text
stringlengths 8
1.01M
|
|---|
Advanced Mathematical Concepts lessons develop mathemati...show morecs using numerous examples, real-world applications, and an engaging narrative. Graphs, diagrams, and illustrations are used throughout to help students visualize concepts. Directions clearly indicate which problems may require the use of a graphing calculator.
New Features :
A full-color design, a wide range of exercise sets, relevant special features, and an emphasis on graphing and technology invite your students to experience the excitement of understanding and applying higher-level mathematics skills.
SAT/ACT Preparation is a feature of the chapter end matter. The Glencoe Web site offers additional practice: amc.glencoe.com
Applications immediately engage your students; interest. Concepts are reinforced through a variety of examples and exercise sets that encourage students to write, read, practice, think logically, and review |
A course designed to develop basic arithmetic and algebra skills to prepare for courses covering secondary school algebra, the first of which is MATD 0370. Content includes operations on whole numbers, integers, fractions, decimals, ratio and proportions, percent, solving linear equations in one variable applications, and relating simple algebra concepts to geometry.
Course Rationale
The Basic Math Skills course is designed to be the first course in a 3-course sequence for Developmental Math. The other two courses are Elementary Algebra and Intermediate Algebra. Students who pass Basic Math Skills will have a solid foundation in arithmetic of rational numbers, solving linear equations, and the beginnings of polynomial arithmetic.
A pre-test may be given upon request within the first week of class. If you do very well, and think that you might belong in the next-higher level course, Elementary Algebra (MATD 0370), you should discuss this with your instructor as soon as possible. In order to move up a level you will need to take the pre-test for MATD 0370 and do reasonably well on that test. A review for that pre-test is available on line at (or ask your instructor for a copy.) This will help you prepare and also give you an idea of the material that we cover in this course (MATD 0330) and that we will expect you to know as you begin MATD 0370. After looking at the review, you might decide that you actually need to stay in your current class. If, however, you are still interested in switching to the higher class, arrange to take that Elementary Algebra Pre-test as quickly as possible.
Attendance and Dropping:
There are 19 class meetings plus a final. I reserve the right to dropstudents who miss 4 or more classes. If you miss a lot of classes, you are ultimately responsible for withdrawing yourself to avoid a failing grade. Attendance is required for TSI mandated students, and so I will keep roll.
August 1st: Last Day to Withdraw.
Daily Lecture Schedule
Week
Mon
Sections
Wed
Sections
1
5/30
Intro: 1.1 - 1.3
2
6/4
1.4 - 1.6
6/6
1.7 - 1.9
3
6/11
2.1 - 2.3
6/13
2.4 - 2.6
4
6/18
3.1 - 3.4
6/20
4.1 - 4.3
5
6/25
4.4 - 4.6
6/27
5.1 - 5.4
6
7/2
5.5 - 5.7
7/4
no class
7
7/9
6.1 - 6.3
7/11
7.1 - 7.3
8
7/16
7.4 - 7.5
7/18
no class
9
7/26
8.1 - 8.3
7/25
8.4 - 8.7
10
7/30
8.9, 9.1 - 9.2
8/1
10.1, 10.3
11
8/6
10.5 - 10.7
8/8
Review
12
8/13
Final
8/15
Office Hours:
Current classroom if available 30 minutes before class, 4216a if classroom is not available.
Homework Assignments
Quizzes will be given at the end of every class over the previous class assignment. The quizzes will be closed book, but open homework. You must show work to receive credit. Many of the problems will be questions from the homework, on these questions it is expected you copy work from your completed homework. Quizzes will be returned the next classConcepts and skills associated with whole numbers
write the standard form of a whole number
round whole numbers and use rounding to estimate values involving whole number arithmetic
know the appropriate vocabulary and facts about angles, triangles, rectangles, squares, and circles
find perimeters of rectilinear figures
use standard formulas to find perimeters and areas of triangles, rectangles, squares and circles
find complementary and supplementary angles
find angles associated with parallel lines cut by a transversal
Statement on Scholastic Dishonesty
Acts prohibited by the college for which discipline may be administered include scholastic dishonesty, including but not limited to, cheating on an exam or quiz, plagiarizing, and unauthorized collaboration with another in preparing outside work. Academic work submitted by students shall be the result of their thought, work, research or self-expression. Academic work is defined as, but not limited to, tests, quizzes, whether taken electronically or on paper; projects, either individual or group; classroom presentations; and homework.
Statement on Scholastic Dishonesty Penalty
Students who violate the rules concerning scholastic dishonesty will be assessed an academic penalty that the instructor determines is in keeping with the seriousness of the offense. This academic penalty may range from a grade penalty on the particular assignment to an overall grade penalty in the course, including possibly an F in the course. ACC's policy can be found in the Student Handbook under Policies and Procedures or on the web at:
Statement on Academic Freedom
and a respect for a diversity of ideas and opinions. This means that students must take turns speaking, listen to others speak without interruption, and refrain from name-calling or other personal attacks.
Statement on Students with Disabilities
Each ACC campus offers support services for students with documented physical or psychological disabilities. Students with disabilities must request reasonable accommodations through the Office of Students with Disabilities on the campus where they expect to take the majority of their classes. Students are encouraged to do this three weeks before the start of the semester.
It is also recommended that instructors add the following:
Students who are requesting accommodation must provide the instructor with a letter of accommodation from the Office of Students with Disabilities (OSD) at the beginning of the semester. Accommodations can only be made after the instructor receives the letter of accommodation from OSD. developmental registration |
Find a Woodlynne will go over the general concepts. (I give you key points of each chapter so you will get a big picture)
2. I will get into problems.
3. Checkpoints (reviews) will be provided whether you fully understand or not.
4. |
User dmitry - MathOverflowmost recent 30 from of Analytic geometry in modern undergraduate curriculumDmitry2011-03-28T07:20:12Z2011-03-29T22:52:41Z
<p>Hello.
I am a freshmen student in mathematics at Moscow State University (in Russia) and I'm confused with placing the subject called "analytic geometry" into the system of mathematical knowledge (if you will). </p>
<p>We had an analytic geometry course in fall; now we are having a course in linear algebra and it seems like most of the facts from "analytic geometry" are proved in a much more systematic and easier manner (quote from <a href=" rel="nofollow">wikipedia</a> "Linear algebra has a concrete representation in analytic geometry"). Many of our progressive professors also think that analytic geometry should be eliminated from the curriculum to clear more space for a linear algebra course. </p>
<p>So I'm confused:
1) if analytic geometry is a "concrete representation" of <em>linear algebra</em>, then why is it studied along with <em>calculus</em> (and not along with linear algebra) in US universities? (e.g. textbooks like <a href=" rel="nofollow">Simmons</a> )</p>
<p>There were, however, interesting parts of the course that were not covered in linear algebra: synthetic high-school-style treatment of beautiful topics like non-Euclidian and projective geometries.
Then
2) why <em>is not there a separate course</em> for such topics in US curricula? As I understand US freshman math majors study 2 basic subjects - real analysis and (abstract+linear) algebra (math 55 at Harvard, 18.100 and 18.700-702 at MIT). Are these geometric topics <em>integrated</em> into one of these courses or <em>are not they considered worth studying</em> for a modern math major?</p>
<p>Thank you</p>
<p>PS. This question is also important for me because it helps a lot to browse through US top universities for textbooks they use and notes. Unfortunately, Russian mathematical school is now in tatters and US textbooks are often significantly better. And since in high school geometry was among my favorite subjects I am particularly concerned about our geometry sequence and want to browse through best geometry syllabi.</p> |
Collins Revision Algebra
This interactive maths resource will identify trouble areas and suggest further studies, and is full of video tutorials and real-life examples to help you revise and practise, progress and get top exam results. |
Mathematics
As a Middle School student, you'll build confidence in mathematics as you apply concepts to real world situations in every discipline. You'll explore a variety of problem solving techniques using technology and communication skills. IXL Math will give you the opportunity to review and practice your math skills and to advance at your own pace. The course of studies is customized to meet the needs of the academic ability of each student. The progression includes fundamental topics in grades six and seven up to and including Algebra I and Geometry for students who qualify by the end of grade 8. Our curriculum is based on the standards as defined by the National Council of Teachers of Mathematics (NCTM):
Math Topics-Grade 6/7
Includes fractions, decimals and percents; ratios and proportions; number theory concepts such as primes, factors and multiples, estimation; algebraic concepts; statistics and the construction and interpretation of tables, charts and graphs; geometric figures and measurement.
Pre-Algebra-Grade 8
This course prepares the student for Algebra I in Grade 9. Integers, rational numbers, linear equations and inequalities are covered. Critical thinking skills and problem solving strategies are developed through use of data analysis and probability.
Algebra I-Grade 7 and 8
Upon successful completion of this course over two years, the student will be placed in Geometry in grade 9 |
Master Math: Solving Word Problems (Master Math Series)
Get ready to master the unknown number! Master Math: Solving Word Problems is a comprehensive reference guide that explains and clarifies the difficulties people often face with word problems, in a simple, easy-to-follow style and format. Beginning with the most basic types of word problems and progressing through to the more advanced, Solving Word Problems shows you how to focus first on the words in the problem, and then on the numbers, breaking down the problem into smaller segments to help you work through. Using familiar situations from everyday life such as percents and discounts, interest, motion and speed, and probability, each type of word problem is taught using step-by-step procedures, solutions, and examples. And end-of-chapter problems will help you practice what you learned Solving Word Problems will help you master everything from simple equations and percents to statistics and probability!
Customer Reviews:
Highly recommended for either general or school libraries
By Midwest Book Review - October 16, 2009
Master Math: Solving Word Problems provides a comprehensive reference guide that explains word problems and offers alternatives for understanding them. From the most common types of word problems to more advanced issues, Master Math: Solving Word Problems shows how to focus on the words in a problem, breaking them down into smaller segments and choosing the right math tools to solve them. Highly recommended for either general or school libraries.
Good book from a great series
By John R. Moser - August 27, 2010
First off, there's nothing impressive in here for anyone who has a modicum of reading comprehension. Interpreting word problems requires understanding the subject matter and what in the hell you're reading. For example, early in the book they cover phrases such as "At Least" and "At Most" with relation to inequalities. When someone says "More Than" you should immediately recognize this as "Greater than" or '>'; when someone says "At Least" you should understand English well enough to know that this does not mean it has to be bigger, and thus means "Greater Than or Equal To" or ">=" (or the single character sign).
Too bad most adults in the US have a 5th grade reading level.
I would strongly recommend studying reading comprehension instead of buying this book; however, since you don't have that kind of time if you're looking at this book at all, that's not really an option. The material presented in this book covers specific reading comprehension problems with... read more
Very good book!
By Seta - December 17, 2007
I got this book on time and it is very good book for my kids to improve their math abilities.
How many skyscrapers are there in New York City? How many muscles do you use to frown? How fast can a turkey run? Together with clever clues, these intriguing questions get kids excited about solving ...
The premise behind Daily Word Problems is simple and straightforward-frequent, focused practice leads to mastery and retention of the skills practiced. When you guide your students in solving a word ... |
If you hated Math and disliked your Algebra teacher with the force of a thousand Reddit downvotes, then you will envy GeoGebra. In all fairness, no one in their right mind would try and plot algebraic equations unless it were required. You seldom hear people say, "I'm going to chill out with this geometric theorem", but for those that are still doing sums and plotting lines, this app is heaven sent. GeoGebra is a Mac app that plots algebraic equations for you. It also lets you place any two points on a graph and find out the resulting equation, plot angles & geometric shapes, and find their coordinates. Life would indeed have been easier if this app were allowed in school.
The app has four different views, and all views (called perspectives) are interlinked; that is, the variables entered in one view are remembered and can be referenced when working in another one. The four views are Algebra & Graphics, Basic Geometry, Geometry, and Spreadsheet & Graphics.
The Algebra & Graphics view allows you to enter and get algebraic equations. To enter an equation, type it in the Input field at the very bottom. To plot any two random points, use the buttons at the top. The New Point button allows you to place any number of points on the graph, and the Line through two points button lets you connect two points. As you enter and connect points, the panel on the left displays the coordinates of all points and any equations that are formed.
Additional buttons at the top allow you to create polygons and circles, create an angle, and more. If you feel this isn't quiet what you need, you can always switch over to the simple geometric view, and plot the figure you want, enter points that you want coordinates of, and create angles wherever needed. Return to the algebraic view and equations and points will have been detailed for you.
The spreadsheet view allows you to enter statistical formulae and conduct a one-variable analysis. The app, with its simplicity and comprehensive set of features is perhaps a dream come true for people plagued with sums and figures |
Introduction to Calculus
The Collins College Outline for Introduion to Calculus tackles such topics as funions, limits, continuity, derivatives and their applications, and integrals and their applications. This guide is an indispensable aid to helping make the complex theories of calculus understandable. Completely revised and updated by Dr. Joan Van Glabek, this book includes a test yourself seion with answers and complete explanations at the end of each chapter. Also included are bibliographies for further reading, as well as numerous graphs, charts, illustrations, and examples.
The Collins College Outlines are a completely revised, in-depth series of study guides for all areas of study, including the Humanities, Social Sciences, Mathematics, Science, Language, History, and Business. Featuring the most up-to-date information, each book is written by a seasoned professor in the field and focuses on a simplified and general overview of the subje for college students and, where appropriate, Advanced Placement students. Each Collins College Outline is fully integrated with the major curriculum for its subje and is a perfe supplement for any standard textbook.
Elementary Algebra... |
Carnegie Learning develops textbooks that support a collaborative, student-centered classroom. Our classroom activities address both mathematical content and process standards. Students develop skills to work cooperatively to solve problems and improve their reasoning and sense-making skills.
