With these skills they will solve equations and come up with a fun way to teach the quadratic formula to a class of alien students from the planet Nomathus.
Introduction
At 9 o'clock this morning, as you were walking into your second period
class, a huge silver UFO overheated and crashed onto the PE field!
As
the dust and steam settled, a silver sliding door opened and 3 aliens
from the planet Nomathus crawled out.
While the unsuspecting sixth
graders got changed in the locker rooms, the devious aliens crept down
the ramp to explore the strange new planet they found themselves on.
They made their way to room 217 and stood in the doorway to your
classroom. By the time their UFO cools down enough for them to take off
again, you are going to have the opportunity to teach them a lesson:
The Quadratic Formula. | 677.169 | 1 |
INTERMEDIATE ALGEBRA
FALL 2012
PURPOSE: Intermediate Algebrais the state wide prerequisite
for students who will be taking mathematics courses which will count
towards bachelors degrees and satisfy general education requirements.
A major goal of this course is to increase students' mathematical
fluency.
Homework is the most important part of the course. If you keep up
with the homework you will probably do well. If you do not, you
probably will not do well. The midterms and final exam will cover the
material on the homework. The final exam is the deadline for all late
work.
TENTATIVE TEST DATES:
Midterm 1
Expressions
Sept. 12
Midterm 2
Equations
Oct. 10
Midterm 3
Graphing
Nov. 7
Midterm 4
Exponentials, Logarithms, Etc.
Dec. 5
OFFICE
Dar 114N
OFFICE HOURS
MW 10 - 10:30
TTh 10 - 11:35
PHONE
664 - 2116
e-mail address: [email protected]
url:
Students will need either a scientific or a graphing calculator
for this class.TI 89 or better are not allowed. The final exam is the deadline for late work.
Students are responsible for announcements made in class. | 677.169 | 1 |
ALGEBRA II
Meets - All Year1 Credit
6301ALGEBRA IILevel - HonorsGrades 9-10
Meets - All Year1 Credit
Prerequisite: Geometry
Algebra II briefly reviews the principles taught in Algebra I and further develops these ideas with more advanced topics.Concepts include solving and graphing: equations and inequalities, system of equations and inequalities, polynomials, quadratic equations and some higher degree equations.A study is made of functions (linear, quadratic, absolute value, exponential, logarithmic, and power), and the operation of functions and their composition. Topics also include complex numbers and determinants.Problem solving and practical applications are emphasized.Conics and matrices are also included at Level 1.A graphing calculator is required for this course.
Calendar
June 19, 2013
Metacomet School 4th Grade Promotion Ceremony9:30 AM
Bloomfield High School Graduation - Belding Theater at the Bushnell6:00 PM | 677.169 | 1 |
Casio Takes New Approach to Graphing Calculator for Students
Casio's Prizm fx-CG10 plots graphs over full-color images to help students visualize concepts.
Casio Education has introduced the Prizm fx-CG10, a new concept in educational graphing calculators that aims to impart mathematical concepts in addition to providing standard graphing functions. Using a new tool known as Picture Plot, the Prizm enables users to plot graphs over full-color photographic images, such as an Egyptian pyramid or the jets of an outdoor fountain, as way of relating complex mathematical functions to real-world concepts such as design and engineering.
Casio also offers teachers online training using streaming video and downloadable supplemental activities, as well as a loaner program, which enables interested educators to try the Prizm for 30 days. An application for the program is | 677.169 | 1 |
When 'studying calculus, you should have a good understanding of the following tables of formulas so you can efficiently and correctly solve calculus problems. An introduction to the basic concepts of calculus. The derivative ... The derivative, then takes a type of formula and turns it into another simiilar type of formula. | 677.169 | 1 |
Mathematics
Middle School mathematics classes equip students with the mathematical skills of a competent citizen in today's world. These skills include the ability to model situations mathematically, to estimate and compare magnitudes, to interpret graphs and statistics, to calculate probabilities, to evaluate numerical and spatial conclusions, to solve problems mentally as well as with paper, calculator, and computer, and to communicate effectively in these areas. Finally, while much of the above is exercised in the context of individual work, we have the further goal of fostering the skills and value of doing mathematics cooperatively with others.
Algebra I and Algebra I Honors: A rigorous high school-level first-year algebra course with emphasis on theory and application beyond mechanical processes. Problem solving is integral to both regular and honors level courses.
Geometry Honors: A high school course offered on the middle school campus for students who have completed Algebra I or Algebra I Honors. The study of geometry provides students with the opportunity to develop mathematic reasoning. Reasoning mathematically means developing and testing conjectures through deduction. Teaching students to make conjectures requires a spirit of experimentation and exploration in the classroom. Students will learn how to follow a proof and to determine whether a proof is valid or invalid. Initially, students will learn to write simple proofs and then advance to writing more difficult proofs. Algebra skills will also be integrated throughout each chapter and reinforced within the geometry exercises. | 677.169 | 1 |
This is an instruction
system for a modern course in Trigonometry. It is designed for students who have
successfully completed Beginning, Elementary, and Intermediate Algebra courses.
The instruction emphasizes the Circular Functions. Other topics are developed
from the basic six circular functions.
Every objective
in the course is thoroughly explained and developed. Numerous examples illustrate
every concept and procedure. Student involvement is guaranteed as the presentation
invites the student to work through partial examples. Each unit of material ends
with an exercise specifically designed to evaluate the extent to which the objectives
have been learned and encourage re-study of any skills that were not mastered.
The instruction
is dependent upon reasonable reading skills and conscientious study habits. With
those skills and attitudes in place, the student is assured a successful experience
in learning those concepts associated with Trigonometry. | 677.169 | 1 |
MERLOT Search - category=2513&materialType=Drill%20and%20Practice
A search of MERLOT materialsCopyright 1997-2013 MERLOT. All rights reserved.Tue, 18 Jun 2013 22:26:43 PDTTue, 18 Jun 2013 22:26:43 PDTMERLOT Search - category=2513&materialType=Drill%20and%20Practice
4434Graphing the line y = mx + b
This learning object gives the student the equation y = mx + b and first asks the student to move the line to the correct y-intercept and then rotate for the correct slopeFinding the Domain of a Function
This applet guides the user through the process of finding the domain of a function. Hints and feedback are plentiful and useful. New problems are generated at the click of a button.Exponent Rules
This site generates problems that test students' understanding of exponent rules. Hints and feedback are availableFinding the Domain and Range of a Function
Find the domain and range of a function given its graph.Level of Measurement
This module helps students identify level of measurement by giving them ten exercises in which they must determine whether a variable is being measured at the nominal, ordinal, or interval-ratio level.COW -- Calculus on the Web
This site is devoted to learning mathematics through practice. Many dozens of practice problems are provided in Precalculus, Calculus I - III, Linear Algebra, Number Theory, and Abstract Algebra. The last two subject areas -- referred to as "books" on the site -- are under construction. To each topic within a book (for example, Epsilon and Delta within Calculus I) there is a "module" of approximately 20 to 30 problems. Each module also includes a help page of background material. The modules are interactive to some extent and often provide suggestions when wrong answers are entered.Discrete Math Resources
This site consists of examples, exercises, games, and other learning activities associated with the textbook, Discrete Mathematics: Mathematical Reasoning and Proof with Puzzles, Patterns and Games by Doug Ensley and Winston Crawley. Requires Adobe Flash player.Classroom Activities for Calculus
This is a collection of activities for use in precalculus and single variable calculus. It is prefaced by a brief summary of what I know about group learning and how I use the activities. Many activities are quick combinations of discovery and practice. The statistics gets a bit lengthy, but I thought I'd include it anyway. As far as I recall, my text is only mentioned once and this posting should not be considered a commercial. Use the activities any way you want.Matrix Multiplier
This site contains a tool that allows a user to rapidly compute the product (or other formula) of two matrices.Inference for Means Activity
This activity enables students to learn about confidence intervals and hypothesis tests for a population mean. It focuses on the t-distribution, the assumptions for using it, and graphical displays. The activity also focuses on how to interpretations a confidence interval, a p-value, and a hypothesis test. | 677.169 | 1 |
This
class is open to all homeschooled students in 9th - 12th grades and who have
successfully completed Algebra 2. Academic performance should be average or
above while a passion for math is not required. Assuming you have met the
Algebra 2 requirement and the class is not full, you will be accepted into the
class.
AP
Statistics is not your typical math class and often you will need to think
critically and intuitively to address the statistical issues presented to you.
While this class is neither reading nor writing intensive you will be required
to do some of both. Past students report they spend 1 to 2 hours per day on AP
Statistics.
Why should you take statistics?
Statistics is the most widely applicable
branch of mathematics and is used by more people than any other kind of
math.AP Statistics is a great option
for students headed to a math- or science-related major, and who are looking
for another math course before graduation.
For students not headed into a math- or
science-related major, statistics is a useful and practical topic in today's
society and some argue that these students are better served by taking statistics
than calculus. The course does not depend heavily on advanced mathematical
computation but rather you are asked to use your critical thinking skills to
explain concepts and interpret results. To cement these concepts and assist you
with interpreting results hands-on investigations are used throughout the
course. Technology, such as the graphing calculator and statistical software,
is used to lower the drudgery of computation.
Class Meeting Time: Students do not "meet" at a scheduled
time, but work asynchronously to do their studying within their own
schedule.The Daily Message is posted
prior to midnight EST for the following school day permitting students in the Far East to work on today's assignment, today. Class
assignments for the upcoming two to three weeks are posted online permitting
students to work ahead if needed. Past families have found that I am very
accommodating to student and family travel plans and special events.
Course Format:
AP Statistics is a college level introductory
course in statistics in which students will learn to collect, organize,
analyze, and interpret data. These broad conceptual themes are:
Exploring
Data
Producing
Models Using Probability and Simulation
3.Experimental Design
4.Statistical Inference
Our class day begins with a Daily Message posting which expounds on the
day's statistical concepts. On a daily basis we read a few pages from our text
and apply these new concepts to problems. Students are able to daily test their
knowledge through multiple choice questions. Throughout the course we have
hands-on data collection assignments where we learn to apply what we are
learning to real data. These assignments never require the student to survey
neighbors or strangers and can be done from within the home. At the end of
every chapter the student has a multiple choice exam and a Free-Response
component that develops their ability to "pull all the pieces together."
Students are encouraged to ask questions of their peers and of me on our
communication board. The students utilize the online discussion boards to
interact with classmates, to post any questions they have from the reading material
and homework assignments, to answer classmates questions and most importantly
to discuss the interpretation of ourresults. The class operates asynchronously and I am available for live
chats on an as-needed basis.
Assessment:Student assessment will consist of a combination of
class participation, homework, hands-on activities, multiple choice and free
response exams. The exams are graded using a scoring guideline in the same
manner as the AP exam is scored. My experience with designing scoring rubrics
and assessing student responses will help me ensure that the students taking
this course are well-prepared for a good score on the AP® Statistics exam next
spring!
3.2007
& 2002 AP Stat College Board Released exam. (These books are purchased in
bulk by Mrs. Matheny and then repurchased by the students in March 2013, $10)
Instructor Qualifications:
I earned a BS and MS in Ceramic Engineering
from The Ohio State University and an MBA from ClarkUniversity.
Prior to homeschooling , I worked full-time for twenty
years in industry as a Research Engineer and later as a Manager of Engineering.
In addition, I hold five US Patents. During these years I found statistical
methods to be a very valuable tool and an integral part of my work life. While
in Worcester, MA,
I was an adjunct professor for several years teaching both Statistics, and
Production & Operations Management at both AssumptionCollege and AnnaMariaCollege. For the past fifteen years I
have been a home schooling mom to my two sons; one is now in college and the
other is in high school. This will be my fifth year teaching AP Statistics
on-line through PA Homeschoolers. I'm looking forward to this coming year! | 677.169 | 1 |
This textbook, aimed at undergraduate mathematicians, covers the main topics in number theory; that is properties of ordinary numbers and fractions. Many modern aspects are covered, including (briefly) the latest work on Fermat's last theorem. Both elementary and more advanced topics are included, with large problem sections and hints on their solution. The current reprinting of this edition not only includes some minor corrections but also an extra 50 pages containing the latest information on some conjectures, some new facts (for instance about Mersenne primes), new proofs and problems as well as a number of minor
corrections.
Readership: Third year and postgraduate students taking a course in number theory.
H. E. Rose, Lecturer in Mathematics, University of Bristol
"It is of interest both to students and teachers working in this field." - EMS Newsletter, No. 21, 1996
"An extremely demanding text for undergraduates, but well-suited for a mathematician who wants to learn some number theory." - American Mathematical | 677.169 | 1 |
Category theory is a branch of mathematics that emerged in the 1950s to understand how the different areas of mathematics relate to each other. Today, its influence pervades nearly all of mathematics, in addition to being an important area of study in its own right. This course will cover the basic concepts of category theory, with an emphasis on intuition and examples. | 677.169 | 1 |
MATH
►Rick Geiser
►Jen Lawrence
►Matt Zuercher
INTEGRATED MATH II
This course is designed for students who took Integrated Math I. Integrated II completes the second year class format.
ALGEBRA I Algebra I will provide instruction in the following topics: quadratic equations, linear equations, inequalities, polynomials, factoring, functions and graphs, and coordinate geometry. Algebra I is the first course in the college preparatory program. A scientific calculator (TI 30XIIS), not graphing calculator, is required for this course.
GEOMETRY
The course embodies the objectives of geometry and the logic upon which it is based. Through definitions, postulates, and theorems, the student will learn direct and indirect methods of finding lengths, angle measures, perimeters, areas, and volumes of geometric figures. Constructions and projects are offered to enhance concepts. Since the course stresses deductive reasoning, it is highly recommended for college preparatory students. A scientific calculator (TI 30XIIS), not a graphing calculator, is required for this course.
ALGEBRA II
This is the third course in the college preparatory math program. In addition to a more detailed study of Algebra I topics, Algebra II introduces matrices, radicals, complex numbers and quadratic relations and systems. A scientific calculator is required for this course.
TRIGONOMETRY
Trigonometry is the study of the sine, cosine, tangent, and their reciprocal functions in relation to right triangles. Students will investigate the properties of the trig functions and their inverses, study their graphs and transformations, solve trigonometric equations, and verify/prove identities. Students will also learn techniques to solve both right and non-right triangles. The course is a prerequisite or co-requisite for Pre-Calculus. Students are encouraged to take the course while also taking Algebra II or in the fall while taking Pre-Calculus. A graphing calculator is highly suggested.
PRE-CALCULUS
This is the 4th course in the college preparatory math program. This course offers a detailed study of circular and trigonometric functions, matrices, theory of education, Polar coordinates, complex numbers, vectors, sequences and series, exponential and logorithmic functions, and intro to calculus. Graphing calculator is strongly suggested!
ADVANCED PLACEMENT CALCULUS AB (Calculus AB)
This is the fifth course in the college preparatory math program. Topics include limits and their properties, differentiation and its applications, integration, exponential & logarithmic functions, integration techniques & applications, parametric equations, etc. Graphing calculator is strongly suggested! Students may take the AP exam in May with the possibility of testing out of college math classes. The cost is approximately $89.00.
***AP Calculus is offered on a five point grade point average system, requiring the taking of the AP Calculus exam in May. The option of taking this course on a four point grade point system eliminates the AP Calculus exam requirement.
TRANSITIONS
Transitions to college mathematics is designed to be a mathematics course for seniors who will need to take college courses in mathematics and have completed Algebra I, Geometry, and Algebra II/Algebra II Basic. A commitment to do many problems on a daily basis is essential. Algebra and Geometry concepts are presented in concrete problem settings, approached arithmetically through numerical computation. A scientific calculator is required for this course.
BRIDGING THE GAP TO COLLEGE MATH
Instead of learning in the traditional classroom, students are pre-tested (COMPASS or ACT) and
placed into the course at the level that is right for them. From there, students work through a series of online modules, progressing at their own pace, and practicing skills in class and at home through a combination of online tools and instructor support. This course is designed to help students identify the areas they need to strengthen and develop their skills so they are ready for college algebra and equipped for success in college. Bridging the Gap to College Math is based on the concept of "mastery learning", which involves practicing a skill until it is learned and can be demonstrated. When the student is ready, he/she takes a post-test. With a score of at least 85%, the student demonstrates mastery competence and is ready to progress to the next module. Instructors are available during class time to answer questions and guide the students. Columbus State Community College is our partner for this course. If a student attends CSCC upon high school graduation, they will earn placement into the appropriate credit bearing math course instead of a non-credit remedial course. | 677.169 | 1 |
@inbook {MATHEDUC.05865082,
author = {K\'antor, T\"unde},
title = {J. K\"ursch\'ak a world-famous scholar teacher (1864-1933).},
year = {2010},
booktitle = {Problem solving in mathematics education. Proceedings of the 11th ProMath conference, Budapest, Hungary, September 3--5, 2009},
pages = {76-86},
publisher = {Budapest: Univ. Budapest, Mathematics Teaching and Education Center},
abstract = {},
msc2010 = {A30xx},
identifier = {2011b.00015},
} | 677.169 | 1 |
Were it not for the calculus, mathematicians would have no way to describe the acceleration of a motorcycle or the effect of gravity on thrown balls and distant planets, or to prove that a man could cross a room and eventually touch the opposite wall. Just how calculus makes these things...
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A solid foundation of basic math skills is essential for early success in math. Children who can connect their understanding of math to the world around them will be ready for the challenges of mathematics as they advance to more complex topics. The games and puzzles in this workbook are designed...
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Success in math includes mastery of geometry skills and requires children to make connections between the real world and geometry concepts in order to solve problems. Successful problem solvers will be ready for the challenges of mathematics as they advance to more complex topics. The activities in this workbook are designed...
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Poetry of the Universe
Written by Robert Osserman
Format: Trade Paperback
ISBN: 9780385474290
Our Price: $15.00
One of the delights of life is the discovery and rediscovery of patterns of order and beauty in nature—designs revealed by slicing through a head of cabbage or an orange, the forms of shells and butterfly wings. These images are awesome not just for their beauty alone, but because they suggest...