Program Components Click icons for details »
Program Components Click icons for details »
Supplemental & Intervention Solutions
Some students will need additional support and intervention to meet the high expectations of state standards. Carnegie Learning can help you implement tiered interventions in mathematics. In addition to the core instruction we provide in our textbooks, we provide interactive math instruction in our Cognitive Tutor software.
Our Algebra Readiness curriculum is a one-year course designed to remediate students who have completed a middle school math sequence of instruction but still exhibit gaps in their math knowledge and skills. The course covers the five major NCTM strands: Number and Operations, Algebra, Geometry, Measurement, Data Analysis and Probability.
Whitepapers
In 28 years of teaching, I would have to say that I've seen more students be successful, I've seen more students know mathematics than I ever have before. And I think it wouldn't be possible without the integrated curriculum and without the materials provided by both the state and Carnegie Learning that we are using. |
This course provides students with a combined foundation in introductory and intermediate algebra topics that are NECESSARY skills for the study of a college-level mathematics course. Topics include real numbers, equations and inequalities, coordinate grid topics, exponents and polynomials, factoring, rational expressions, roots and radicals, systems of equations and quadratic equations. |
Question on the Boas Math Methods book.
I'm going to pick up a math methods book to beef up my more physicsy math, as it were, since the math program at my school is less geared to physics and engineering and more towards education, business, and computer science (and the physics program itself is falling apart).
All the rage seems to be around the Boas book. So I looked it up on Amazon and found that in the used and new section I can get 2e for about fifteen bucks, while I can't get the 3e for less than seventy.
Is there a significant difference between these two editions that would warrant the investment in the third edition when I'm just going to use it for some casual self-study? |
0321279220 and Intermediate Algebra (3rd Edition)
Lial/Hornsby/McGinnis s Introductory and Intermediate Algebra, 3e gives students the necessary tools to succeed in developmental math courses and prepares them for future math courses and the rest of their lives. The Lial developmental team creates a pattern for success by emphasizing problem solving skills, vocabulary comprehension, real-world applications, and strong exercise sets. In keeping with its proven track record, this revision includes an effective new design, many new exercises and applications, and increased Summary Exercises to enhance comprehension and challenge students' knowledge of the subject matter |
Short description
IGCSE Mathematics is a new text book written specifically for the Cambridge International Examinations syllabus.
Long description
IGCSE Mathematics is a new text book written specifically for the Cambridge International Examinations syllabus. It has been written and trialled by experienced IGCSE teachers and endorsed by CIE, ensuring that it is up to date and comprehensive in its coverage of the syllabus.
Product details
Publisher:
Cambridge University Press
ISBN:
9780521011136
Publication date:
June 2002
Length:
245mm
Width:
188mm
Thickness:
11mm
Weight:
694g
Audience:
Age: 18 - NA
Pages:
308
Illustrated:
True
Review
'This is a readable and engrossing book. This book reviews the many factors that influence reproduction. Sixth formers, students and zoo educators would benefit from reading the book if they have an interest in conservation. Long time biologists like me may be absorbed in the topic and heartily encouraged.' Journal of Biological Education |
Courses
AS/A2 Further Mathematics
Central Foundation Boys' School & Highbury Grove School
Course Outline
This course will allow you to delve into maths at a far greater depth and explore all the complex facets of the subject.
Areas that are covered include the series unit, comprising complex numbers, numerical solution of equations, coordinate systems, matrix algebra and proof. You will also examine inequalities of series, first order differential equations; second order differential equations; further complex numbers, Maclaurin and Taylor series. Finally, the further matrix algebra unit explores vectors, hyperbolic functions; differentiation, integration, further coordinate systems.
Entry Requirements
Six GCSEs at grade B or above including at least a grade A in Maths.
Assessment
100% examination.
Progression
This qualification can lead to further study at university in fields such as science, pure maths, economics and engineering.
The skills learnt in Further Maths are also very transferable to a host of related areas of study and employment. |
stella2java - Shodor Education Foundation, Inc.
Use Stella2java to make Java applets out of the modeling software package Systems Thinking Experimental Learning Laboratory with Animation (STELLA). Copy and paste your equations from Stella into a web form, answer a few questions, and download your applet.
...more>>
STELLA - isee systems
A model building and simulation software package. Read about STELLA-based materials such as Lessons in Mathematics: A Dynamic Approach. Get help with STELLA training, seek live support building a model, see tutorials, purchase supporting books and videos,
...more>>
Stella: Polyhedron Navigator - Robert Webb
"Small Stella" is a program for viewing polyhedra and printing their nets so you can build your own. It has over 150 built-in models, plus their duals. Models include Platonic solids, Archimedean, Kepler-Poinsot, Johnson solids, "Near Misses," and Stewart
...more>>
Stella's Stunners - Rudd CrawfordSteven Strogatz - The New York Times Company
Mathematics from an adult perspective -- from the basics of math to the baffling -- by Steven Strogatz, a professor of applied mathematics at Cornell University. This New York Times series is not meant to be remedial, but rather to give readers a better
...more>>
Stock-Trak - Stock-Trak
Stock-Trak is a virtual stock exchange simulator and fantasy stock market game. It allows its users to practice online stock trading within all of the major securities. Browse the site for information on stock investing research and fantasy stock market
...more>>
Strawberry Macaw's Puzzle Page
Although simple, this collection of four logic puzzles provides a challenge for students of any age. The interactive puzzles are: The Fox, the Duck, and the Bag of Corn; The Three Gallon and Five Gallon Cans; The Twenty-Three Matches Game; and The Game
...more>>
Stressed Out: Slope as Rate of Change - Cynthia Lanius
It's the night of the big game. You're in the locker room. The coach is pumping the team up. "Now, I know you people are nervous. That's okay, in fact, that's what we want. You're going to perform better on the court (stage) if you're a little nervous."Studying Mandelbrot Fractals - Suzanne Alejandre
What is a fractal? A definition and a Java applet to help in exploring the Mandelbrot set, redrawing small areas to fill the fractal screen and noticing how the images compare. Also links to other sites with fractal information for middle-schoolers.
...more>>
Studying Polyhedra - Suzanne Alejandre
What is a polyhedron? A definition and a Java applet to help in exploring the five regular polyhedra to find how many faces and vertices each has, and what polygons make up the faces. Also links to a page of information about buckyballs, stories written
...more>>
Study Island
Internet-based standards-mastery products, based on state standards. Subscriptions are available for single classes through districts, with individual subscriptions available for GED products.
...more>>
studymaths.co.uk - Jonathan Hall
Free help on your maths questions. See also the bank of auto-scoring GCSE maths questions, games, and resources such as revision notes, interactive formulae, and glossary of terms.Stupid Calculations - Josh Orter
Repository "where practical facts get rendered into utterly useless ones." Posts, which date back to May, 2013, have included "Monophone," musing on the size of the screen made from ripping the displays out of every iPhone ever sold and combining them
...more>>
subtangent.com - Duncan Keith
With Flash, explore interactive investigations such as Number Stairs and Diagonal Differences. Play Mathionaire, based on the popular TV game, but with maths questions. Quizzes include Function Machines, Number Properties, Pythagoras, and Quadratics 1.udoku
Flash-based game: enter a 9x9 grid so that every column, every row and each of the nine 3x3 segement contains the numbers 1 to 9. The game provides hints when you are stuck and has different levels.
...more>>
Sudoku - Pappocom, aka Wayne Gould
Finish filling in the 9x9 grid so that every row, every column, and each of the nine 3x3 boxes contains the digits 1 through 9. Different from a magic square, this puzzle requires no arithmetic, only reasoning and logic to deduce which digit to put where.
...more>>
A Su Doku solver
Solvers for sudoku puzzles, with documentation, source code, and binaries. Frequently asked questions about this numeric puzzle include "Su Doku" or "Sudoku"? How does the solver work? How do I compose a Su Doku problem? How few cells could appear on
...more>>
Sudoku Widget - Brian DeBoer
Macintosh OS X users familiar with Dashboard use its mini-applications to perform common tasks and get fast access to information. The Sudoku Widget by Brian DeBoer generates random puzzles with four different levels of difficulty, has the option to showSumdog - Peter Beckham, Crocodile Clips Ltd.
Free multi-player maths games designed to improve numeracy for students aged
9-13. Players compete either against the computer or other students around the world. The one hundred available games, which adapt to the skill level of each student, range
...more>>
Sumizdat Home Page - Sumizdat
Website of the publisher "Sumizdat", currently featuring the English translation of a classical Russian geometry textbook: Kiselev's Geometry/Book I. Planimetry, Kiselev's Geometry/Book II. Stereometry, and Arithmetic for Parents, translated from the
...more>> |
TERC and Tufts University Early Algebra, Early Arithmetic This site, developed by a research team from TERC and Tufts University, features a teaching and learning approach where traditional topics of early mathematics are taught in deeper, more challenging ways. This approach allows students to go beyond computational fluency as they begin to develop the ability to make mathematical generalizations using algebraic notation.
This book, based on a four-year research project, offers strategies to help teachers become skilled facilitators of classroom discussion that enhances the teaching and learning of mathematics in grades 1 through 6. There are specific sections of the book that focus on the mathematics in particular, including: concepts, procedures, problem solving, reasoning, terminology, symbols, definitions and forms of representation.
This book with accompanying CD-ROM is written to help teachers introduce and develop fundamental algebraic concepts with students in grades 3 to 5. Important ideas of algebra–such as patterns, variables and equations, and functions–are the focus of this book. Its student activities introduce and promote familiarity with these ideas. The supplemental CD-ROM features interactive electronic activities, master copies of handouts, and additional readings. |
- Get to grips with converting your mathematics teaching over to Moodle - Engage and motivate your students with exciting, interactive, and engaging online math courses with Moodle, which include mathematical notation, graphs, images, video, audio, and more - Integrate multimedia elements in math courses to make learning math interactive and fun - Inspiring, realistic examples and interactive assessment exercises to give you ideas for your own Moodle math courses
In Detail Moodle is a popular e-learning platform that is making inroads into all areas of the curriculum. Using moodle helps you to develop exciting, interactive, and engaging online math courses. But teaching math requires use of graphs, equations, special notation, and other features that are not built into Moodle. Using Moodle to teach Mathematics presents its own challenges.
The book will show you how to set-up a Moodle course to support the teaching of mathematics. It will also help you to carefully explore the Moodle plugins that allow the handling of equations and enable other frequently used mathematical activities.
Taking a practical approach, this book will introduce you to the concepts of converting mathematics teaching over to Moodle. It provides you with everything you need to include mathematical notation, graphs, images, video, audio, and more in your Moodle courses. By following the practical examples in this book, you can create feature-rich quizzes that are automatically marked, use tools to monitor student progress, employ modules and plugins allowing students to explore mathematical concepts. You'll also learn the integration of presentations, interactive math elements, SCORM, and Flash objects into Moodle. It will take you through these elements in detail and help you learn how to create, edit, and integrate them into Moodle.
Soon you will develop your own exciting, interactive, and engaging online math courses with ease.
What you will learn from this book? - Convert mathematics teaching over to Moodle - Enhance your course with interactive graphs, images, videos, and audio - Integrate interactive presentations and explore different ways to include them in your course - Create your own SCORM activities using both free and commercial tools - Add rich animation and fun games by incorporating Flash games and activities for engaging your students - Build feature-rich quizzes and set online assignments - Monitor student progress and assess your teaching success - Configure Moodle to display the complete set of mathematical symbols and objects
Approach The book presents the reader with clear instructions for setting up specific activities, based around an example maths course (Pythagorean Theorem) with plenty of examples and screenshots. No Moodle experience is required to use the book, but the book will focus only on activities and modules relevant to teaching mathematics. We will assume that the reader has access to a working installation of Moodle. The activities will be appropriate for teaching math in high schools and universities.
Who this book is written for? The book is aimed at math teachers who want to use Moodle to deliver or support their teaching. The book will also be useful for teachers of "mathematical sciences", or courses with a significant mathematical content that will benefit from the use of some of the tools explored in the book. No Moodle experience is required to use the book.
Moodle 1.9 Math |
Functional Maths - Maths in
A selection of 10 Functional Maths worksheets from Axis Education's brand new maths series Maths in. Full of practical Functional Maths tasks with students required to collect, present and analyse their own data, Maths in helps to engage students by demonstrating how mathematics can be applied to everyday life. |
The videos on this page relate to topics from Section 2.3 of our current text. The section title is arithmetic combinations of functions. In this section, the authors address to a small extent how to sketch the graph of a function that is an arithmetical composition of a pair of functions |
Berkeley, IL CalculusPrealgebra is the time we take to start familiarizing students to this very useful mathematical language that we use to note and analyze our thinking. It has its own vocabulary, syntax, and grammar. For example, when we say x=2, everybody *just knows* that we're talking about a single x equaling 2. 1x is written as x. |
Sample chapters for download
About the book
The aim of this Guide is to help students prepare for the Cambridge IGCSE International Mathematics (0607) Extended examinations.
This Guide covers all eleven Topics in the Cambridge International Mathematics (0607) syllabus. Each Topic has a summary of key facts and concepts followed by a set of 'Skill Practice' questions. There are over 500 'Skill Practice' questions in total.
Following topics 1-11 are three Practice Exams, divided into Paper 2, Paper 4, and Paper 6 as per the IGCSE International Mathematics (0607) Extended examination.
Each Paper 2 has 10 - 11 short response questions to be completed within
45 minutes. To be answered without the use of a calculator.
Each Paper 4 has 11 - 12 medium to extended response questions to be
completed within 2 hours 15 minutes. A graphics calculator may be used.
Each Paper 6 has more open-ended questions divided into two parts:
A. Investigation and B. Modelling, to be completed within 1 hour 30 minutes.
Fully worked solutions are provided for all questions in this Guide.