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This enlightening and stimulating approach to mathematics will entertain lay readers while improving their mathematical literacy. We all learned that the ratio of the circumference of a circle to its diameter is called pi and that the value of this algebraic symbol is roughly 3.14. What we weren't told, though, is...
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If you need to know it, it's in this book.Cracking the AP Calculus AB and BC Exams, 2013 Edition has been optimized for e-reader viewing with cross-linked questions, answers, and explanations, and includes:
Success in math requires children to make connections between the real world and math concepts in order to solve problems. Successful problem solvers will be ready for the challenges of mathematics as they advance to more complex topics. The activities in this workbook are designed to help children see how math...
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Introduction to MapleMaple is a very powerful Computer Algebra system that can do many of the calculations that you might encounter in many branches of mathematics, science and engineering. We'll look at some of its capabilities. Maple has two modes: "Document Mode", which can be used to make fancy-looking documents, and "Worksheet Mode", which is what we'll use. So when you have a choice of Worksheet or Document, choose Worksheet. You can also make Worksheet the default format for new files under Tools, Options, Interface.We're looking at a Maple worksheet. Worksheets can have text, such as this, as well as Maple input and Maple output. Here is some Maple input and output.The multiplication sign in Maple is the asterisk *. The division sign is /. For powers we use ^5HRiQ2JFEiM0SSVtc3VwR0YkNiUtSSNtaUdGJDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnLUYjNiNGSi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRjM2LVEiO0YnRi9GNi9GOkZmbkY7Rj1GP0ZBRkNGUC9GSVEsMC4yNzc3Nzc4ZW1GJw==LCYiIiQiIiIqJiIiJUYkKUkieEc2IkYmRiRGJA==This input was in "2D input". Some of the older material posted online uses "Maple notation". In the next example we input an expression from the menu on the left hand 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IyIiIiIiJA==When you click on a Maple input region and press Enter, Maple performs whatever command you gave it, prints whatever it will print, and goes on to the next region (or makes a new input region if there's no next one). You can also insert a new input region in the middle of your worksheet by clicking on [> on the tool bar or a new text region by clicking on the T beside it. 3+5;IiIpNote the ";" at the end of the command. After you press Enter, Maple computes and prints the result and gives you another promptLVEiOkYnRi9GNkY5RjtGPUY/RkFGQy9GRlEsMC4yNzc3Nzc4ZW1GJy9GSUZRThis time I used ":" instead of ";". This tells Maple to compute the result, but not print itM0YRiw2JFEiNEYnRi8=IiM5Maple uses the standard algebraic precedence rules , so this is interpreted as 2+(3*4), not (2+3)*4. Maple can act as a calculator, but there are several key differences. The following is an integer that would be too large for your calculator to 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Maple writes fractions as fractions (automatically reducing them to lowest terms), without resorting to decimal approximationsmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjNGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2Iy1GLzYkUSI5w==IyIiIiIiJA==If you do want to see this as a decimal, you can use the "evalf" command. As with almost every Maple command, the input to "evalf" is enclosed in parenthesesidGQQ==JCIrTExMTEwhIzU=The default (what Maple does unless otherwise specified) is to use 10 significant digits. This can be changed, using a variable called "Digits". Let's see this number to 25 digits instead of 10MyNURiM2Iy1JI21uR0YkNiRRIjFGJy9GM1Enbm9ybWFsRictRiM2Iy1GQDYkUSIzRidGQy8lLmxpbmV0aGlja25lc3NHRkIvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGTi8lKWJldmVsbGVkR1EmZmFsc2VGJ0ZDLUkjbW9HRiQ2LVEiO0YnRkMvJSZmZW5jZUdGUTExMTExMTExMTExMJCEjRA==Maple is case-sensitive. "Digits" is not the same as "digits" or "DIGITS". Those wouldn't affect the number of digits Maple uses.":=" is the assignment sign in Maple. It means "assign the value on the right to the variable on the left". This is different from "=" which makes an equation.Once "Digits" has been set, Maple uses this setting every time it computes a decimal result until you change "Digits" again. If you want to change the number of digits for one "evalf" command only, you can specify this as a second input to "evalf". The inputs are separated by a commaictSSNtb0dGJDYtUSIsRidGQS8lJmZlbmNlR0ZRLyUqc2VwYXJhdG9yR0YxLy+NiRRIzQwRidGQUZBJCJJTExMTExMTExMTExMTExMTExMTEwhI1MIMxMEM1Maple can do lots of symbolic calculations. For example, it knows thisiNEYnRjIvksvJSliZXZlbGxlZEdGMUYyLCQqJiMiIiIiIiNGJSlGJkYkRiVGJQ==It doesn't have a symbolic value for the next one, so it just returns unevaluatedjMzFGJ0YyLLyUpYmV2ZWxsZWRHRjFGMg==LUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJComIyIiIiIjSkYsSSNQaUdGJUYsRiw=Again, if you want a numerical value, you can get one with "evalf". You can use "%" to refer to the previous maple resultGLDYlUSIlRidGL0YyL0YzUSdub3JtYWxGJw==JCI6Mi8neXhAVigpPktvNjUhI0QRzaW5GJy9GMFEmZmFsc2VGJy9GM1Enbm9ybWFsRictRjY2JC1GIzYjLUkmbWZyYWNHRiQ2KC1GLDYlUSNQaUYnRj1GPy1GIzYjLUkjbW5HRiQ2JFEjMzFGJ0Y/WLyUpYmV2ZWxsZWRHRj5GP0Y/LUkjbW9HRiQ2LVEiO0YnRj8vJSZmZW5jZUdGPi8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0Y+LyUqc3ltbWV0cmljR0Y+LyUobGFyZ2VvcEdGPi8lLm1vdmFibGVsaW1pdHNHRj4vJSdhY2NlbnRHRj4Mi8neXhAVigpPktvNjUhI0Q=Maple can do almost any computational task that might arise in undergraduate mathematics. It doesn't do proofs, but it can be used to help with proofs by exploring what might or might not be true.Maple is incredibly powerful, but to learn to use it effectively takes some effort. One thing to remember: Maple has absolutely no intelligence. It will try to do exactly what you tell it to do, no more and no less.Unfortunately, what you tell it to do is not always the same as what you thought you were telling it to do, or what you wanted it to do. It has no idea of what you want to do, or why you want to do it. It can't read your mind. So to get it to do something, you have to know what command would make it do that, and how to use that command. This is a common theme in all programming languages and software packages. Maple has thousands of functions and commands. Probably no one person knows all the details of all of them. Fortunately, Maple has an extensive help system. To get help on a particular command, you can enter a question mark followed by the name of the command9HRiQ2LVEiPwwLjExMTExMTFlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2JVEmZXZhbGZGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljOr you can use the Table of Contents, or Topic Search or Text Search from the Help menu.Roots of Functions, Differentiation and Plotting: Part IMany problems of scientific interest involve finding the root or roots of a function. That is, finding the value or values of x for which f(x) = 0 where f is a given function. In real applications, it is unlikely that the Example 1 Find the roots of f(x) = x^5 - x^3 + 2*x^2 + 1First, let's plot the function to get an idea of how many roots there are and where they are 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It looks like there is one real root somewhere near x = -1.5. Let's suppose that this is the root of interest to our application problem and see how we can get a more accurate value using the solve command. First, let's try it out on a quadratic equationLS1JJW1zdXBHRiQ2JS1GLDYlUSJ4RidGL0YyLUYjNiMtSSNtbkdGJDYkUSIyKCZtaW51cztRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRmpuLUZDNiRRIjNGJ0ZGLUZMNi1RIn5GJ0ZGRk9GUkZURlZGWEZaRmZuL0ZpblEmMC4wZW1GJy9GXG9GZG9GPS1GTDYtUSIrRidGRkZPRlJGVEZWRlhGWkZmbkZobkZbb0ZCLUZMNi1RIj1GJ0ZGRk9GUkZURlZGWEZaRmZuL0ZpblEsMC4yNzc3Nzc4ZW1GJy9GXG9GXXAtRkM2JEZKRkYtRkw2LVEiLEYnRkZGTy9GU0YxRlRGVkZYRlpGZm5GY28vRlxvUSwwLjMzMzMzMzNlbUYnRj1GRi1GTDYtUSI7RidGRkZPRmRwRlRGVkZYRlpGZm5GY29GXnA=NiQiIiMiIiILi1JJW1zdXBHRiQ2JS1GLDYlUSJ4RidGL0YyLUYjNiMtSSNtbkdGJDYkUSI1In5HRmpuLUZMNi1RKiZ1bWludXMwO0YnRkZGT0ZSRlRGVkZYRlpGZm4vRmluUSwwLjIyMjIyMjJlbUYnL0Zcb0Zhb0ZLLUY7NiVGPS1GIzYjLUZDNiRRIjNGJ0ZGRkhGSy1GTDYtUSIrRidGRkZPRlJGVEZWRlhGWkZmbkZgb0Ziby1GQzYkUSIyRidGRkZLLUY7NiVGPS1GIzYjRl1wRkhGam8tRkM2JFEiMUYnRkZGRi1GTDYtUSI7RidGRkZPL0ZTRjFGVEZWRlhGWkZmbkZobi9GXG9RLDAuMjc3Nzc3OGVtRicMaple cannot make progress on this problem analytically, so leaves the five roots unsolved in an array. This array is assigned to a variable below. Then we look through the roots, evaluating them until we find the real 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Polynomials have a lot of structure that general functions do not have. For example, Maple knows that a fifth order polynomial has five (possibly repeated) roots and has built-in methods to evaluate them accurately. For general functions, we can use the fslove command to find roots in given intervals. QyQ+SSJmRzYiLCoqJEkieEdGJSIiJiIiIiokRigiIiQhIiIqJEYoIiIjRi9GKkYqRio=LCoqJEkieEc2IiIiJiIiIiokRiQiIiQhIiIqJEYkIiIjRixGJ0YnQyQtSSdmc29sdmVHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JC9JImZHRigiIiEvSSJ4R0YoOyEiI0YsIiIiJCErIT1uXmUiISIqMaple objects introduced in this lesson: ;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
:
+
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Digits sin Pi plot solve fsolve | 677.169 | 1 |
I am somehow missing what are your goals - perhaps introduction to proofs, exposition to higher mathematics, or indicating what does it involve to do research?