Good examination techniques come from good examination and practice. We hope this guide will help you succeed. |
Designed as a companion to The Economist Style Guide, the best-selling guide to writing style, The Economist Numbers Guide is invaluable to anyone who wants to be competent and able to communicate effectively with numbers.
In addition to general advice on basic numeracy, the guide points out common errors and explains the recognized techniques for solving financial problems, analysing information of any kind, and effective decision making. Over one hundred charts, graphs, tables, and feature boxes highlight key points. Also included is an A–Z dictionary of terms covering everything from amortization to zero-sum game. |
Core Abilities (Note: since this course may be taken in partial fulfillment of the general education requirements, this syllabus includes the following set of core ability goals.)
1. Thinking: Students engage in the process of inquiry and problem solving that involves both critical and creative thinking.
Students will be exposed to the logic of mathematical proof
Students will develop their problem-solving skills
Calculus is a major intellectual development in human history and students will think through the concepts
2. Communication: Students communicate orally and in writing in an appropriate manner both personally and professionally.
Students will develop their skills of written mathematical communication, specifically learning to properly use the language and notation of the Calculus
Students will develop their verbal mathematical communication skills, both in small groups and in class discussions
3. Life Values: Students analyze, evaluate and respond to ethical issues from informed personal, professional, and social value systems.
Students will see the importance of integrity regarding their own scholarship
4. Community Involvement: Students demonstrate skills of interdependent group participation and decision-making.
Students will work in groups, learning to share their ideas and skills, and respecting the ideas and skills of others
Specific Course Goals:
From the perspective of mathematical content, this course should allow the student to expand and apply skills and knowledge gained in the first semester of Calculus to the topics of integration and applications of integration.
The student will gain knowledge and skills, and the ability to apply these, to a variety of situations which might be encountered in the world of mathematics, science, or engineering.
The student will further improve his/her ability to communicate mathematical ideas and solutions to problems.
The student will improve her/his problem-solving ability.
From a most general perspective, the student should see growth in his/her mathematical maturity. The three-semester sequence of calculus courses form the foundation of any serious study of mathematics or other mathematically-oriented disciplines.
Assessment Procedures:
Semester grades in this course will be awarded according to a standard scale:
729—810pts (90% and above) = A
648—728pts (80%--89%) = B
567—647pts (70%--79%) = C
486—566pts (60%--69%) = D
Less than 486pts (Below 60%) = F You may, however, still hand the work in so that you can benefit from corrections and be certain you know how to do a question that could well appear on an exam
Practice Exams 100 pts
There will be four group practice exams worth 25 pts apiece before each in class midterm and before the final exam
Examinations 300 pts
There will be threeLabs 160 pts
There will be eight labs each of which carries 20 pts
Cumulative Final Examination 200 pts
Total 810 pts
Attendance Policy:
You can afford to miss no more than the equivalent of one week of class. Any more absences are a dangerous loss of classtime percentage. Once you have had 3 unexcused absences, every unexcused absence from that point onward will incur a penalty of 10 pts from your participation and attendance score.
Homework: Let me urge you to make it a regular part of your day to try working the homework problems. There will never be enough time for us to go through every listed problem in class, and it is probably unrealistic to think that you will be able to find the time to work through every listed problem, but you should at least spend some time thinking about virtually every problem, and working the more interesting or challenging to completion. The daily homework
You should view homework assignments as a test to see how well you understand the material and you should bring to the next class any questions you might have.
However, from time to time, certain homework problems will be assigned and collected as mentioned above. I will award semester points for homework by calculating the percentage you got on all assigned homework and awarding this as a score out of 100pts
Schedule, Fall Semester 2005
29 Aug [4.9] Anti-derivatives p 334 #1-15 odd, 25, 43
31 Aug [5.1] Area, Distance p 355 #1-7 odd, 11-15 odd
1 Sep [5.2] The Definite Integral p 367 #1-11 odd
2 Sep p 367 #15, 19, 21, 29
(n.b. This is the last day to add or change sections of a class)
5 Sep Labor Day Break ;-)
7 Sep [5.3] Evaluating Definite Integrals p 377 #1, 3, 9-27 odd, 49
8 Sep Lab #1 (20pts)
9 Sep [5.4] The Fundamental Theorem of Calculus p 386 #3-15 odd, 19
12 Sep [5.5] Substitution Rule p 395 #1-27 odd, 37-45 odd
(13 Sep: Last day to take a course Credit/No Credit)
14 Sep [5.6] Integration by Parts p 401 #1-21 odd
15 Sep p 401 #25-33 odd
16 Sep Lab #2 (20pts)
19 Sep [5.7] More Integration Techniques p 408 #1-15 odd
21 Sep p 408 #17-31 odd
22 Sep [5.8] Integration Tables, Using CAS p 414 #1-21 odd, 25
23 Sep Group Practice Exam #1 (25 points)
26 Sep EXAM #1 (100 Points)
28 Sep [5.9] Approximation Techniques p 425 # 1-9 odd, 15-19 odd
29 Sep [5.10] Improper Integrals p 436 #1-23 odd
30 Sep p 436 #39-49 odd
3 Oct [6.1] More on Areas p 452 #1-13 odd, 21, 23, 27
5 Oct [6.2] Volumes – Solids of Rotation p 463 #1-13 odd
6 Oct p 463 #21, 23, 35
7 Oct Lab #3 (20pts)
10 Oct [6.3] Arc Length p 471 #1-7 odd, 11, 17, 21
12 Oct [6.4] Average Value of a Function p 475 #3-11 odd
13 Oct Group Practice Exam #2 (25 points)
14 Oct EXAM #2 (100 points)
17 Oct [6.7] Probability and Random Variables p 498 # 1-7 odd
(n.b.This is the last day for submitting D/F slips)
19 Oct p 498 # 9-13 odd
20 Oct Lab #4 (100pts)
(n.b.This is the last day to drop a full semester course and have it removed from the record) |
New Syllabus Mathematics (6th Edition) Specific Instructional
On this page you can read or download New Syllabus Mathematics (6th Edition) Specific Instructional in PDF format. We also recommend you to learn related results, that can be interesting for you. If you didn't find any matches, try to search the book, using another keywords.
Before plotting graphs of functions, revise with the pupils the general method on the choice of scales for the straight line graph and the quadratic graphs that they had learned in Secondary 2 and the plotting of travel graphs and conversion graphs that they learned in SecondaryRemind them to label the graphs clearly. Pupils should be encouraged to draw the curves free hand as well as to use curved rules to assist them. There are many opportunities for teachers and pupils to explore this chapter using softwares such as Graphmatica, Winplot and others. |
A Beginner's Guide to Finite Mathematics
For Business, Management, and the Social Sciences
This concise text takes a distinctly applied approach to finite mathematics at the freshman and sophomore level. Topics are presented sequentially: the book opens with a brief review of sets and numbers, followed by an introduction to data sets, histograms, means and medians. Counting techniques and the Binomial Theorem are covered, which provides the foundation for elementary probability theory; this, in turn, leads to basic statistics. Graph theory is defined, with particular emphasis on its use in mathematical modeling. Matrices and vectors are discussed, along with several elementary commercial applications. The book concludes with an introduction to linear programming, including the simplex method and duality. Ample examples and illustrations are provided throughout; each section contains two sets of problems, with solutions provided for the first set.
Contents:
Preface.
Numbers and Sets.
Counting.
Probability.
Graph Theory.
Matrices.
Linear Programming.
Your Turn Solutions.
Answers to Exercises A.
Index.
Book category: Undergraduate textbook
Main Audience: High school students with two years of basic algebra; undergraduates in business, liberal arts, social sciences; instructors |
Math 20F
MATLAB Assignments
This is the gateway page for the Math 20F MATLAB
assignments. This portion of Math 20F is an introduction to using
computer software for topics in linear algebra. The labs will
explore not
only how to use the software but also how linear algebra arises in
practice. The material will also give additonal
persepective and
add to topics covered in lecture.
There are three main packages for general purpose
scientific computation: Maple, Mathematica, and MATLAB, known as the
3Ms. While this course focuses solely on MATLAB, all three
packages
are similiar and if you know one, you can usually pickup another one
within an hour or two. Many students enrolled in Math 20F will
use one
of these packages (or more specialized software of a similiar nature)
heavily in their major and in future careers.
Basic information for using MATLAB on campus ACS
computers
can be found on the What
You Need To Know About MATLAB portion of 20F page, while due dates
for homeworks can be found on the MATLAB Assignment Due
Dates page. In general,
though, each lab is self-contained and can be completed without prior
MATLAB experience, although some assignments depend on commands learned
in previous assignments.
The following optional
labs expand upon many of the topics from class. Feel free to take
a look and see if any of the topics interest you. After each the
prerequisite needed to complete the lab is listed. |
Talk About Us On Facebook!
I have a PhD in Mathematics from Yale
and won the Gold Medal in the National Math Olympiad and Silver Medal at the International Math Olympiad. If you are an aspiring math student, or the
parent of one, you can schedule an appointment with me here. My
experience in math competitions gives me a special advantage in helping the most serious students reach their full potential in preparing for the AP
Calculus exam, Math Olympiad, or Putnam Competition. I can also tutor aspiring scientists, hedge fund quants and financial engineers wishing to master
advanced probability theory and other math topics. For more information about me, please readmy Tutor Hero profile page. To see a complete list of my blog posts, go here. You can email me
here.
In this post I am going to talk mainly about how to prepare for Math Olympiad. I am going to discuss two different approaches. At the bottom of this post are two videos I created with more information on me, Math Olympiad prep, and my online tutoring services.
The first method is to start off with solving Olympiad-type questions. You can, for example, find past IMO exams here and see how well you can do. There are many other websites and books containing Olympiad-type problems and solutions. In this method I'd suggest you start with old exams. They tend to be much easier. In the process, you will find out which subjects you need to work on. Try to spend at least 2 hours on each problem before looking up their solutions. You will most probably not be able to solve many of the problems and you will find some subjects in the solutions that you might not be familiar with. Then you can work on those subjects and theorems. This method is good if you feel confident that you know the subjects in Math Olympiad fairly well or you are at least fairly comfortable with the materials. Otherwise this method won't work for you. Many solutions to Olympiad problems have similar ideas. So the more problems you solve the more experienced you get.
The second method is to try to learn all subjects well before starting to solve any problems. This method is a lot more time consuming and I'd suggest it to 10th or 11th grade students who have enough time to prepare for Olympiad. The advantage of this method is that what you learn not only helps you with Olympiad preparation, but it is also helpful for you in the future as it gives you a better understanding and insight of Math. Also this method ensures you that you have covered all the materials needed for Math Olympiad. In contrast the first method makes you a problem solver which is very good and may be enough to be successful in Math Olympiad. However it may not give you a good mathematician or may not give you a good understanding and insight of Math.
These two general approaches remain valid for Putnam preparation or any similar exams.
In the end, if you want to be successful you need to do A LOT of problems. Even if you find a solution to a problem, look at the solutions and try to understand all different solutions in case there are more than one solutions. Each solution gives you a new method. Have all these methods in mind as they are going to help you some day in solving a problem.
Try to keep a few latest official exams from IMO, USAMO or similar exams untouched. When you are a few weeks away from you official exam give yourself 9 hours and solve these exams separately. This would help you understand how you are doing. However, keep in mind that you won't necessarily perform the same in the actual exam.
I enjoy working with students to help them prepare for advanced mathematics competitions. The first video below presents my approach towards mentoring students. The second video discusses more my credentials and then demonstrates how I work with students online using Tutor Hero's professional technology for 1-on-1 tutoring. Click here if you'd like to sign-up for a tutoring session with me.
In one of my classes I was asked if I could give a proof for the Pick's Theorem. I decided to share the proof here. This is an interesting proof that anybody who is preparing for Math Olympiad would find interesting. But first what is the Pick's Theorem? To state the Pick's Theorem I need to first define "lattice points".
Definition: Any point on the -plane with integer coordinates is called a lattice point.
Here is the statement of the Pick's Theorem:
Pick's Theorem: For any polygon on the -plane whose vertices are lattice points we have where is the area of the polygon, is the number of its interior lattice points and is the number of its boundary lattice points.
Here is an elementary proof for the Pick's Theorem.
First of all one can show this equality holds for any lattice rectangle whose sides are parallel to the axes. This is not very hard but needs a bit of calculation.
Now, for any polygon lets call the RHS by , i.e., for the polygon . We need to show . It is easy to show if a polygon if the union of two polygons and then and . Since any polygon can be divided into triangles we only need to prove Pick's Theorem for triangles. Now again if you use this additivity you can see that you only need to show this equality for a triangle when there is no interior or boundary lattice points except for the vertices.
Now, I first show . Again by induction you only need to show this inequality for when is a triangle with no interior or boundary lattice points except for its vertices. One can calculate to get so we need to show . To show this we only need to show but is the area of a parallelogram with lattice point as its vertices. But the area of a parallelogram is the the magnitude of the cross product of two vectors forming this parallelogram. This can be easily shown to be at least 1.
If you don't know what a cross product is try this alternative method for evaluating the area of the triangle. Lets say we have a triangle whose vertices are lattice points. As shown in the picture below draw a vertical line from A so that this line intersects at .
Use coordinated of and to write down an equation of the line . Find coordinates of using the equation of this line and the -coordinate of . Now using this information evaluate the area of as the sum of two areas of triangles and and show this area is at least .
This shows that for any polygon , .
Now assume for a triangle , we have . Using two vertices of this triangle you can draw a rectangle whose sides are parallel to the axes and contains this triangle and two of its vertices are the vertices of this triangle as shown in the following picture.
As shown in the above picture, divide this rectangle into four triangles. For each one of this triangles we know that , but for the rectangle we already showed that which shows for the triangle the equality should hold also.