Nevertheless, you may be interested in the book The Enjoyment of Mathematics: Selections from Mathematics for the Amateur by H. Rademacher and O. Toeplitz if you can get hold of it (very unfortunately, it is out of print, but the table of contents can be checked on amazon). It contains short pieces not requiring anything beyond high school math, yet many of them are full of elegance and joyful to read. As the students certainly should be able to get through the chapters independently, covering few of them can provide a good start. | 677.169 | 1 |
Mathematics Textbooks
This textbook provides a comprehensive collection of examples of the topics of iGeometrical vectors, Vector spaces and Linear maps.
The reader will obtain the necessary routine of handling these topics by working through these examples.
This textbook provides a comprehensive collection of examples of the topics of Eigenvalue problems, Systems of differential equations and Euclidean vector spaces.
The reader will obtain the necessary routine of handling these topics by working through these examples.
This textbook provides a comprehensive collection of examples of the topics of Quadratic equations in two and three variables, including Conic sections, Surfaces of conic sections, Rectilinear generators, Second order cones and Quadratic forms.
The reader will obtain the necessary routine of handling these topics by working through these examples. | 677.169 | 1 |
Abstract
The solution of linear ordinary differential equations (ODEs) is commonly taught in first year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognising what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to tables of solutions, is an important skill for students to carry with them to advanced studies in mathematics. In this study we describe a teaching and learning strategy that replaces the traditional algorithmic, transmission presentation style for solving ODEs with a constructive, discovery based approach where students employ their existing skills as a framework for constructing the solutions of first and second order linear ODEs. We elaborate on how the strategy was implemented and discuss the resulting impact on a first year undergraduate class. Finally we propose further improvements to the strategy as well as suggesting other topics which could be taught in a similar an electronic version of an article published in [International Journal of Mathematical Education in Science and Technology]. [International Journal of Mathematical Education in Science and Technology] is available online at informaworldTM with the open URL | 677.169 | 1 |
Get the Math
Special Collection
Get the Math is a multimedia project about algebra in the real world. See how professionals working in fashion, videogame design, and music production use algebraic thinking. Then take on interactive challenges related to those careers.
Get the Math is funded by Next Generation Learning Challenges and the Moody's Foundation
Using segments and web interactives from Get the Math, this self-paced lesson helps students see how Algebra I can be applied in basketball, challenging them to use algebraic concepts and reasoning to calculate the perfect free throw shot.
Using segments and web interactives from Get the Math, this lesson helps students see how Algebra I can be applied to the world of fashion, challenging them to use algebraic concepts and reasoning to modify garments and meet target price points.
Using segments and web interactives from Get the Math, this lesson helps students see how Algebra I can be applied in the music world, challenging them to use algebraic concepts and reasoning to calculate the tempos of different music samples.
Using video segments and web interactives from Get the Math, this lesson helps students see how Algebra I can be applied in the world of videogame design and challenges them to use algebraic concepts and reasoning to plot the linear paths of items in a videogame.
7-10
Self-paced Lesson
Major funding for Teachers' Domain was provided by the National Science Foundation. | 677.169 | 1 |
Book DescriptionMore About the Author
Product Description
Review
'For researchers and more mathematically oriented readers, this book is a treasure trove of algorithms difficult or impossible to find elsewhere.' Mathematical Reviews
Book Description
This comprehensive reference provides a solid theoretical foundation for applied mathematicians, scientists, and engineers who wish to understand the fundamental computations that support a wide variety of practical applications. Suitable for graduate teaching, it includes problems, exercises and an extensive bibliography. A solutions manual is also available for instructors.
There are several books on computer arithmetic (examples of good ones are Koren; and Ercegovac & Lang... and this new one). The particularity of this one is an in-depth, detailed presentation of the various number systems that are and/or may become interesting for computer arithmetic. I especially appreciated the rigor of the presentation. The arithmetic algorithms are too often presented in a rough way: it is a pleasure to see a good, solid analysis of them. Both authors of this book are highly respected in the computer arithmetic scientific community. | 677.169 | 1 |
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Starting at $5MATLAB for Engineers
MATLAB for Engineers
Summary
With a hands-on approach and focus on problem solving, this introduction to Matlab uses examples drawn from a range of engineering disciplines to demonstrate Matlabrs"s applications to a broad variety of problems.Encourages readers to type in examples as they go for immediate application of techniques presented. Includes numerous broad-based examples embedded in the text, practice exercises with solutions, and hints related to commonly encountered problems. Introduces m-files early in the text to make it easier for readers to save their work and develop a consistent programming strategy.For those interested in learning Matlab. | 677.169 | 1 |
GRAPHS for IIT-JEE aspirants : Tutorial sheet-{II}
Description My dear students, In a wide range of subjects , graphs play an important role in data interpretation and analysis, and serve as a tool for understanding the data in pictorial form.
In IIT-JEE/AIEEE syllabus, graphs are not explicitly mentioned but from the track of past 30-32 years of IIT question papers it can be traced out that graphs play a vital role in answering and interpretation of the analytical and tricky questions.Most of the time JEE aspirants puzzle in between the analytical and graphical approach, few gets depressed while other put their extra time in commanding the graphs.The most important fact about graphs for engineering entrances is the basic understanding of the functions which are mentioned in the syllabus.
Following important facts about graphs should be kept in mind while preparing the subject of mathematics for engineering entrance examinations.
Some of the questions which are based on graphs can also be solved analytically but demands more calculations and extra time.Following basic graphs and their elementary transformations must be prepared exhaustively for their graphical interpretations: | 677.169 | 1 |
Product Description
From the Back Cover
Get up to speed quickly with worked-out problems
Understand the how and the why of trigonometry
Confused by cosines? Perplexed by polynomials? Don't worry! This friendly guide takes the torture out of trigonometry by explaining the basics in plain English, offering lots of easy-to-grasp examples, and adding a dash of humor and fun. You'll see how trig applies to everyday life — and why it's important to a wide variety of careers.
Discover how to:
Solve equations
Graph functions
Figure out formulas
Identify identities
Solve practical problems with trig
About the Author
Mary Jane Sterling, the author of the highly successful Algebra For Dummies, has taught mathematics at Bradley University in Peoria for more than 20 years.
4.0 out of 5 starsExcellent Book But Could Have Used a Proofreader Or TwoDec 19 2007
By Thomas P. Connolly - Published on Amazon.com
Format:Paperback
I was in a bit of a quandary as to how to rate this book. I bought the book and the companion "Trigonometry Workbook for Dummies" to refresh my trig skills, long rusted after nearly 50 years of little use. Both books are really quite good although the workbook could be more comprehensive. The big problem with the workbook, and to a lesser extent with the "Trigonometry for Dummies" book, is the large number of errors in the book. One works out a very complicated identity problem only to find that the stated problem is different from the problem answered due to typographical errors. I don't think I went seven pages in the workbook without finding an error. Most of the errors were changed minus or plus signs. This made maintaining confidence in the book very difficult.
One would think that a big publisher like Wiley would employ competent proofreaders. I would also expect them to have an errata sheet somewhere on their web page. But, nooo, nothing helpful there at all except a glossary they forgot to put in this book.
Overall, both books were very helpful, with the exception of not having a lot of confidence that the answer to the problem I was trying to solve would be correct.
41 of 41 people found the following review helpful
5.0 out of 5 starsBest book for any Trigonometry student who is strugglingJun 4 2006
By Judge - Published on Amazon.com
Format:Paperback
I bought this book and two others at the beginning of my college Trig class. This book is the only one that I used. It was the best investment for the class that I could have made. Trigonometry for Dummies provided all the fundamental concepts that were covered in college Trig and explained them so that even a non-math major like myself could understand. I would highly recommend this book for anyone struggling with college Trigonmetry, or if you are looking for a great book to refresh your skills.