Some parts of this proof needs a bit of work that is left to the reader.
I discussed FLT in an earlier post and stated a problem that if solved FLT for will be deduced from there. Below is a solution to that problem.
Assume is a "non-trivial" triple of integers that satisfies
(1) .
By "non-trivial" we mean "". Obviously we can assume that and are positive. If we show for any such triple, there is another triple satisfying the same equation with a smaller , then using the method of "infinite descent" we get a contradiction, and therefore we can deduce that there is no "non-trivial" solutions for .
Now one can show that and are relatively prime. Otherwise you can find a "smaller" solution for the equation (1). Therefore is a Pythagorean triple and we have two relatively prime integers and such that:
Using the fact that is odd (why?) and the equation we can deduce that is odd and is even (why?). Now since and are relatively prime and is a perfect square we can deduce that and are perfect squares (why?). Therefore there are two relatively prime integers and such that and .
Now look at the equation and use the formula for Pythagorean triples. So there are relatively prime integers and such that:
Now since is a perfect square, should be a perfect square. Therefore both and are perfect squares. Therefore there are integers and such that and . Combine this with the equations and and you get . So, the triple is a triple satisfying (1) which is what we were looking for. We only need to show this triple is "non-trivial" and that . I leave this to the reader, but it is fairly easy.
International Mathematics Olympiad is a highly respected competition which is held yearly. It is a place where many mathematicians are hoping to motivate the best students to continue their studies in Math. A lot of participants end up becoming the best mathematicians later in their career. My Ph.D. adviser Professor Gregory Margulis who won the Fields Medal in 1978- among many other prestigious Math prizes- won a silver medal in the 4th IMO. Two other examples of these mathematicians are 2006 and 2010 winners of Fields Medal, Terence Tao and Elon Lindenstrauss.
Different countries have different policies toward IMO. Some countries like China and my home country Iran train their teams for a long time, up to a year. Others may only hold a few exams and select their teams with a brief training.
This year the USA Math Olympiad exam is going to be held on April 27-28, 2011. As you might know, the exam is a 9 hour, 2 day exam with 3 questions each day. Generally, each day the 3 problems are sorted in the order of their difficulty. Meaning that you can generally expect the first and fourth problems to be the easiest problems. The third and sixth problems are usually the hardest ones. You can get more information about USAMO from their website here.
One of the most important achievements of the 20th century in Math is a proof of the Fermat's Last Theorem. It states:
Fermat's Last Theorem. Let and be 4 integers such that and . Then .
In our previous post we discussed all solutions of this equation for as Pythagorean Triples. Proof of FLT involves advanced Mathematics. Here I would like to bring up a especial case of this theorem for . More generally one can prove the following.
Problem. If for 3 integers and , then .
One can prove the above statement using infinite descent and combining it with Pythagorean Triples. Think about it if you get a chance. A proof will be posted later.
Any three integers and that can be lengths of sides of a right triangle is a called Pythagorean triple. But we can also think of negative numbers as Pythagorean triples when they satisfy the equation . Here I would like to show you a simple method to find all Pythagorean triples.
Asssume is the greatest common divisor of and , i.e. . If we divide and with obviously we get another Pythagorean triples. Therefore to find all Pythagorean triples it is enough to find all triples with g.c.d.=1. Therefore we may assume and have no common factors. One can check that one of or has the same parity as . (why?) Assume and have the same parity. Now write the equation as: . Now one can show and are co-prime integers. (why?) Therefore both of them are perfect squares. (why?) Therefore there are integers such that:
and . Therefore . Hence we have the following:
We may drop for since and range over all integers. If we multiply these by we get a formula for all Pythagorean triples. Therefore any Pythagorean triple is of the following form:
where and are three integers.
Try to fill in the gaps of this proof. This is especially important if it is your first time seeing this proof or similar proofs.
Infinite descent is a common mathematical method that we use in solving problems and proofs. It is based on a very simple and intuitive fact: every non-empty set of natural numbers has a smallest number. This means if you show a set of natural numbers has no smallest number that set should be empty. This method is commonly used to attack some problems in number theory. Especially for finding solutions to some specific Diophantine equations.
I understand that wikipedia is not the most reliable source of information out there, but a lot of their articles are very useful, so I suggest you take a look at this wiki article to find out more about Infinite Descent. Make sure to look at the examples.
By Sylow Theorem we know that the number of -Sylow subgroups should divide . On the other hand this number is congruent to modulo . So, we have either or , Sylow subgroups. If there is no normal subgroup of order we should have Sylow subgroups.
Let be the set of all -Sylow subrgoups of . One can check the number of elements in is . Notice that all 's are conjugate. Therefore, we have , where is the normilizer of in . Hence, , which means for any .
Take an element outside of all 's and take an element . We have . One may check that all elements are different when . These are elements that are conjugate to , hence none of them is inside any . Since there is only elements outside of all 's these are the only elements outside of 's. Therefore has exactly conjugates. Hence, . therefore . Since elements of 's have order or , intersects all 's at the identity element. Therefore consists of the identity and all elements of outside of all 's. Obviously no conjugate of has an element of order , therefore is normal in .
I remember as a freshman in college I was given a group theory problem in an exam that I couldn't solve at the time. (There was no hints though ) I may have heard the solution later but a few days ago I was thinking about that problem. So here is the problem and some hints. It is a nice and challenging problem. You might want to think about it before looking at the solution. The solution will be posted later.
Problem. Let be a group of size where is a prime number. Show that has a normal subgroup of size either or .
Hint #1: Use the Sylow theorem and count the number of -Sylow subgroups of . Show that if a -Sylow subgroup is not normal then there is only elements outside of these Sylow subgroups which form a group.
Hint #2: Prove that these elements commute and deduce they form a normal subgroup. To show this, count the number of conjugates of an element outside of all of these -Sylow subgroups.
Before posting my solution to the first problem I thought I'd post some basic facts and notations that I am going to use. If you are not familiar with these basic facts it is good to check them. Everybody should check these at least once in their lifetime.
Let be a group and its subgroup. denotes the set of all elements such that . One can check that is a subgroup of containing . is called a conjugate of . You can check that the number of conjugates of is .
is the set of all elements in that commute with . One can check this forms a subgroup of . Furthermore, the number of conjugates of equals . |
Math for Moms and Dads: A dictionary of terms and concepts...just for parents
Kids are struggling with math in school, on tests, and with homework. Parents feel stressed, helpless, and math-phobic. They struggle to encourage and assist on the very subject they are least prepared to manage: MATH.
Broken down using straightforward, simple language, this guide offers parents who are easily intimidated by math instructive and handy concepts to use when helping their students with homework or studying for a big test.
Parents banish math phobia once and for all by facing math head-on in Math for Moms and Dads. Frequently, the issue isn't "how to," it's actually "what do they want me to do?" Learning the language of math in context is the first step in the right direction for helping yourself in today's math morass so parents can help their child find his or her way out of any math quagmire.
Using a similar methodology applied in SAT Score-Raising Math Dictionary, Kaplan now focuses on the parent in this no-nonsense guide to the lexicon of math. Math terminology and key concepts are defined and decoded into regular, everyday language to promote authentic understanding of what's at the heart of any math problem.
Other helpful elements are sample problems (with answers, so parents won't sweat it!) broken down step-by-step; calculator tips so parents can troubleshoot technology-related concerns facing their kids; visual representations of math for visual learners; and National Council of Teachers of Mathematics standards so parents can plan for what their children are responsible for in the upcoming grade and get the help they may need in the appropriate time frame. Finally, a handy timeline detailing which ages/grades kids need to know and master certain math skills helps parents understand the overall math snapshot for the middle school and high school years ahead.
Parents (and then students) learn how to kick word problems to the curb once they figure out how to simplify the language of math with Math for Moms and Dads' easy-to-follow lexicon and resource guide!
This unique and authoritative reference work contains around 2,000 clear and concise entries on all aspects of modern and contemporary art. Its impressive range of terms includes movements, styles, ...
A Dictionary of Skiri Pawnee is the first dictionary ever published of a Caddoan language. Formerly an independent tribe living along the North Fork of the Loup River in central Nebraska, the Skiris ...
"Another day, another dollar," "There's no such thing as a free lunch," "Better to live one day as a tiger than a thousand years as a sheep," "There is more than one way to skin a cat"--readers will ...
This first edition of A Dictionary of Dentistry provides over 4,500 definitions covering all the important terms and concepts used in dentistry today. Entries are written in clear and concise English ... |
Algebra 2
Description
Help your students discover the logic, order, beauty, and practicality of algebra. Throughout the course, students are encouraged to use their reasoning ability as they work with the axioms, rules, and principles of algebra. Concepts are developed and mastered through an abundance of worked examples and exercises, with an emphasis on word problems that relate to the physical world. Reviews at the end of each unit measure student progress, and special sections challenge the mathematically talented student. This text calls for a scientific calculator that has the trigonometric functions, statistics, powers, and roots |
Polar Form of Complex lesson that shows the relation between rectangular coordinates, polar coordinates, and complex numbers.
This addresses the first half of CA Trigonometry 17.0: Students are familiar with complex numbers. The can represent a complex number in polar form and know how to multiply complex numbers in their polar form. The second half of the standard is in the PowerPoint "Products & Quotients of Complex Numbers in Polar Form"
Presentation (Powerpoint) File
Be sure that you have an application to open this file type before downloading and/or purchasing.
541.5 |
Learning mathematics can be a challenge for anyone. Math Flight can help you master it with three ... graphics and sound effects, your interest in learning math should never decline. Help is always available in ... up on there basic arithmetic skills. Improve your math by taking a trip with Math Flight! ...
The objective of this Times Table Program is to make math fun and interesting. As the student continues to get correct answers to the questions, the Times Table grid will begin to fill up more and more. This the T-SQL scripting environment so you can perform mathematical operations on your data from within the database ... including 20 matrix-based functions and operations. - 7 table-valued numerical series generators including arithmetic, geometric and harmonic series, alternating harmonic series, the p-series, prime numbers up to 263, and the Fibonacci sequence. - ...
Looking for a software utility that would help math students plot various graphs? You've just stumbled upon ... perfectly suited for use by high-school and college math students. The program is capable of plotting Cartesian, polar, table defined, as well as specialty graphs, such as ... customizable axis options (color, style, width, grid), and table data import/export options. The one feature that makes ...
... solution to users who want to apply basic math functions to fields (columns) in MS Access tables. Easily add, subtract, multiply or divide between two fields or change one field by a constant number. This software will save you time by text file with data arranged in a space-separated table, and drawing up to 8 pages of histograms and XY plots, up to 64 graphs per page. The way in which the data is presented is defined in a simple Windows inifile, and most graph attributes can be adjusted as needed. ...
... site visitors to perform easily complicated real estate math. It features very UNIQUE lead generation feature - ... on the paper sheet. Other features are: amortization tables in almost every calculator, multi-lingual support, template-driven design, customizable interest compounding, currency symbol and initial values settings to match your market. This collection is ...
... ...
... combining graphics and complicated formatted text such as math equations in electronic and printed documents. A WYSIWYG ... allows precision alignment of equations. Fonts for special math characters and the periodic table are included in the price. This is a ...
... OpenOffice Writer, protection of cells in OpenOffice Writer table, OpenOffice Calc documents and sheets protection. Password loss is not as uncommon as you may think. Users can lose a password if it was entered with a typo, or using a different keyboard layout, or simply because they forgot where they ...
... to edit, to print and to copy the table into other applications. The software is able to work with arithmetic-, scientific-, memory-, percent-, statistic, base-n-calculations, scientific constants and units conversion. ...
... the stock pile on the left of the table, while the topmost card on the stock pile will be placed face-up on the table. Each player has a scoreboard on their left ... The current sum of the cards on the table is shown in the bracket on top of ... a prime number with the cards on the table, he wins the trick and scores points same ...
... and division problems are based on the multiplication table from 1 to 10, it teaches "mental math" in a painless way. Progressive help is given as needed when the student is having difficulty with a particular problem (not just a Wrong! ...
... units are also available. ProKon provides a periodic table of the elements (with pertinent data on each element) and many mathematical formulas, along with the density of over 625 different materials -- some common and some not so common. Context sensitive help is easily accessed ...
... calculations within calculations. Store calculation results in a table. Show a running total, group totals, grand totals, and item counts. Print and save tapes. Use up to 20 tapes per file to organize calculations. ...
... of useful information such as required electronics theory, math formulae and RF exposure safety information. All of this is just a mouse click away even while taking an on-screen practise test. Now you can study for that ham radio license at home with complete confidence. Of special interest is ...
... was designed to be a fast an easy-to-use mathematical function plotting application. This handy tool can be ... colors (background, axes, functions...), speed, precision, font size... Table of values for functions and sequences Plotting functions and sequences with a parameter. Easy navigation on the graph: move, zoom, scale... Print: choose scale, ... |
Getting
Assistance
When
Get help as soon
as you need it. Don't wait until the test is near. The new
material builds on the previous sections, so anything you don't understand now
will make future material difficult to understand.
Use the
Resources You Have Available
Ask questions in
class. You get help and stay actively involved in class.
Visit the
Instructor's Office Hours. Instructors like to see students who want
to help themselves.
Ask friends,
members of your study group, or anyone else who can help. The
classmate who explains something to you learns just as much as you do, for
he/she must think carefully about how to explain the particular concept or
solution in a clear way. So don't be reluctant to ask a classmate.
All students
need help at some point, so be sure to get the help you need.
Asking Questions
Don't be afraid to
ask questions. Any question is better than no question at all (at
least your Instructor/tutor will know you are confused). But a good
question will allow your helper to quickly identify exactly what
you don't understand.