52 of 56 people found the following review helpful
5.0 out of 5 starsEXCELLENT TRIG BOOK!!April 17 2005
By REVIEWER - Published on Amazon.com
Format:Paperback
I have been out of school for 30+ yrs. and wanted to learn trig for graphics programming. Of all the trig books I have looked at, this is by far the best!!. Highly recommended!! | 677.169 | 1 |
Joseph Malkevitch Department of Mathematics York College (CUNY) Jamaica, New York 11451
Graph theory provides a powerful tool for constructing mathematical models in a variety of situations. Given "objects" one can represent them by dots and the relationship between the objects can be indicated using straight or curved line segments. Dots might represent people, street corners, or books. Line segments could indicate that the people are friends, street corners are connected by a street, or that the books have the same author. | 677.169 | 1 |
MicrosoftInternetExplorer4 Intended for a 2-semester sequence of ElementaryandIntermediate Algebrawhere students get a solid foundation in algebra, including exposure to functions, which prepares them for success in College Algebra or their next math course. Operations on Real Numbers and Algebraic Expressions; Equations and Inequalities in One Variable; Introduction to Graphing and Equations of Lines; Systems of Linear Equations and Inequalities; Exponents and Polynomials; Factoring Polynomials; Rational Expressions ... MOREand Equations; Graphs, Relations, and Functions; Radicals and Rational Exponents; Quadratic Equations and Functions; Exponential and Logarithmic Functions; Conics; Sequences, Series, and The Binomial Theorem; Review of Fractions, Decimals, and Percents; Division of Polynomials; Synthetic Division; The Library of Functions; Geometry; More on Systems of Equations For all readers interested in elementary and intermediate algebra. Intended for a 2-semester sequence of Elementary and Intermediate Algebra where students get a solid foundation in algebra, including exposure to functions, which prepares them for success in College Algebra or their next math course. | 677.169 | 1 |
Combinatorial Introduction To Topology (94 Edition)
by Michael Henle Publisher Comments
Excellent text for upper-level undergraduate and graduate students shows how geometric and algebraic ideas met and grew together into an important branch of mathematics. Lucid coverage of vector fields, surfaces, homology of complexes, much more. Some... (read more)
College Algebra (5TH 11 Edition)
by Mark Dugopolski Publisher Comments
This package consists of the textbook plus an access kit for MyMathLab/MyStatLab. Dugopolski's College Algebra, Fifth Edition gives readers the essential strategies to help them develop the comprehension and confidence they need to be... (read more)
Linear Algebra With Applications (6TH 02 - Old Edition)
by Steven J. Leon Publisher Comments
This thorough and accessible book from one of the leading figures in the field of linear algebra provides readers with both a challenging and broad understanding of linear algebra. The author infuses key concepts with their modern practical... (read more)
Testing Structural Equation Models (93 Edition)
by Kenneth A. Bollen Synopsis
What is the role of fit measures when respecifying a model? Should the means of the sampling distributions of a fit index be unrelated to the size of the sample? Is it better to estimate the statistical power of the chi-square test than to turn to fit... (read more)
Statistical Inference (2ND 02 Edition)
by George Casella Publisher Comments
This book builds theoretical statistics from the first principles of probability theory. Starting from the basics of probability, the authors develop the theory of statistical inference using techniques, definitions, and concepts that are statistical and... (read more)
Glencoe Mathematics Geometry (04 Edition)
by Cindy J. (ed.) Boyd Publisher Comments
A flexible program with the solid content students need Glencoe Geometry is the leading geometry program on the market. Algebra and applications are embedded throughout the program and an introduction to geometry proofs begins in Chapter 2.... (read more)
Numerical Analysis -study Guide (9TH 11 Edition)
by Richard L. Burden Publisher Comments
The Student Solutions Manual and Study Guide contains worked-out solutions to selected exercises from the text. The solved exercises cover all of the techniques discussed in the text, and include step-by-step instruction on working through the algorithms.... (read more)
Mathematical View of Our World - With CD (07 Edition)
by Harold Parks Publisher Comments
Harness the power of mathematics in school and your future career with A MATHEMATICAL VIEW OF OUR WORLD. This liberal arts textbook helps you see the beauty and power of mathematics as it is applied to the world around you. You will recognize the... (read more)
Numerical Methods With Matlab (00 Edition)
by Gerald Recktenwald Publisher Comments
This book is an introduction to MATLAB and an introduction to numerical methods. It is written for students of engineering, applied mathematics, and science. The primary objective of numerical methods is to obtain approximate solutions to problems that | 677.169 | 1 |
Work at the biology bench requires an ever-increasing knowledge of mathematical methods and formulae. In Lab Math, Dany Spencer Adams has compiled the most common mathematical concepts and methods in molecular biology, and provided clear, straightforward guidance on their application to research investigations. Subjects range from basics such as scientific notation and measuring and making solutions, to more complex activities like quantifying and designing nucleic acids and analyzing protein activity. Tips on how to present mathematical data and statistical analysis are included. A reference section features useful tables, conversion charts and "plug and chug" equations for experimental procedures. This volume is an excellent, structured source of information that in many laboratories is often scattered and informally organized.
"This is a practical text for the lab. It covers the basics about numbers and generic types of measurements, numbers used in chemistry, calibration and the use of lab equipment, methods and short cuts for making solutions, methods used in molecular biology, an introduction to statistics and reports and the communication of numerical data, and reference tables and equations. The book is spiral–bound."
—PBS Teacher Source
"This volume is a handy reference for anyone who has kept equations and reagent recipe calculations plastered in strategic locations around their laboratory. Seasoned bench researchers will spend less time coaching collaborators and students stalled over elusive calculation details. Its tone is that of a clear and patient teacher who carefully explains essential mathematical details so almost anyone can understand how and why the calculations are done....Lab Math will certainly save time researchers might otherwise spend explaining how to find reference tables, make measurements, do laboratory calculations, make solutions, work with proteins and nucleotide calculations, or perform basic statistics to undergraduates, graduate students, or visiting fellows."
—The Quarterly Review of Biology | 677.169 | 1 |
Mathematics is the foundation of the sciences and is at the core of a liberal arts education. Many great ideas in human history are mathematical in nature or are easily understood by viewing them mathematically. The idea of infinity was first explained by mathematicians, for example, although originated by philosophers and theologians. While mathematics has practical applications to many academic disciplines, including business, computer science, psychology, political science, music, chemistry and physics, most mathematicians do not study mathematics because it is useful. Instead, they study mathematics for the same reason that other people study art, music or literature – because it interests them.
The math major
Berry's broad-based mathematics major is designed to prepare you for graduate study or a professional career. You also can earn a degree to teach mathematics in grades 6-12. In your first two years as a math major you'll get a solid foundation of calculus, differential equations and linear algebra, as well as an introduction to proof. Then you'll study abstract algebra, real and complex analysis, and other electives. Faculty members also teach "special topics" courses. Subjects that have been offered or are under consideration include topology, combinatorics, knot theory, differential geometry, chaos theory, fractal geometry, graph theory and functional analysis. In addition, you'll have the opportunity to take directed-readings courses in areas that are of particular interest to you. Students have studied partial differential equations, number theory and topology. They also have prepared to take the mathematics GRE subject test and the first actuarial exam.
Students who are declaring a major in mathematics should use the documents to the right of the screen to work with their advisor to build an appropriate plan of study. The information represents tentative degree plans for students majoring in mathematics. It presupposes that the students decide to be mathematics majors at the beginning of their academic careers.
Working with faculty members on research projects. Recent subject areas have included number theory, dynamical systems, geometry and complex analysis.
Working in the mathematics tutoring lab, earning extra money as you explain mathematics to others.
Helping to plan and implement regional mathematics competitions for middle-school and high-school students.
Joining mathematics professional organizations and honor societies, including a chapter of the Kappa Mu Epsilon mathematics honor society and a student chapter of the Mathematical Association of America.
Joining the Georgia Council of Teachers of Mathematics, if you are a mathematics-education major.
Attending annual professional meetings with members of the faculty.
Scholarships are available
Outstanding upper-class students are eligible for special mathematics scholarships, including the:
Barton Mathematics Award.
Hubert McCaleb Memorial Scholarship.
Mary Alta Sproull Scholarship.
The faculty
Berry College's mathematics faculty members have a diverse range of teaching and research interests. In addition, they simply enjoy working with students – inside and outside of the classroom. You'll find that it is common to see students talking with their professors. You'll also discover that there is a real sense of community among the mathematics faculty and students.
Graduate study
Berry College mathematics students have gone on to graduate school at such places as Duke University, the University of Virginia, the University of North Carolina at Chapel Hill, Georgia Tech, Georgia State, the University of Georgia, Auburn University, Syracuse University, Tulane, Clemson and Harvard. | 677.169 | 1 |
I hate math and am trying to get ready for Culinary School in March so I have been reading everything I can get my hands on to help. This is a very simple book, with easy to understand examples.
Algebra (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)
Editorial review
Reviewed by Jason Schorn "j_schorn", (USA)
are complete, challenging and manageable. Enjoy!
Reviewed by sowmya, (Sunnyvale,CA,USA)
s of the same concepts given in the book.Not at all recommended.Better buy a Fraleigh or Herstein or Thomas Hungerford even if your teacher recommends this one.
Reviewed by a reader
becomes clear after one needs to use these tools in other areas.If you are new to the subject, however, the texts by Dummit and Foote or Fraleigh, e.g., are more appropriate.