Not too helpful
comment: "I don't understand this section." The best you
can expect in reply to such a remark is a brief review of the section, and
this will likely overlook the particular thing(s) which you don't
understand.
Good comment: "I
don't understand why f(x + h) doesn't equal f(x) + f(h)." This
is a very specific remark that will get a very specific response and
hopefully clear up your difficulty.
Good question:
"How can you tell the difference between the equation of a circle and
the equation of a line?"
Okay question:
"How do you do #17?"
Better question:
"Can you show me how to set up #17?" (the Instructor can
let you try to finish the problem on your own), or "This is how I
tried to do #17. What went wrong?" The focus of attention
is on your thought process.
Right after you get
help with a problem, work another similar problem by yourself.
You Control the Help You
Get
Helpers should be coaches,
not crutches. They should encourage you, give you hints as you need
them, and sometimes show you how to do problems. But they should not,
nor be expected to, actually do the work you need to do. They are
there to help you figure out how to learn math for yourself.
When you go to office
hours, your study group or a tutor, have a specific list of questions
prepared in advance. You should run the session as much as
possible.
Do you allow yourself
to become dependent on a tutor. The tutor cannot take the exams for
you. You must take care to be the one in control of tutoring
sessions.
You must recognize that
sometimes you need some coaching to help you through, and it is up to you
to seek out that coaching. |
We've heard you say that all students are not created equal when it comes to reasoning and math skills. Furthermore, we share your belief that the ability to reason in an organized and mathematically correct manner is essential to solving problems. That's why helping students improve their reasoning skills is also one of Cutnell & Johnson's primary goals. The following features will help students improve their reasoning skills:
Video Help, available through WileyPLUS, provides 3–5 minute office hour style videos tailored to the more challenging problems that bring together two or more physics concepts. These videos do not solve the problems, rather they point the student in the right direction by using a proven problem–solving technique: 1. Visualize the problem 2. Organize the data 3. Develop a reasoning strategy.
Math Skills appears as a sidebar throughout the text. It is designed to provide additional help with mathematics for students who need it, yet be unobtrusive for students who don't.
There's also a math skills module in WileyPLUS (a chapter 0) for students who want even more help.
Explicit reasoning steps in all examples explain what motivates the procedure for solving the problem before any algebraic or numerical work is done.
Reasoning Strategies for solving certain classes of problems are called out to encourage frequent review of the techniques used and help students focus on the related concepts
Analyzing Multiple–Concept Problems prompt students to combine one or more physics concepts before reaching a solution. First, they must identify the physics concepts involved in the problem, then associate each concept with an appropriate mathematical equation, and assemble the equations to produce a unified algebraic solution.
In order to reduce a complex problem into a sum of simpler parts, each Multiple-Concept example consists of four sections: Reasoning, Knowns and Unknowns, Modeling the Problem, and Solution.
Homework problems with associated Guided Online (GO) Tutorials have increased by 45% in this edition. Each of these problems in WileyPLUS includes a guided tutorial option (not graded) that instructors can make available for student access with or without penalty.
* GO tutorials facilitate strong problem–solving skills by providing a step by step guide on how to approach a problem. Multiple–choice questions in the GO tutorial include extensive feedback for both correct and incorrect answers. These multiple–choice questions guide students to the proper conceptual basis for the problem. The GO tutorial also includes calculational steps
Interactive LearningWare, available in WileyPLUS, consists of interactive examples, presented in a five-step format, designed to help improve each student's problem–solving skills.
Interactive Solutions, available in WileyPLUS, enable students to work out problems in an interactive manner while providing a model for the corresponding homework problem. |
Courses: Non-FL Students
Course Name:
Algebra I
Course Code:
1200310
Honors Course Code:
1200320
AP Course Code:
Description:
Algebra I is the foundation—the skills acquired in this course contain the basic knowledge needed for all future high school math courses. The material covered in this course is important, but everyone can do it. Everyone can have a good time solving the hundreds of real-world problems algebra can help answer.
Each module in this course is presented in a step-by-step way right on the computer screen. Hands-on labs make the numbers, graphs, and equations more real. The content in this course is tied to real-world applications like sports, travel, business, and health.
This course is designed to give students the skills and strategies to solve all kinds of mathematical problems. Students will also acquire the confidence needed to handle everything high school math has in store for them Quadratic Equations: Solving Quadratic Equations by Factoring and Using the Quadratic Formula
Graphical Parts of Quadratics Honors Only
Solving Real-World Problems Involving Quadratics
Using Graphing Technology
Radical Expressions
Simplifying Algebraic Ratios and Proportions
Simplifying Radical Expressions |
Another good book though starts at an elementary level but covers lot of fundamental topics such as geometry, topology and calculus and could be highly recommended for the honors programs is: What is Mathematics? By Richard Courant and Herbert Robbins.
Another good book though starts at an elementary level but covers lot of fundamental topics such as geometry, topology and calculus and could be highly recommended for the honors programs is: What is Mathematics? By Richard Courant and Herbert Robbins. |
Detail Table of Contents
Buy Now
Please allow 5 to 10 days for delivery.
Detail Table of Contents
Matrices : Chapter 5
SUMMARY:
Matrix is a set of 'm × n' numbers arranged in the form of rectangular array having 'm' rows and 'n' columns. It is called an m x n matrix. Matrices play an important role in modern techniques of quantitative analysis of managerial decisions. Matrices provide a compact way of representing a system of equations.
This chapter discussed about determinants, adjoint and inverse of a matrix. To the end of the chapter we have discussed how managers can use matrix methods like Cramer's Rule, matrix inversion method and Gauss - Jordan elimination method to solve linear equations related to various managerial problems. Thus, matrices play a vital role in a manager's decision making process. |
MATHEMATICS DEPARTMENT
The mathematics program at Mercy is designed to meet the needs of all our students and prepare them for the necessary college mathematics courses in their field of study. We encourage each student to consider her ability, goals and motivation, along with the teacher recommendation, when choosing her math course. The sequence outlines the four-year math program.
All students are required to have a graphing calculator. Mercy is currently using the TI-84 Plus.
Any student wishing to move up from College Prep level courses to Honors level courses must have a 95% average for the year thus far in the current math course and/or the recommendation of the current math teacher.
In this course, standard Algebra skills are introduced and developed. The topics include: real number system, linear equations and inequalities, compound inequalities, functions, slope and equation of lines, systems of equations and inequalities, exponents, radicals and polynomials. Some students registered for this course will be required to have math support throughout the year.
This course will introduce students to higher level high school work and can lead to Advanced Geometry/Algebra 2 or Honors Geometry placement in the sophomore year. The same material as in other Algebra 1 courses will be covered but in greater depth and a faster pace. Students are also introduced to some Algebra 2 concepts.
This course stresses the basic structure of geometry including, line , angle, triangle and circle relationships, polygons, right triangle trigonometry, unit circle trigonometry, area and volume of plane and solid figures. Algebra 1 skills are integrated within the context of the geometric concepts. Additional topics in Algebra 2 will be covered including the complex number system, polynomial functions, radical functions and rational exponents.
The goals of these course are to prepare students to work with more advanced mathematics and to give them the basic tools to apply Algebra in other courses of study. There is a major emphasis on identifying, graphing and solving quadratic equations. It is an expansion of the topics mastered in Algebra 1 along with applications.
*NOTE: Only 133 Algebra 2 includes trigonometry and provides the necessary preparation for Pre-Calculus as well as Physics.
FOUNDATIONS OF COLLEGE ALGEBRA
Course 140 CP
Grade 12 First Semester 1/2 credit
Prerequisite: An average of 80% in Algebra 2 and recommendation
This one semester college prep course is an introductory course to probability and statistics. It includes the topics of permutations and combinations and involves practical applications to statistical information.
HONORS PRE-CALCULUS
Course 143 Honors
Grade 12 Year 1 credit
Prerequisites: An average of 85% in Honors Algebra 2 and recommendation of teacher.
This course is designed primarily for the senior Honors math student who wishes to advance her studies in math in preparation for college. It will continue to build on and integrate all prior Algebra topics as well as introduce the following topics: polynomial, exponential, logarithmic, rational functions; sequence and series; and trigonometry. ADVANCED PRE-CALCULUS
Course 144 Advanced (2 weight)
Grades 10, 11 Year 1 credit
Prerequisites: 85% average in Advanced Geometry/Alg 2 or 94% average in Honors Algebra 2 and recommendation of teacher.
This course is for sophomores and juniors intending to take AP Calculus. It is a rigorous study and expansion of topics mastered in Algebra 2 including properties and graphs of functions; polynomial, rational, radical, exponential, logarithmic and sequential functions; trigonometric functions and identities; and vectors. Applications for the previous topics will be a major component of this class. STATISTICS 1
Course 152 Advanced (2 weight)
Grades 11, 12 Elective First Semester 1/2 credit
Prerequisite: Honors Algebra 2 or Advanced Geometry/Algebra 2
The focus of this course is learning the different data collection techniques and the many ways to organize, interpret, and present statistical information. The uses and misuses of statistics will be discussed. There will be an introduction to probability. Counting rules and discrete probability distributions will be applied. This course may be taken concurrently with another math course. STATISTICS 2
Course 153 Advanced (2 weight)
Grades 11, 12 Elective Second Semester 1/2 credit
Prerequisite: Statistics 1
This course is an extension of Statistics 1. Topics include understanding the normal distribution, confidence intervals and sample sizes, hypothesis testing, correlation and regression, and other analysis and testing procedures.
This is an intensive course in Differential and Integral Calculus. It is the culmination and integration of all previous math courses. Applications to real problems are used throughout the year. Students are expected to take the Advanced Placement (AB) Test or register for dual credit.
This course is a one semester extension of AP Calculus (AB). Topics from the AB course will be briefly reviewed as new topics are introduced and learned. Applications to real problems are used throughout the semester. Students are expected to take the AP Calculus (BC) Test or register for dual credit. Students will meet with the instructor during a common free time arranged during the day. MATH SUPPORT
Course 160
Grades 9, 10, 11, 12 Elective Time to be arranged
Prerequisites: Recommendation and/or testing |
Pattonville Precalculus application problems is not just math. Included concepts come from English, science, history, and others. Using common formulas for business, elementary geometry, science, and other subjects show the importance of algebra |
In preparation for the CompTIA A+ exam, this chapter covers many important details regarding the safe assembly and disassembly of your PC, voltage and power checks, working with and replacing the power supply, and power-saving tips.
This chapter takes you through some formula basics, including constructing simple arithmetic and text formulas, understanding the all-important topic of operator precedence, copying and moving worksheet formulas, and making formulas easier to build and read by taking advantage of range names |
Calculus, CourseSmart eTextbook
Description
This book is designed for a three-semester or four-quarter calculus course covering single variable and multivariable calculus for mathematics, engineering, and science majors.
Drawing on their decades of teaching experience, William Briggs and Lyle Cochran have created a calculus text that carries the teacher's voice beyond the classroom. That voice–evident in the narrative, the figures, and the questions interspersed in the narrative–is a master teacher leading students to deeper levels of understanding. The authors appeal to students' geometric intuition to introduce fundamental concepts and lay the foundation for the more rigorous development that follows. Comprehensive exercise sets have received praise for their creativity, quality, and scope.
CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book.
Table of Contents
1. Functions
1.1 Review of Functions
1.2 Representing Functions
1.3 Trigonometric Functions and Their Inverses
2. Limits
2.1 The Idea of Limits
2.2 Definitions of Limits
2.3 Techniques for Computing Limits
2.4 Infinite Limits
2.5 Limits at Infinity
2.6 Continuity
2.7 Precise Definitions of Limits
3. Derivatives
3.1 Introducing the Derivative
3.2 Rules of Differentiation
3.3 The Product and Quotient Rules
3.4 Derivatives of Trigonometric Functions
3.5 Derivatives as Rates of Change
3.6 The Chain Rule
3.7 Implicit Differentiation
3.8 Related Rates
4. Applications of the Derivative
4.1 Maxima and Minima
4.2 What Derivatives Tell Us
4.3 Graphing Functions
4.4 Optimization Problems
4.5 Linear Approximation and Differentials
4.6 Mean Value Theorem
4.7 L'Hôpital's Rule
4.8 Antiderivatives
5. Integration
5.1 Approximating Areas under Curves
5.2 Definite Integrals
5.3 Fundamental Theorem of Calculus
5.4 Working with Integrals
5.5 Substitution Rule
6. Applications of Integration
6.1 Velocity and Net Change
6.2 Regions between Curves
6.3 Volume by Slicing
6.4 Volume by Shells
6.5 Length of Curves
6.6 Physical Applications
7. Logarithmic and Exponential Functions
7.1 Inverse Functions
7.2 The Natural Logarithmic and Exponential Functions
7.3 Logarithmic and Exponential Functions with Other Bases
7.4 Exponential Models
7.5 Inverse Trigonometric Functions
7.6 L'Hôpital's Rule Revisited and Growth Rates of Functions
8. Integration Techniques
8.1 Integration by Parts
8.2 Trigonometric Integrals
8.3 Trigonometric Substitutions
8.4 Partial Fractions
8.5 Other Integration Strategies
8.6 Numerical Integration
8.7 Improper Integrals
8.8 Introduction to Differential Equations
9. Sequences and Infinite Series
9.1 An Overview
9.2 Sequences
9.3 Infinite Series
9.4 The Divergence and Integral Tests
9.5 The Ratio, Root, and Comparison Tests
9.6 Alternating Series Review
10. Power Series
10.1 Approximating Functions with Polynomials
10.2 Power Series
10.3 Taylor Series
10.4 Working with Taylor Series
11. Parametric and Polar Curves
11.1 Parametric Equations
11.2 Polar Coordinates
11.3 Calculus in Polar Coordinates
11.4 Conic Sections
12. Vectors and Vector-Valued Functions
12.1 Vectors in the Plane
12.2 Vectors in Three Dimensions
12.3 Dot Products
12.4 Cross Products
12.5 Lines and Curves in Space
12.6 Calculus of Vector-Valued Functions
12.7 Motion in Space
12.8 Length of Curves
12.9 Curvature and Normal Vectors
13. Functions of Several Variables
13.1 Planes and Surfaces
13.2 Graphs and Level Curves
13.3 Limits and Continuity
13.4 Partial Derivatives
13.5 The Chain Rule
13.6 Directional Derivatives and the Gradient
13.7 Tangent Planes and Linear Approximation
13.8 Maximum/Minimum Problems
13.9 Lagrange Multipliers
14. Multiple Integration
14.1 Double Integrals over Rectangular Regions
14.2 Double Integrals over General Regions
14.3 Double Integrals in Polar Coordinates
14.4 Triple Integrals
14.5 Triple Integrals in Cylindrical and Spherical Coordinates
14.6 Integrals for Mass Calculations
14.7 Change of Variables in Multiple Integrals
15. Vector Calculus
15.1 Vector Fields
15.2 Line Integrals
15.3 Conservative Vector Fields
15.4 Green's Theorem
15.5 Divergence and Curl
15.6 Surface Integrals
15.6 Stokes' Theorem
15.8 Divergence Theorem |
Video Summary: This learning video is designed to develop critical thinking in students by encouraging them to work from basic principals to solve a puzzling mathematics problem that contains uncertainty. One class session of approximately 55 minutes is necessary for lesson completion. First-year simple algebra is all that is required for the lesson, and any high school student in a college-preparatory math class should be able to participate in this exercise. Materials for in-class activities include: a yard stick, a meter stick or a straight branch of a tree; a saw or equivalent to cut the stick; and a blackboard or equivalent. In this video lesson, during in-class sessions between video segments, students will learn among other things: 1) how to generate random numbers; 2) how to deal with probability; and 3) how to construct and draw portions of the X-Y plane that satisfy linear inequalities |
This book guides students as they construct and manipulate geometric figures, and discover relationships and theorems on their own. It features over 100 activities covering virtually every concept st... More: lessons, discussions, ratings, reviews,...
These activities provide students with the opportunity to explore geometric concepts such as symmetry, transformations, and even fractal geometry in a way no other teaching tool can. The dynamic ca... More: lessons, discussions, ratings, reviews,...
This book guides students through a variety of proofs and applications of the Pythagorean theorem. By constructing and dynamically manipulating figures, students visualize the theorem and gain insight... More: lessons, discussions, ratings, reviews,...
Author Michael Battista has built what he calls the Shape Makers computer microworld, a series of explorations in which students develop dynamic mental models for thinking about geometric shapes an... More: lessons, discussions, ratings, reviews,...
A video that focuses on the TI-Nspire graphing calculator in the context of teaching algebra. In this program the TI-Nspire is used to explore the nature of linear functions. Examples ranging from ... More: lessons, discussions, ratings, reviews,...
Cabri 3D is interactive solid geometry software based on 3rd generation Cabri technology. It enables users to build and manipulate figures in 3D. It is entirely designed and developed by Cabrilog, and... More: lessons, discussions, ratings, reviews,...
Geocadabra is dynamic geometry software that supports students learning 2D and 3D geometry, functions and curves (with analysis), and probability.
The software was developed in Holland, and is avai...Students explore the relationship between equations and their graphs in this hands-on learning environment where they investigate, manipulate, and understand linear, quadratic and other graphs. They ...A test and worksheet generator for Pre-Algebra teachers. Create exactly the types of questions you are looking for. Lay out the questions on the page with automatic or manual spacing. Over 90 Pre-A... More: lessons, discussions, ratings, reviews,...
Tutorial fee-based software for PCs that must be downloaded to the user's computer. It covers topics from pre-algebra through pre-calculus, including trigonometry and some statistics. The software pos... More: lessons, discussions, ratings, reviews,...
QuickMathFacts is a tool that can be used at school or at home to increase proficiency in math fact memorization. It presents problems, within a selected set and a selected operator (addition, sub... More: lessons, discussions, ratings, reviews,...
Small Stella is the ideal entry-level polyhedron program for schools or anyone interested in geometry, with hundreds of polyhedra provided. Print out the nets required to build your own paper model... More: lessons, discussions, ratings, reviews,...
Cram is test preparation software to use on a mobile device. It allows you to create, import, share, and study for tests. Cram is suited for studying for job training, certifications, homework help, t |
Study theoretical or applied mathematics, statistics or actuarial science and build problem-solving skills that will prepare you for a wide range of careers.
As a mathematician, your expertise will allow you to make contributions to many areas like business, industry, government, education and more. The study of mathematics includes comprehensive training in thinking, reasoning and problem-solving skills. These skills will strengthen your education, make you a well-rounded individual and enhance your appeal to employers worldwide. |
Hello students, Welcome back from summer break. Locate your course from the following : Math Studies year 2 - you will be testing out this year. We will review all seven topics including calculator functions. We will begin with a brief overview of STATS followed by continued lessons relating to Differential Calculus. You will also have an internal assessment most of you have already completed as part of your STATS case study paper which you completed last year. Math Studies year 1: IB STATS/Differential Calculus - you will be taking the AP stats exam at the end of the year followed by Differential Calculus lessons during fourth quarter. Advanced Placement Stats students you will also complete the AP stats exam at the end of the year. Quantitative Analysis (dual enrollment) students will be completing this college level course as part of the BCC dual enrollment program, hence this is in fact a college level course within high school setting and it will be treated as such. Please remember to access all resources and websites I provided for your use to prepare for the up and coming assessments. Year one IB students. Please remember that the primary goal of this course is to prepare you for the AP stats exam. We will spend three quarters preparing you for the exam and the fourth quarter on differential calculus. There is an overview of differential calculus throughout the AP stats course as Calculus concepts are covered in this curriculum as well. You will also be working on your internal assessment throughout this portion of the course. Your internal assessment will be due during Math Studies year 2. YEAR 1 students please check out the link labeled summary of formulas and concepts by chapter. Math Studies year 2 students must turn in their internal assessment in order to be eligible to take the IB external assessment. You can access Sample Exams from prior years in the website: In addition the following sites: apcentral free response questions, PURPLEMATH, Stattrek, IBAP STATS LESSONS, Hyper stat tables, z-score table, SAT prep, and MATH TUTOR are informative websites. There is a website which I lined as: All Stats tables in one website that has ALL of the stats tables you need to know how to use. For AP Calculus, Pre-Calculus or Algebra 2 Help students who need extra help with selected topics, you can watch a video tutorial on the topic of your choice on All Quantitative Analysis dual enrollment students you will have access to You have also the possibility of accessing the ipod component relating to this course. You can also access the online learning center and the BCC campus website. There is another website I strongly recommend called ALEKS. This website can be used by all courses as the program covers all subjects taught throughout K-12. There are many interesting ways to improve your math and logic skills. Try Brainteasers. Or try joining Mensa, admission test required for membership. I look forward to providing you all of the resources, support, and instruction to facilitate your school year and ensured success. Keep tabs on your child's grades by logging into Pinnacle. Important links: ALEKS All Stats tables in one website AP Calculus Tutorials apcentral free response questions Brainteasers IBAP STATS LESSONS Hyper stat tables MATH TUTOR Mensa Miramar High School Pinnacle PURPLEMATH SAT prep Stattrek Summary of formulas and concepts by chapter z-score table.
Tutoring link: Khan Academy
Additionally, if you are interested in learning more about my academic and professional background you should log onto Linkedin.com where you can preview my credentials.
Welcome back! Dr. B
Advanced Placement Statistics
Hi all,
Please use the following webstie to access all materials and information. |
Linear Algebra The Eighth Edition of Gareth Williams' classic text is designed for the introductory linear algebra course, and provides a flexible blend of theory and engaging applications for students within engineering, science, mathematics, business management, and physics. The text's 29 core sections within 8 chapters are organized into 3 Parts: Part 1 introduces the basics, presenting systems of linear equations, vectors and subspaces of R(n), matrices, linear transformations, determinants, and eigenvectors. P... MOREart 2 builds on the material presented in Part1 and goes on to introduce the concepts of general vector spaces, discussing properties of bases, develops the rank/nullity theorem, and introduces spaces of matrices and functions.Part 3 completes the course with many of the important ideas and methods of numerical linear algebra, such as ill-conditioning, pivoting, and LU decomposition.Throughout the text the author takes care to fully and clearly develop the mathematical concepts first and then provide modern applications to reinforce those concepts. The applications range from theoretical applications within differential equations and least square analysis, to practical applications in fields such as archeology, demography, electrical engineering and more. |
Want to learn more about Maple? These recorded webinars provide an in-depth demonstration of Maple.
Maple 16 Training for Educators and Researchers (45 min)
Industry Applications of Maple 16 (45 min)
This webinar offers a quick and easy way to learn some of the fundamental concepts for using Maple. Learn the basic steps on how to compose, plot and solve various types of mathematical problems. This webinar will also demonstrate how to create professional looking documents using Maple, as well as the basic steps for using Maple packages.
New to Maple? These video tutorials that are specially tailored and student oriented to demonstrate Clickable Math techniques for solving the most common math problems arising in high school, college, or university math courses. |
When I was at Buffalo 30 years ago, Tony Ralston advocated teaching discrete math instead of calculus to 1st year students. I taught it out of some notes he had prepared, and thought the students found it harder than calculus. It was easier to relate calculus topics to things they already knew about than it was to do that for the topics in his notes.
I'm pretty sure those notes became a textbook, so you can probably get a copy and see one man's idea of what should/could be taught to students before calculus. |
Summary: This module is intended to help teachers explore methods by which students work with numbers to formulate generalizations about operations. By expanding students understanding of the properties that underlie the number systems introduced in the elementary grades, they will be prepared to think algebraically for success in middle school and beyond |
A Potpourri of Graphical Solutions Using the TI-82
Alex Bezjak and David A. Young
The TI-82 Graphics Calculator, Texas Instrument's latest entry in the graphing calculator fields, can be quite useful in enhancing the teaching and learning of a wide range of mathematical topics.
This article will offer detailed instructions on the key-strokes necessary to analyze and illustrate problems dealing with
1. iterations with tables of values
2. graphing the orbits of iteration
3. descriptive statistics
4. inferential statistics
The authors will assume that the reader is vaguely familiar with appropriate function, editing, window, and mode setting keys. Make sure that the calculator is in the default mode - for this accept the entire left side of all menu choices when pressing the [ We will use the convention that a word in a represents a key on the TI-82, a word in BOLD represents an option from a menu listing, and I talics indicates a function key, which is accessed by the blue key in the first column.] key.
I. Iteration With Tables Of Values
We will look at two methods of iterating a function. They are
1. using theANS key
2. using the seq mode found in the menu of the key.
Method One
Let's produce six iterations of f(x) = x2 using the ANS key. Also let's start with a "seed" value of 0.5. Now enter these key-strokes:
These successive strokes produce an outcome of .25 which is the value of f(.5) = (.5)2. Now to generate the other five iterations, try these strokes:
. These steps set up an iterative algorithm that will generate the remaining iterations by pressing four consecutive times, resulting in a value of 5.42101086 E-20. The reader should note that pressing takes each f(x) value and places it in the domain and squares it.
Method Two
Let's attempt to iterate f(x) = x2 six times using the sequence mode. Press and use the arrow keys to highlight the seq option and press . These strokes place the calculator in the sequence mode. Now press which is the QUIT option that returns you to the home screen. Now enter and the screen should read:
" Un = "
" Vn = "
With the cursor blinking at " Un = " and any previous function cleared, key in these steps: . These steps place the function f(x) = x2 in the sequence mode which can be iterated by establishing the appropriate values in the window settings. For the window settings for this problem in the sequence mode try these numbers by pressing and using these values:
Un Start = 0.5, Vn Start = 0, n Start = 0,
n Min = 0, n Max = 6, Xmin = 0, Xmax = 6,
Xscl = 0, Ymin = 0, Ymax = 0.5, Yscl = 0
After setting these values press which lists the "Table" values for the first six iterations. You can confirm your values from the previous method.
II. Graphing the Orbits of Iteration
We will look at two methods of graphing an iterated function. They are
1. using the Time graph
2. using the Web graph.
Method One
If the reader wants to look at the relationship for f(x) = x2, (Un = Un-1 2), in terms of the number of iterations (n ) and the value of the function (Un ) on a graph, she will need to set the "Window" and "Format" to appropriate values. The current setting in the "Window" from part I will suffice for the "Time" graph, if you set the "Format", accessed from the key by high-lighting the FORMAT with the cursor keys and selecting the Time option. Now press to see the graph. You may press and use the cursor keys to see your values along the graph.
Method Two
To look at the Web plot of the function f(x) = x2 while in the seq mode, you will need to change the FORMATin the menu and change the values for x and y.
First press toggle right to FORMAT and press . This will place the blinking cursor on the word Time in the FORMAT menu. Now toggle right to the word Web and press . Press again to change the values for x and y. Select x to range from -1 to 1 and y the same so that you will see your function and the line f(x) = x. This will work if your seed "Un Start" is appropriate. Now press and and repeatedly press the right arrow, to create the Web, until you reach a cycle, a point of attraction, or it blows up. When you return to the Time plot make sure you reset your window values for x and y.
III. Descriptive Statistics
Statistical Analysis
Descriptive statistics and a histogram can be shown on the TI-82 as in the following example. Before entering these data, you might clear out the list remaining from a former problem. To clear old list, press and high-light 4:ClrList and press . The screen shows ClrList and a blinking cursor.