Reviewed by a reader, (USA)
This text is designed for beginning graduate students. The book includes all the basic parts of algebra any mathematician should know. The presentation and proofs are clear and easy to follow. People with no prior exposure to abstract alg
Calculus and Pizza: A Math Cookbook for the Hungry Mind
Editorial review
Reviewed by Alec "Call me Alex" Singer, (Jupiter)
once you have those down, reading any normal calculus text will be a breeze.The book is also very poetic. Pickover is a great writer, besides being a great mathematician.
Reviewed by S. A. Corning, (Gurnee, IL USA)
This is a great book on many levels. The basics of Calculus are clearly communicated. There are lots of interesting examples, and problems to solve. The story of the pizza parlor involves great imagery, and fascinating characters. Plus th
Calculus is very important today in many branches of science, economics, and other fields. I am a high school calculus teacher and will be advising all my students to get this book in the fall. It covers all the essential calculus materia | 677.169 | 1 |
Help with Algebra on Growing-Stars
The understanding of the possibilities and limitations in the use of technology (such as program-Derive and Cabri-Geometry) encourage the emergence of pedagogic control and cognitive activity of students. This is considered as an important point to develop students' ability in research, related to why and how they should be use a particular technology such as microworlds and computer algebra systems (CAS). The most important step of thinking visually is a move to establish the framework of hypotheses about possible ways of solving the problem with the analysis and forecasting of feasibility outcomes. The second component is to develop a theory of mathematical creativity.
Help with Algebra
Part of mathematics that is widely used for this purpose is algebra. But algebra is often considered as a difficult subject for most people, so learning this knowledge in a comfortable and attractive way will help students. Help with algebra on growing-stars is a site which emphasizes the quality of education with one-to-one tutoring method. Here, students will not only feel comfortable to learn, but also will be able to discuss algebra. You can find that learning algebra is no longer hard, they will make algebra as easy and fun subject for you. | 677.169 | 1 |
Speakers to access the audio of the text.
A printer for the worksheets
A notebook or binder for notes.
Materials to be ordered via the DLD
The DLD Registrar may order the following materials via the DLD upon registering the student:
No additional materials required for this course.
Description
In Geometry 1 students will be introduced to the building blocks of Geometry including lines, planes, points, angles, triangles, and some Euclidean constructions. Students will be introduced to the basic processes and elements of geometric reasoning and logic including conjectures, inductive reasoning, deductive reasoning, theorems, conditionals and biconditionals. Students will apply properties, postulates and theorems find missing measures, measures of similar figures, and for direct and indirect proof proofs. | 677.169 | 1 |
Student Learning Profile
Within a well-balanced mathematics curriculum, the primary focal points for Algebra I are to continue to build and apply basic understandings developed in K-8, develop symbolic reasoning, understand functions and their relationships with equations, and be able to use a variety of tools and technology to represent functions with multiple representations.
The student will:
·Understand that a function represents a dependence of one quantity on another.
·Understand that a function can be described in a variety of ways.
·Gather and record data, or use data sets, to determine functional relationships between quantities. | 677.169 | 1 |
Highly interactive tutorials and self-test system for individual e-learning, home schooling, college and high school computer learning centers, and distance learning. The product emphasizes on building problem-solving skills. tutorials include the reviews of basic concepts, interactive examples, and standard problems with randomly generated parameters. The self-test system allows selecting topics and length for a test, saving test results, and getting the test review. Topics covered: rectangular coordinate system, functions and graphs, linear equations and inequalities in one variable, systems of linear equations and inequalities, determinants and Cramer s rule, operations with polynomials, factoring polynomials, roots of polynomial equations, rational expressions, exponents and radicals, complex numbers, quadratic functions, conic sections, exponential and logarithmic functions, sequences and series, binomial theorem, counting principles. The demo version contains selected lessons from the full version. The demo is designed to demonstrate the functionality and all features of the product.
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Talmagi 2.2 by dmagic- Software Download
Using keen logic and problem-solving skills, you.ll face multiple math problems that are set up crossword-style. The math equations are set up horizontally, while a set of numbers in glass beakers overlap multiple problems vertically. By moving the numbers in the beakers up or down, try to find the right configuration to solve all of the equations.Talmagi features gorgeous graphics and exciting sound effects to enhance the...
4)
010 Memorizer
010 Memorizer is a powerful program for memorizing numbers. The system works by converting a number into a word or phrase that creates a vivid image in your mind....
5....
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EMSolution Trigonometry Equations short theorem. A translation option offers a way to learn m...
7)
Indefinite Integrals Problem Solving Ebook Software
Effective indefinite integrals training using problems selected with resolution stepwise of graphical form and with mathematical formThe resolution of indefinite integrals is a primordial factor in any student. The main problems that are presented are not understanding the professor's explanation, not to see the information and the mechanical resolution of the problems that they tell us. To get it it is necessary to have a method of resolution of problems that is effective, simple, elegant and t...
10)
Mathomir
Basically an equation editor, however not focused over one single equation, but you can write your mathematical artwork over several pages. Illustrate your equations using hand-drawing tools. Use symbolic calculator and function plotter.... | 677.169 | 1 |
Educator - Mathematics: College Calculus Level I with Professor Switkes
English | VP6 650x350 29.970 fps | MP3 128 Kbps 44.1 KHz | 8.37 GB
Genre: eLearning
Dr. Jenny Switkes will help you master the intricacies of Calculus from Limits to Derivatives to Integrals. In Educator's Calculus 1 course, Professor Switkes covers all the important topics with detailed explanations and analysis of common student pitfalls. Calculus can be difficult, but Professor Switkes will show you how to reap the rewards of your hard work, all while showing you the beauty and importance of math. Whether you just need to brush up on your calculus skills or need to cram the night before the final, Professor Switkes has taught mathematics for 10+ years and knows exactly how to help.
Application-oriented introduction relates the subject as closely as possible to science. In-depth explorations of the derivative, the differentiation and integration of the powers of x, theorems on differentiation and antidifferentiation, the chain rule and examinations of trigonometric functions, logarithmic and exponential functions, techniques of integration, polar coordinates, much more. Examples. 1967 edition. Solution guide available upon requestStochastic analysis is not only a thriving area of pure mathematics with intriguing connections to partial differential equations and differential geometry. It also has numerous applications in the natural and social sciences (for instance in financial mathematics or theoretical quantum mechanics) and therefore appears in physics and economics curricula as well.
Calculus is about the very large, the very small, and how things change. The surprise is that something seemingly so abstract ends up explaining the real world. Calculus plays a starring role in the biological, physical, and social sciences. By focusing outside of the classroom, we will see examples of calculus appearing in daily life.
Calculus does not have to be difficult. Dr. William Murray knows what it takes to excel in math and will show you everything you need to know about calculus. Dr. Murray demonstrates his extensive teaching experience by clarifying complicated topics with a wide array of examples, helpful tips, and time-saving tricks. Topics range from Advanced Integration Techniques and Applications of Integrals to Sequences/Series. Dr. Murray received his Ph.D from UC Berkeley, B.S. from Georgetown University, and has been teaching in the university setting for 10+ years.
Professor Raffi Hovasapian helps students develop their Multivariable Calculus intuition with in-depth explanations of concepts before reinforcing an understanding of the material through varied examples. This course is appropriate for those who have completed single-variable calculus. Topics covered include everything from Vectors to Partial Derivatives, Lagrange Multipliers, Line Integrals, Triple Integrals, and Stokes' Theorem. Professor Hovasapian has degrees in Mathematics, Chemistry, and Classics and over 10 years of teaching experience.
For over three decades, this best-selling classic has been used by thousands of students in the United States and abroad as a must-have textbook for a transitional course from calculus to analysis. It has proven to be very useful for mathematics majors who have no previous experience with rigorous proofs. Its friendly style unlocks the mystery of writing proofs, while carefully examining the theoretical basis for calculus.
This twelve-lesson series will cover the ins and outs of vector calculus and the geometry of R^2 and R^3.
The first 8 video lessons look specifically at vectors and the geometry of R^2 and R^3. This set of videos will cover Coordinate Geometry in Three Dimensional Space, Vectors in R2 and R3, the Dot Product, Orthogonal Projections, the Cross Product, Geometry of the Cross Product, and Equations of Lines and Planes in R3.
Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. | 677.169 | 1 |
Methods of solving polynomial equations lie at the heart of classical algebra. There are two interpretations of the problem of solving an equation, leading to two different approaches to its solution. In most courses, the emphasis is on the structure of the equation and finding a way to express the roots as a formula in terms of the coefficients. The simplest example of such a formula is the quadratic formula, which gives the solution of the equation ax2 + bx + c = 0 as
This approach is elegant and leads to some exceedingly profound mathematics. However, for one who actually needs to know a number that satisfies the equation, this approach leaves something to be desired. It works with maximum efficiency in the case of the quadratic equation, but even in that case, if the quantity under the radical is not the square of a rational number, one is forced to resort to approximations in order to get a usable number. For cubic and quartic equations, there are formulas, but they work even less well, since they often involve taking the cube root of a complex number, which is a problem just as complicated as the original equation was, if not more so. Once again, one is forced to resort to numerical approximations. Beyond the fourth degree, the only formulas involve non-algebraic expressions, and are of little practical use. Higher-degree equations are the realm of numerical methods. To understand how numerical methods work, it is useful to begin with the simplest cases and the simplest methods. That is what we are about to do | 677.169 | 1 |
This set of Mathcad documents provides an overview of some fundamental calculus operations required of physical chemistry students. There is an introduction to taking derivatives and integrals in Part 1 and Part 2. Part 3 focus on preparing surface and contour plots, which can lead to discussions of partial derivatives. Part 4 provides an introduction to the Runga-Kutta method for solving differential equations. Each document has exercises to enable students to practice the techniques and later use them for preparing homework during the course. These documents require Mathcad 12 or higher. The documents presented here build on concepts learned by working through the Basics collection of documents. | 677.169 | 1 |
Academics
Mathematics 221. Linear Algebra
How might you draw a 3D image on a 2D screen and then "rotate" it? What are the basic notions behind Google's original, stupefyingly efficient search engine? After measuring the interacting components of a nation's economy, can one find an equilibrium? Starting with a simple graph of two lines and their equations, we develop a theory for systems of linear equations that answers questions like those posed here. This theory leads to the study of matrices, vectors, linear transformations and geometric properties for all of the above. We learn what "perpendicular" means in high-dimensional spaces and what "stable" means when transforming one linear space into another. Topics also include: matrix algebra, determinants, eigenspaces, orthogonal projections and a theory of vector spaces. | 677.169 | 1 |
Emilie Wiesner
Research
My mathematical research is in representation theory. The idea behind representation theory is to study an algebraic object by looking at how it acts on something else (that is, some "representation" of the original object). For example, the set of transformations that leave a square unchanged form a mathematical object called a group. (One such transformation is rotation by 90° around the center of the square.) We can try to learn more about the abstract group by looking at what it does to the square.
More generally I am an algebraist, which means I like to think a lot about ideas from Linear Algebra (Math 231), Abstract Algebra (Math 303), Combinatorics (Math 421) and other ideas from Discrete Mathematics (Math 270, Math 420). I have recently started to learn about applications of discrete mathematics to biology.
As a teacher, I am also interested in how students learn mathematics. This has led me to get involved with research in math education. I am particularly interested in the role of mathematics textbooks in undergraduate classes and the ways that students use mathematics textbook.
If you would like to learn more about any of my research, feel free to stop by to talk with me. You can find a list of my publications here. | 677.169 | 1 |
Dublin, GA Geometry...In this subject, the student will learn probability in terms of the basic definition, the binomial distribution, and the normal distribution. Probability is used in inferential statistics. ACT Math basically consists of every branch of Mathematics except for CalculusMost five. | 677.169 | 1 |
This handbook is essential for solving numerical problems in mathematics, computer science, and engineering. The methods presented are similar to finite elements but more adept at solving analytic problems with singularities over irregularly shaped yet analytically described regions. The author makes sinc methods accessible to potential users by limiting... more...
This book provides a lens through which modern society is shown to depend on complex networks for its stability. One way to achieve this understanding is through the development of a new kind of science, one that is not explicitly dependent on the traditional disciplines of biology, economics, physics, sociology and so on; a science of networks. This... more...... more...
Whether you are returning to school, studying for an adult numeracy test, helping your kids with homework, or seeking the confidence that a firm maths foundation provides in everyday encounters, Basic Maths For Dummies, UK Edition, provides the content you need to improve your basic maths skills. Based upon the Adult Numeracy Core Curriculum,... more... | 677.169 | 1 |
Precalculus: Functions
Functions
Calculus is the mathematical study of change, and real-life things that change
are modeled by functions. Precalculus is essentially the study of
functions, with a few other related topics that supplement the study of
functions and prepare students for calculus. In this text we'll concern
ourselves first with learning about general functions, and later with certain
types of common functions with special properties, like
polynomial,
exponential,
logarithmic, and
trigonometric functions. First,
it is of critical importance to understand exactly what a function is. In the
following lessons, we'll discuss what makes a function a function, some general
properties of functions, and a few basic categories of functions. In this text
we'll assume a general knowledge of algebraic principles of solving equations,
working with the real numbers, and working with sets. In the last of the
upcoming sections, we'll learn how functions behave under operations like
addition, subtraction, etc. | 677.169 | 1 |
Thorough, well-written, and encyclopedic in its coverage, this text offers a lucid presentation of all the topics essential to graduate study in analysis. While maintaining the strictest standards of rigor, Professor Gelbaum's approach is designed to appeal to intuition whenever possible. Modern Real and Complex Analysis provides up-to-date treatment of such subjects as the Daniell integration, differentiation, functional analysis and Banach algebras, conformal mapping and Bergman's kernels, defective functions, Riemann surfaces and uniformization, and the role of convexity in analysis. The text supplies an abundance of exercises and illustrative examples to reinforce learning, and extensive notes and remarks to help clarify important points.
Read Online Now
at Wiley Online Library
An online version of this product is available through our
subscription-based content service. Read Online | 677.169 | 1 |
Calculus for the 21st Century
Philosophy of the Course
Traditionally, calculus has been presented from an analytical point of view often devoid of meaningful applications. Calculators and computers, with their powerful numeric, graphic, and symbolic tools, provide new opportunities for taking a multiple representation approach to the study of calculus. In particular, greater use of visualization, approximation, and prediction can be made in calculus instruction.
A modern calculus course should foster in students an appreciation and skill that allows them to apply their mathematical knowledge in a variety of practical situations. Ideally, successful completion of the course would provide students with the ability to pick up a newspaper and recognize the calculus that surrounds them. We hope students will apply their knowledge to situations that they face in their everyday lives.
Calculus students should look back on their learning experience with favor and in such a way that they desire to continue their pursuit of mathematics. Through technology, students may now take an active role in their learning. We are now able to create an environment which is rich with technology, nurtures curiosity, and promotes action. Mathematics is an experimental science and should be treated as such. Therefore, employing lesson plans that include laboratory activities, discovery exercises, individual projects, applied problems, writing exercises, and open-ended questions should be an integral part of the course.
A Sampling of the Course
It is not our purpose to detail a first year calculus course. However, the following illustrates an approach to calculus that utilizes hands-on experience and technology. This approach makes learning functions, limits, continuity, derivatives, integrals, approximation, and their applications a more enriching experience for the students and teachers.
LIMITS AND CONTINUITY
Limits are critical to the study of calculus. While the development of a rigorous definition is necessary, formal proofs may be de-emphasized in a first course. Limits should be approached numerically, graphically, and analytically. Graphing calculators are wonderful tools to help develop a clear-sighted concept of limits. An intuitive understanding of the e and d definition can be explored using the idea of local linearity.
Looking at problems like
(1 + )x
both numerically and graphically greatly enhances understanding. Introducing L'Hopital's Rule early in the course is desirable. Students need to examine, graphically and analytically, the relationship between left and right hand limits, continuity, and local linearity.
DERIVATIVES AND THEIR APPLICATIONS
Because calculus is the study of change, the derivative and anti-derivative continue to be the focal point of this study. The definition of derivative and the relationship between differentiation and continuity must be emphasized as well as important theorems like The Mean Value Theorem. The derivatives of polynomial, rational, trigonometric, exponential, logarithmic and piece-wise functions must be studied. In addition, students need to have a working knowledge of implicit differentiation, logarithmic differentiation, the chain rule, product rule and quotient rule. Numerical estimates of the derivative should also be emphasized.
Applications of the derivative should include related rates, maximum/minimum, and motion problems. Questions in these areas should be realistic and focus on applications. The derivatives and their relationship to slopes, concavity, and the linearization of a curve continue to be important components of calculus. Newton's Method and similar iterative techniques should be part of the curriculum.
INTEGRALS AND THEIR APPLICATIONS
Relating motion and the anti-derivative to area and the Fundamental Theorem of Integral Calculus is a primary goal. Given a rate of change, a student should be able to construct the function. The integral as the infinite sum should be explored by several methods including rectangles, mid-point, trapezoid, and Simpson's Rule. With technology, these methods can be explored without tedious computations.
DIFFERENTIAL EQUATIONS
Differential equations are a common theme throughout a first year calculus course. They provide a wonderful opportunity for students to model real life situations. Numerical methods to solve differential equations, along with associated error analysis, help the student to understand the real world of applied mathematics. It is not necessary to solve differential equations solely by analytical methods when other approaches are just as enriching.
SEQUENCES AND SERIES
Students should have a thorough understanding of geometric series and the concept of estimating functions with infinite series. Graphical relationship, the ratio test, the comparison test, intervals of convergence, and error analysis should be addressed, especially with new technology.
Course Books and Resources
Several major calculus reform projects are currently in progress throughout the country. In selecting a calculus textbook, much consideration should be given to both the use of technology and the curriculum content. Major projects have been undertaken at Duke, Harvard, NCSSM, Ohio State, Oregon State, Smith, and St. Olaf's College among others. Associated with many of these are training institutes which are funded by the NSF. Other institutes and inservice opportunities exist. These programs are exciting opportunities for teachers to learn how to incorporate technology into the teaching of calculus and select curriculum materials based on current thinking in the field. Also, close attention should be paid to periodicals, newsletters and journals as a means for staying current with new ideas, technology, and trends in calculus reform.