Key in then press toggle left one space, press . These strokes clear all data in list one and list two. Now press and with 1:Edit... high-lighted press . In the L1column, key in these 25 test scores, press after each. The scores are:
The bottom left of the screen should show that L1(25) = 72 which means that 25 data items have been entered with the last being 72.
To sort these data in L1 and L2 in a descending manner try these steps: and toggle down to 2:SortD( andpress . Complete this option by typing in . These steps arrange all items in L1 and L2 as pairs from the largest to the smallest for values in L1 since it was listed first in the sort command. In this problem we choose to give each individual score, so we will use a frequency of one. Use the arrow keys to get the cursor in cell L2(1) and key in and and repeat this process until all cells from L2(1) to L2(25) have the value of one. The reader should know that the TI-82 will default to a frequency of one in the plot mode, if selected.
For the univariate statistical analysis of these data press , toggle over to CALC and press twice. The screen shows six items including the mean, =73.6 and a sample standard deviation, = 18.196 (rounded off to three decimal places).
Histogram
To get a frequency chart (Histogram) of these items, press which activates the STAT PLOTmenu. Select 1:Plot1 by pressing . In plot 1 select the following settings: On, and for Type select the 4th icon which is the image of the histogram. For the Xlist choose L1 and for the frequency choose L2.
Screen settings for this graph are accessed through the window key. Press and try these values: Xmin = 25, Xmax = 95, Xscl = 10, Ymin = -5, Ymax = 10, Yscl = 10. Make sure all the functions in are turned off. Press and high-light the 9th choice 9:ZoomStat and press . A histogram of these given data appears on the screen and using the key, with the arrows, you can see the corresponding ranges of scores and their frequencies.
IV. Inferential Statistics
Linear Regression
To explore linear regression, lets look at these following data which relates temperature in degrees Celsius to a number that measures viscosity in a certain petroleum product. We chose L1 to contain the temperature and L2 for the measure of the corresponding viscosity. There are 8 pairs of data. L1 is the list {15, 20, 25, 27, 35, 40, 43, 47}. Toggle over to L2(1) and enter these numbers: {12, 13, 17, 19, 23, 26, 30, 31} and remember to press after each entry.
To get a scatter graph of these data, key in and select 2:Plot2 by pressing . Make sure plots 1 and 3 are turned off. In plot 2 select the following settings: On, and for Type select the 1st icon which is the image of the scatter plot. For the Xlist choose L1 and for the Ylist choose L2 and for the Mark choose the box. Key strokes should give a scatter plot of these data.
To get a regression line for these data, go to the select the CALC menu. Toggle down to 4:Med-Med press twice. This will do a regression analysis on the lists selected in the SetUp ( we assume L1 and L2). To place the regression equation in the function window, press , clear off Y1, make sure all other functions are off or cleared. Now enter these strokes: toggle to 5:Statistics... and press . Toggle right to EQ and down to 7:ReqEQ and press . The corresponding values will now appear on the function screen as a regular equation. Press and see the Med-Med regression line with the scatter plot of your data.
Non-Linear Regression
When your data are non-linear you can use the TI-82 to examine the relationship by placing it in a linear form. Consider these following data collected from an experiment:
X Y
1
2.0
2
7.0
3
15
4
27
5
42
6
61
7
83
First we need to plot the data to get a feel for the general shape of the relationship. Place the data in a list by pressing and selecting option 1:Edit by pressing . This places you in the first cell of the list L1. Move up into the heading of the list by pressing the up arrow key. This will place you in the heading of the list. Press if the list is not empty, or if it has more than 7 data points in it, since that is what you are working with. This step is not necessary if you fill the list by using the key or if you use a sequence. Now enter the data for X in list L1and the values for Y in list L2 . This is done by placing the cursor in the appropriate cell, keying in the values, and pressing , then repeating the data entry, since your cursor will move down in the list each time. Once you have the data entered in the two lists you will want to look at their plot.
To plot a set of data select the STAT PLOT by pressing the keys. This will give you a menu of three plots to work with, as well as the possibility of turning all plots on or off. Since you want only one plot, select 1:Plot1 by pressing when it is high-lighted with the cursor. Press to highlight the On choice, move down by pressing thearrow key, and select the scatter plot, the automatic option for this line, by pressing . Now move down to the Xlist line and select, as the independent variable, L1 by pressing . Then move down again to the Ylist line and move right to place the cursor on the L2 option. Press to select this. The last line on this menu is for the type of mark to be used in the plot. Since we have only one plot to work with the previously selected option will suffice. Exit this menu by pressing the key (you should be in the function mode). Make sure all of your functions in the menu are turned off and that the other plots are off. Press and select option 9, 9:ZoomStat , by pressing . You will then get a plot of your data.
As you look at the plot, you should try to recognize the type of graph it is, linear, quadratic, cubic, exponential, logarithmic, etc. In this case, let us say that we think it is quadratic. If this is the case, we could take the square root of the Y values in L2 and compare them to X, expecting a linear relationship. To do this we would like to place into the third list, L3. This can be done from the home screen by pressing: . Now you want to do a linear regression on list 1 and 3. To do this you will need to press: move to the right to high-light CALC press . If you look at the value of r, you should see .9999026873. This is the regression coefficient and, since it is close to 1.0000, you can see you have a good fit. To look at this in greater detail, press and clear off Y1 by pressing . Then place the regression equation into Y1by pressing , the right arrow twice to EQ and then press to select 5:Statistics..., EQ, 7:RegEQ. Now, with all your functions off - except Y1, set up another plot, on STAT PLOT , using 2:Plot2 . Make sure you turn off plot 1, and repeat your zoom adjustment. This graph will be of your linear regression equation and of the data (X, ). If this looks good, and it should, you have a fit (i.e., it was a quadratic).
You must now convert your linear equation Y=aX+b into the form y=Ax2 + Bx + C. To do this take your linear equation and square it, so that you have (1.2866219332929X+.07215863765871)2 as the function that is connected to the data you collected. This would be approximately: f(x) = 1.66x2 + 0.186x + 0.005. If you look at this function plotted against L1 and L2 from your plot 1, you will see the fit.
However, as a matter of accuracy of fit for f(x) = 1.66x2 + 0.186x + 0.005, the reader is advised that the residuals for this function and the actual data be extracted. Explanations of residuals and their use in determining the accuracy of a linearized function can be found in a variety of books on data analysis. Time and space constraints prevent the authors from describing a detailed set of instructions about residuals using the TI-82.
A program for the TI-82 that will give the residuals of a set of data approximated by a function, stored in Y1 is given without explanation. |
Math Readiness
if you obtained a mark under 80% in grade twelve math (especially if you are planning to enter a science or engineering program)
if you feel that you could benefit from a refresher course in math topics that are used in university programmes in the sciences, engineering, or commerce.
At this non-credit math review, you'll learn specific skills (such as solving exponential equations), but we'll also focus on more general abilities, such as being able to understand mathematical writing and being able to express ideas in mathematical notation.
You'll review:
algebraic skills
functions
graphing
geometry
trigonometric functions
exponential and logarithmic functions
and more.
We'll help you figure out how to solve mathematical problems - how problems can be analyzed, types of approaches to different problems, and verifying the correctness of solutions. These skills are useful in any university-level science or math course.
Please note that most students benefit from taking Math Readiness before taking a course in calculus.
Anyone may register for the Math Readiness course, not just University of Saskatchewan students.
Course Content Information
Please visit the Math Readiness Course Content page for further information about the mathematical topics covered in Math Readiness.
Three Types of Courses
Math Readiness Summer Course (Summer Camp)
This is an intense review of mathematical topics to help students prepare themselves for first-year university mathematics. During the summer course, we'll help new university students get comfortable with the university environment, like the lecture format, which is used by most university instructors. Each short "math readiness" lesson will be given as a lecture, followed by a problem session. During the problem session, you'll work with other students in small groups with the guidance of senior class assistants.
This course takes place during two weeks in August, starting at 8:30am (or thereabouts) daily, with an hour or so for lunch.
In addition to the math classes, students who want to will be able to tour the campus to help acquaint themselves with the University of Saskatchewan. And students will have enough free time for other activities, such as familiarizing themselves with the city, or just relaxing.
Please register by phone if you are registering after August 1. Space is limited, so we encourage you to register early (before the end of July).
To register by phone, call the Centre for Continuing and Distance Education's registration office at 966-5539.
Math Readiness Evening Courses
These courses are offered during the fall and winter terms of the University's Regular Session, provided there is sufficient interest. In past evening courses, students have met for two hours on Tuesday and Thursday evenings, or on Monday and Wednesday evenings, for approximately 10 weeks.
Dates and Times for Fall 2010 September-December 2010, Tuesdays and Thursdays, 7-9pm
Start date and end date September 21, 2010 to November 25, 2010
Fee: $270 plus tax
Dates and Times for Winter 2011
Start Date: January-April 2010: TBA
Fee: $270 plus tax
Online Math Readiness Course
If you are interested in registering for the online Math Readiness course, please contact Holly Fraser at [email protected].
__________________________________________________
For more information about the content of the programs phone (306) 966-2742 or e-mail us at [email protected].
For more information about administrative questions, phone (306) 966-1739 or the Centre for Continuing and Distance Education's Registration Office at (306) 966-5539 or e-mail us at [email protected].
To print a copy of our flyer containing a registration form, download the following PDF file: Math Readiness Flyer
To register phone the Centre for Continuing and Distance Education registration office at (306) 966-5539. |
In my district, and many others, Algebra II is a graduation requirement. Given that requirement, I find myself asking what life skills the class can give everyone, whether they continue to practice mathematics or not—and not just from math class in general, but specifically from Algebra II.
For example, an oft-quoted justification for requiring geometry is to teach students to "think logically". In the 1930′s, Harold Fawcett taught a geometry class in which students learned, and practiced, thinking logically in non-mathematical contexts.
I wonder if a good candidate for a life skill that we hope transfers from Algebra II would be this one from Bowen Kerins, one of the authors of CME:
One thing a great context / question also gives you is the experience of figuring out what information is important and what sort of abstraction is most useful for extracting and using the right information thoughtfully. And that's a skill a lot more adults will use than factoring …
If that's to be our transferable skill, then we'll need to practice it: have lots of non-mathematical examples where "extracting and using the right information thoughtfully" is required. And I have to admit: I'm so unconscious of when and how I am using this skill I'm not at all sure how to begin thinking of examples!
>have lots of non-mathematical examples where "extracting and using the right information thoughtfully" is required.
The question in my mind is, is there any evidence that practicing the skill is extraction and selection in a mathematical context helps in any other context? If no, then we should just dump Algebra 2 and have a course on extraction/selection of information.
Until I hear otherwise, I'm going to assume that (like so many things) the mathematical skill of extraction isn't transferable to other domains.
I think that everyone benefits from learning X, even if X is totally useless for them. The most important thing that anyone can leave school with is an accurate understanding of how to learn something new, I mean how to really learn something new, especially if it's difficult, and especially if it's supposed to be miserable.
Most kids have no use for the skill of modeling functions, and most kids have no need for the mathematical skill of extraction/selection of information. That stuff doesn't transfer to new domains. But I'm more confident that an accurate picture of learning math will transfer to other domains, i.e. a person who thinks that math is learned a certain way will believe that other subjects are learned a certain way.
Of course, that's a testable hypothesis. And I'm willing to bet that if we don't make the connection between math and other subjects, the conception of learning won't transfer. But this seems valuable and relatively available for all students in all of my classes.
Agreed. And people benefit from learning math, specifically, even if they don't practice later, just as they do from learning music or poetry–it's exposure to and inclusion in the human experience. But is there really no larger lesson to be taken from Algebra II, that is specific to Algebra II, other than how to do Algebra II? Maybe this is a stupid question, but if I found one, it would sure be easier to focus my year. |
The Calculus Tutor DVD Series will help students understand the fundamental elements of calculus- -how to take algebra and extends it to include rates of change between quantities. Concepts are introduced in an easy to understand way and step-by-step example problems help students understand each part of the process.
This lesson teaches students how to use trigonometric substitutions to recognize integrals, solve integrals, set up the substitution properly, and carry out the integration. Grades 9-12. 23 minutes on DVD. |
Questions About This Book?
The Used copy of this book is not guaranteed to inclue any supplemental materials. Typically, only the book itself is included.
Related Products
Algebra For College Students
Algebra For College Students
Algebra for College Students
Algebra for College Students
Connect Math Access Card for Algebra for College Students
ConnectPlus Math Access Card for Algebra for College Students
Loose Leaf Version for Algebra for College Students
MathZone Student Access Card t/a Algebra for College Students
Student Solutions Manual for Algebra for College Students
Summary
Student Solutions Manual:The Student's Solutions Manual provides comprehensive, worked-out solutions to all of the odd-numbered exercises. The steps shown in the solutions match the style of solved examples in the textbook. |
rier Transform and Its Applications
This text is designed for use in a senior undergraduate or graduate level course in Fourier Transforms. This text differs from many other fourier ...Show synopsisThis text is designed for use in a senior undergraduate or graduate level course in Fourier Transforms. This text differs from many other fourier transform books in its emphasis on applications. Bracewell applies mathematical concepts to the physical world throughout this text, equipping students to think about the world and physics in terms of transforms. The pedagogy in this classic text is excellent. The author has included such tools as the pictorial dictionary of transforms and bibliographic references. In addition, there are many excellent problems throughout this book, which are more than mathematical exercises, often requiring students to think in terms of specific situations or asking for educated opinions. To aid students further, discussions of many of the problems can be found at the end of the book.Hide synopsis
Reviews of The Fourier Transform and Its Applications
A generally excellent book, and, incidentally the one recommended by Osgood in his YouTube course.