Focus on the Future
The power of current and future technology can no longer be ignored in classroom instruction. We are faced with technology that is changing at an exponential pace. Teachers must look at how and what they teach in this environment of change. The availability of technology has caused changes in the curriculum. Some content will receive less emphasis, some content will receive more emphasis, and solutions to problems that were previously inaccessible are now possible. Open-ended problems and mathematical modeling need to be an integral part of the calculus curriculum. Writing and group activities are important to constructing and applying knowledge. Teachers must assume the role of a life-long learner and must convey this role to their students. Modes of assessment, including the Advanced Placement examination will, of necessity, change to reflect the use of technology in instruction. | 677.169 | 1 |
11th Grade Math
Embed or link this publication
Description
Differential Calculus :- Differential calculus is a subfield of calculus concerned
with the study of the rates at which quantities change. It is one of the two
traditional divisions of calculus, the other being integral calculus.
The primary objects of
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11th grade math 11th grade math differential calculus differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change it is one of the two traditional divisions of calculus the other being integral calculus the primary objects of study in differential calculus are the derivative of a function related notions such as the differential and their applications the derivative of a function at a chosen input value describes the rate of change of the function near that input value the process of finding a derivative is called differentiation geometrically the derivative at a point equals the slope of the tangent line to the graph of the function at that point for a real-valued function of a single real variable the derivative of a function at a point generally determines the best linear approximation to the function at that point differential calculus and integral calculus are connected by the fundamental theorem of calculus which states that differentiation is the reverse process to integration know more about how to factor cubic polynomials tutorcircle.com page no 1/4
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differential equations a differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders differential equations play a prominent role in engineering physics economics and other disciplines differential equations arise in many areas of science and technology specifically whenever a deterministic relation involving some continuously varying quantities modeled by functions and their rates of change in space and/or time expressed as derivatives is known or postulated this is illustrated in classical mechanics where the motion of a body is described by its position and velocity as the time value varies newton s laws allow one given the position velocity acceleration and various forces acting on the body to express these variables dynamically as a differential equation for the unknown position of the body as a function of time in some cases this differential equation called an equation of motion may be solved explicitly an example of modelling a real world problem using differential equations is the determination of the velocity of a ball falling through the air considering only gravity and air resistance the ball s acceleration towards the ground is the acceleration due to gravity minus the deceleration due to air resistance gravity is considered constant and air resistance may be modeled as proportional to the ball s velocity this means that the ball s acceleration which is a derivative of its velocity depends on the velocity finding the velocity as a function of time involves solving a differential equation.differential equations are mathematically studied from several different perspectives mostly concerned with their solutions the set of functions that satisfy the equation learn more how to draw a heptagon tutorcircle.com page no 2/4
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random variable random variable or stochastic variable is a variable whose value is subject to variations due to chance i.e randomness in a mathematical sense as opposed to other mathematical variables a random variable conceptually does not have a single fixed value even if unknown rather it can take on a set of possible different values each with an associated probability a random variable s possible values might represent the possible outcomes of a yet-to-be-performed experiment or an event that has not happened yet or the potential values of a past experiment or event whose already-existing value is uncertain e.g as a result of incomplete information or imprecise measurements they may also conceptually represent either the results of an objectively random process e.g rolling a die or the subjective randomness that results from incomplete knowledge of a quantity the meaning of the probabilities assigned to the potential values of a random variable is not part of probability theory itself but instead related to philosophical arguments over the interpretation of probability the mathematics works the same regardless of the particular interpretation in use random variables can be classified as either discrete i.e it may assume any of a specified list of exact values or as continuous i.e it may assume any numerical value in an interval or collection of intervals the mathematical function describing the possible values of a random variable and their associated probabilities is known as a probability distribution the realizations of a random variable i.e the results of randomly choosing values according to the variable s probability distribution are called random variates tutorcircle.com page no 3/4 page no 2/3 | 677.169 | 1 |
Stumbled across a book at Amazon - the Financial Calculations Workbook. It has all the equations I've ever used in finance, from simple operating margins to the Black Schole Model. Each equation has a worked example and there are test questions with solutions. Check it out.
I will be do the teacher interview next week, pls advice me about interview questions, tips and interview process.
You can ref some interview questions as follows:
Tell me about yourself?
What are your biggest strengths for Teacher?
Why did you leave your last job?
What are your career goals for Teacher?
What kind of salary would you require to accept the position: Teacher?
Why should we hire you over the other candidate?
What is your system for evaluating student work?
What would be the ideal philosophy of a school for you?
What have been your most positive teaching experiences?
Could a student of low academic ability receive a high grade in your classes?
You can ref more 170 teacher interview questions & answers at: azjobebooks.info/170-teacher-interview-questions or 103 common interview questions and answers | 677.169 | 1 |
I am going to take Calculus 2 next semester... And I would not say I am a math genius or anything... :/
So do you know of anything helpful to understand Calculus 2 very well?
I want to study some over the break to have a head-start.
Thank you!!! :)
Be distrustful of your grade from Calculus 1. Restudy as much as you can from Calculus 1 before starting Calculus 2, since you might have earned a good grade, but you also probably learned a few things less well than you think, and you could find those things to be necessary for your ability to learn Calculus 2.
Make a stack of flashcards of derivatives/integrals/trig identities and study it until you have it burned into your brain. You should be able to blurt out in your sleep any of the basics with zero hesitation. You will need to able to do u-subs in your head, so if you falter with any of the basic derivatives/integrals, you're setting yourself up for pain.
I'm pretty much in the same position as the OP. Just finished Calc I (which refers to an introduction to limits, derivatives, and integrals) and will be starting Calc II in January. In my opinion, I think it depends on what you learn from best. Myself, I've found that (generally) the textbooks of today are too bloated with silly pictures and whatnot. I enjoy so much more reading from a book written in the 50s-80s.
I'm an engineering student, so as tempting as it is to try something like Spivak or Apostol, they are a bit too rigorous for me, and I've found a book entitled 'Modern Calculus with Analytic Geometry' by A.W. Goodman (1967). There are a few proofs, but not as deep as other books.
My point being, I think if you find something you enjoy, wether it be old books, new books, paul's online math notes, videos, anything, find what that is and learn from it. Older books are written in a way that appeals to me, and it makes it natural for me to keep reading from them, making the learning process more enjoyable. | 677.169 | 1 |
Welcome to Integral Math Solutions. We strive to be mathematical superheroes, and since all superheroes need a good origin story, we want to explain why we exist.
As a kid, I liked math because I was good at it. As a student, I liked math because I thought it was fascinating. As an adult and a professional mathematician, I like math because these days, the world hinges on it. Like it or not, the world is a mathematical place, and just like everyone needs to know how to read, everyone needs to know how to do math. I feel strongly that it should be no more acceptable to say "I am just no good at math," than to throw one's hands in the air and say "I just can't read." Our society does not tolerate the latter, but does largely tolerate the former. I am on a mission to change this.
The title of my course gives an extreme view on the importance and relevance of mathematics. Still, whether you are a student, a teacher, or a professional, you are living in a mathematical world. I started this company in order to help you through it. | 677.169 | 1 |
Design Calculations
COURSE Code: DMAT 100
4 Credits
Course Description
This course covers the fundamentals of solid and analytical geometry, ratio, proportion, trigonometry and elementary statistics. The emphasis is on understanding applied concepts and estimates. This is a bridging course for the degree program in Industrial Design and must be successfully completed to continue in the program. | 677.169 | 1 |
People who don't learn or understand this material probably won't use
it, but people who do may be surprised to find where it is
useful. This applies not just to the content of the course, but to its
association with careful, creative thinking. It will probably be up to
you to find places where you can use this mathematics. But depending
on your career, you may find that things that are now obvious to you
are not known to others; or on the other hand, you may find it taken
for granted that you know this material and much more. But most
likely, you may actually use the subject of this course and the skills
you've gained, without even realizing it.
In reality, the questions and complaints mentioned above are all too
frequently tacit, and it may be that much more difficult to bring
these issues to a point of real discussion. Sometimes these complaints
only show up on teachers' end-of-term evaluations. There are
certainly more useful responses for individual students in individual
situations than those offered here. The key point, however, is for the
teacher to be able to listen to these kinds of questions and implicit
challenges as having serious substance in them, that strike to the
root of the problems of teaching and learning mathematics.
ACKNOWLEDGMENTS
The authors are grateful to the editor for his very useful
suggestions.
BIOGRAPHICAL SKETCHES
Sandra Keith is a professor of mathematics at St. Cloud State
University MN. Just as Einstein allegedly wanted to ride on a ``beam
of light'', she has been interested in getting into the minds of
students to understand how they think! She has worked with
exploratory writing assignments and other interactive teaching
methods. She served as director and edited Proceedings for the
National Conference of Women in Mathematics and Sciences and was
assistant editor of Winning Women (MAA). Her interests
include better public relations for mathematics, improving the
mathematical environment for women and minorities, better advising,
and mathematical networking.
Jan Cimperman is an assistant professor at the same school. Her
interests include mathematics education, particularly, teaching
elementary teachers. She frequently gives workshops on the MCTM
Standards and the use of manipulatives to explore mathematical
concepts at the K-6 level. She is interested in the variety of ways in
which students learn. | 677.169 | 1 |
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