The level is about the advanced undergrad and beginning graduate student and it includes topics such as multidimensional integrals but little coverage of the FFT and a rigorous treatment of the delta |
This book focuses on essential knowledge for teachers about proof and the process of proving. It is organized around five big ideas, supported by multiple smaller, interconnected ideas—essential understandingsThe study of geometry—whether taught as a stand-alone or as a series of topics integrated within other courses—develops core ideas, concepts, and habits of mind that students will need as users of mathematics and as lifelong learners.
The teaching and learning of mathematics involves far more than memorizing procedures and applying algorithms. Problem solving, conjecturing, constructing and critiquing arguments, and communicating and representing mathematical ideas are at the heart of what we are trying to achieve in the classroom. The 2012 Focus Issue of MTMS provides examples and ideas for teachers to implement in their classroom toward these goals.
A valuable resource to any mathematics teacher, this rich collection of mathematical tasks will enliven students' engagement in mathematical thinking and reasoning and help them succeed in the classroom.
The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research. |
Tapping into mathematicsBy the end of this unit you should have:
started to become familiar with your scientific or graphics calculator and its use in investigating everyday problems;
developed good practice in relation to calculator use;
be able to use your calculator for the following:
arithmetic involving the operations of +, −, ×, ÷ and the use of brackets;
squaring and square rooting numbers;
reciprocals and powers of numbers;
calculations involving percentages, large and small numbers, scientific notation and ;
be able to understand the concepts of a mathematical function and its inverse (doing and undoing), rounding answers appropriately, fixing the number of decimal places displayed by a calculator, storing numbers in a calculator memory.
Tapping into mathematics
Introduction
This module is designed for students who have a graphics or scientific calculator. It gives some examples from the TI-84. So if you have a different calculator, some things may be a little different and you may need to consult your instruction booklet. There is a lot to learn about any calculator and it may take you some time to get to know how to use its many facilities. This module focuses on using it to do arithmetic. Even in this limited role, you will find it a powerful tool with many advantages. Depending upon your previous experience using a calculator, this module may take you more or less time than others.
If you intend to register for the Open University's MU120 course you will need to purchase the TI-84 calculator, however, you will still be able to complete this unit by using any other graphic or scientific calculator |
Mathematics Web Resources
Educational Sites
Adventures in Education™ Adventures in Education™ is an interactive site that offers information and services to help you finance your education, select a school, and plan a career. The Texas Guaranteed Student Loan Corporation (TG) sponsors this site.
Cornell Theory Center Math & Science Gateway The Cornell Theory Center is committed to providing a wide range of educational services to the national community. This Gateway provides links to resources in mathematics and science for educators and students in grades 9-12.
e-Math Home Page The American Mathematical Society continues to fulfill its mission with programs that promote mathematical research, increase the awareness of its value to society, and foster excellence in mathematics education.
Pathways to School Improvement Pathways to School Improvement discusses critical education issues such as at-risk children and youth, safe and drug-free schools, parent and family involvement, and the transition from school to work. |
CCGPS changes are coming this year 2012-2013. Unit 1 Number Systems. Students will continue to apply and extend rational numbers. We will learn more about integers, opposites, & absolute value. Unit 2 consist of our pre-algebra unit: expressions and equations. These two units are the foundation for a successful year in 8th and 9th grade algebra. |
Math to Build On: A Book for Those Who Build
Description
This is a simple and straightforward book which explains the basic math used in the construction trades, manufacturing, and design. Since everything assembled consists of either straight lines, curved lines or a combination of both, the ability to calculate circles and right triangles is essential for anyone who builds and wants to be in command of their work every step of the way. Written in a refreshingly casual style, this book uses an easy-to-follow, stair step learning format to help you master that information. It starts with fractions and decimals and guides you through the information needed to solve practical problems. The result is increased efficiency, productivity and confidence in your work. |
Welcome to the Math Lab Home Page
Purpose
The purpose of the Math Lab at WWCC is to provide a comfortable, quality, learning environment. Tutoring services are offered free of charge to all currently enrolled WWCC students. We help with mathematics while encouraging student independence and responsibility.
Services
Experienced and knowledgeable math tutors available throughout the day to help with all math courses offered at WWCC
Apple and Windows computers with math and science software
Calculators and textbooks
The Math Lab is a peer-led service that is primarily staffed by WWCC students.
You do not need an appointment. We work on a drop-in basis only.
Best Practices
Many students find the most successful way to use the Lab is on a daily basis as an addition to their classroom experience.They find that completing their homework in the lab serves the dual purpose of getting the work done and having their questions answered by a knowledgeable tutor.
We have a few things we expect of those who use the Tutoring and Learning Center.
Be respectful of others studying.
Cell phone ringers must remain off.
Talking on a cell phone is prohibited.
Eating or drinking at the computers is not allowed.
Excessive noise is not allowed.
Noise from headphones is not allowed (headphones are allowed, but must not be audible to others). |
Singapore
Singapore Math approaches math with the distinct goal of teaching students to think mathematically. Students are challenged to take the skills of math to the next level with challenging word problems and analytical math practice activities.
The Singapore Primary Mathematics U.S. Edition (for grades 1-6) series of elementary math textbooks and workbooks uses a progression from the concrete concept to the pictorial to the abstract.
This takes students from the basic concrete instruction (illustrated clearly with pictures and diagrams) to abstract concepts that engage them at an analytical level. This approach develops students who are able to think mathematically, to engage in an active thinking process and to communicate mathematical ideas. Thus, Singapore Math sets out to prepare students for more advanced mathematics.
The Singapore New Elementary Mathematics Syllabus D—Levels 1-4 are designed for grades 7-10. In the Syllabus D series, students are challenged to develop a stronger understanding of mathematical concepts and their applications. The goal is to develop students who are proficient in problem solving, mathematical reasoning and higher order thinking. The books integrate algebra, geometry and trigonometry throughout each level.
The Singapore Math program is a favorite among schools and homeschoolers seeking a more advanced approach to math. We recommend that you purchase the additional activity books to ensure the practice and repetition needed to master each concept. |
Top Picks for Twelfth Graders
Preparing students to enter calculus, advanced topics are introduced. These include recursion and induction, vectors, polar coordinates, complex numbers and derivatives. Polya's guide to problem solving will help students as they enter this new level.
University of Chicago School Mathematics Project
G. Polya
Topic: math Age Level: advanced |
Well there are just two people who can guide me right now, either it has to be some math guru or it has to be the Almighty himself. I'm fed up of trying to solve problems on yr 9 factorization test and some related topics such as angle complements and solving a triangle. I have my midterms coming up in a week from now and I don't know how I'm going to face them? Is there anyone out there who can actually spare some time and help me with my questions? Any sort of help would be really appreciated.
You seem to be more freaked out than confused. First you need to control your senses. Do not panic. Sit back, relax and look at the books with a clear mind. They will seem tough if you think they are tough. yr 9 factorization test can be easily understood and you can solve almost every problem with the help of Algebra Buster. So relax.
You must go through Algebra Buster. I had always found math to be a difficult subject but this program made it very easy to study. You can type in the question and it gives you the answer, just like that! It is so easy that learning becomes a fun experience.
I am a regular user of Algebra Buster. It not only helps me get my assignments faster, the detailed explanations provided makes understanding the concepts easier. I strongly advise using it to help improve problem solving skills. |
Site Search
Action Menu
Section Navigation
Mathematics
Apply the central concepts of Mathematics and Logic to any career path.
If you like solving puzzles and figuring things out, then our mathematics major may interest you. Applications of mathematics are everywhere and a strong background in mathematics can help you in many different careers.
Ashland's Mathematics program is taught in small classes that allow you to explore and learn the language of numbers in-depth.
You will have many opportunities to participate actively in class and to get to know your professors well. Your professors have earned three awards for excellence in teaching, a testimony to their exceptional classroom skills and the strong mentoring relationships they develop with students.
What You'll Love About the Mathematics Program:
Unlike Mathematics programs in large universities where you're no more than a face in a crowd, at Ashland you get to know each of your professors well and benefit from their knowledge of Mathematics.
All classes are taught exclusively by our Mathematics professors and not by graduate students or teaching assistants.
You have many opportunities to participate in mathematics challenges and contests such as programming competitions and activities made available through the Ohio conference of the Mathematical Association of America (MAA).
The department actively participates in the national Mathematical Association of America (MAA) as well as in the Ohio section of the organization, attending conferences and presenting papers and workshops.
As a student you will have opportunities to make presentations at the Ohio section of MAA and at national meetings.
You have full access to the extensive computer resources within the department's technology center including a variety of hardware running Linux, Solaris, MacOS and Windows operating systems. The resources also include computer algebra systems, statistical and geometric software and other applications that will facilitate your learning.
Reach Your Career Goals
In addition to pursuing graduate school, our graduates are well prepared to begin careers as:
Actuaries in insurance companies
Operations and research analysts
Quality control engineers
Mathematics consultants
In addition, the analytical and logical abilities developed through the program equip you to pursue further study in areas such as business, law or medicine.
Outstanding Educators
Faculty members are very active in the field of mathematics often attending regional and national meetings with student groups.
Professors are excellent classroom educators who mentor students both in and out of the classroom through problem solving challenges and in-depth discussions of math topics.
Organizations for Mathematics Majors
Academic Department Info
Explore the language of numbers in small class settings.
Mathematics is the doorway to science and technology. Computer Science is the study of algorithmic processes to ultimately...read moreMeet our Faculty...
Also Solved by Paul S. Bruckman: An Interview by Dr. Thomas P. Dence, Professor of Mathematics Read More
Career Outlook for Mathematics Majors
Mathematics training often leads to careers in actuarial science, statistics, engineering and physics. Those with a bachelor's degree and proper licensure often become teachers of mathematics. Many mathematicians work for the federal and state governments including the Department of Defense. Private sector employers include research and development companies, technical consulting firms and insurance companies. Experts anticipate average job growth of about 10 percent between 2006 and 2016.1 Learn More about careers for mathematics majors!
What Students Say About Ashland
"Ashland University has played a large role in developing my character, providing me with the opportunities, resources, and experiences I needed to become a scholar, a leader and servant to others." -- Rachel Cordy from Elyria, Ohio, involved in Alpha Phi sorority, Judicial Board, Math Club, Orientation Team and Kappa Delta Pi. |
About the Teacher
NAME:
Felix K. Colon
SCHOOL:
Manhattan Village Academy
CLASS:
Math Technology - Portfolio/Algebra II/Trigonometry
SCHOOL PHONE:
212 242 8752
Welcome to Mr. Colon's home page.
This is my 14th year of teaching, 10th year at MVA, and my 2nd year teaching
this course. In the past, I have taught elementary school students (1st two
years), as well as students from grades 6-12. In 2005, I won the "Teacher of
the Year" award and the "New York State Lottery/Telemundo Educator of the
Week" award. In 2007 and 2008, I was voted "Faculty Speaker for the
Graduating Class".
2:10 - 3:10 Section B
The purpose of this course is to assist in the development of the MVA Math
Portfolio, which is a graduation requirement, while at the same time preparing
the student for the Algebra II/Trigonometry Regents exam in June. For each
unit in this course there will be a project component, which will supplement
the material learned on that topic. The student's mastery of the material will
be developed on the context of applications with a focus on the Fundamental
Elements of Thought. Understanding of the concepts will be greatly enhanced
through the extensive use of technology. |
Trigonometry - 7th edition
Summary: Gain a solid understanding of the principles of trigonometry and how these concepts apply to real life with McKeague/Turner's TRIGONOMETRY. This book's proven approach presents contemporary concepts in brief, manageable sections using current, detailed examples and interesting applications. Captivating illustrations drawn from Lance Armstrong's cycling success, the Ferris wheel, and even the human cannonball show trigonometry in action. Unique Historical Vignettes offer a fascinating...show more glimpse at how many of the central ideas in trigonometry began. ...show less
Charles P. McKeague Charles P. "Pat" McKeague earned his B.A. in Mathematics from California State University, Northridge, and his M.S. in Mathematics from Brigham Young University. A well-known author and respected educator, he is a full-time writer and a part-time instructor at Cuesta College. He has published twelve textbooks in mathematics covering a range of topics from basic mathematics to trigonometry. An active member of the mathematics community, Professor McKeague is a popular speaker at regional conferences, including the California Mathematics Council for Community Colleges, the American Mathematical Association of Two-Year Colleges, the National Council of Teachers of Mathematics, the Texas Mathematics Association of Two-Year Colleges, the New Mexico Mathematics Association of Two-Year Colleges, and the National Association for Developmental Education. He is a member of the American Mathematics Association for Two-Year Colleges, the Mathematics Association of America, the National Council of Teachers of Mathematics, and the California Mathematics Council for Community Colleges. Mark Turner Mark D. Turner earned his B.A. in Mathematics from California State University, Fullerton. Professor Turner worked in the aerospace industry for two years with the Systems Modeling and Analysis group at The Aerospace Corporation before completing his graduate work at California Polytechnic State University, where he earned his M.S. in Mathematics and Secondary Teaching Credential. Turner is a full-time instructor at Cuesta College in San Luis Obispo, California. He has been a leading influence in the use of graphing calculator and multimedia technology in the classroom, as well as a leading innovator in instructional website design at his institution. Mark has also created educational materials through his own company, Turner Educational Publishing, including a series of Web-based tutorials on the use of the TI-83 graphing calculator. He is a member of the American Mathematics Association for Two-Year Colleges and the California Mathematics Council for Community Colleges, and is a frequent speaker at annual conferences. Professor Turner has received the CMC3 Award for Teaching Excellence214.82 +$3.99 s/h
VeryGood
BookFool FORT WAYNE, IN
1111826854 Hardcover. Cover shows slight wear and pages are clean with no marks or highlighting. Original supplements/access codes not guaranteed. Very good |
Next: Ecuaciones en un Paso
Chapter 3: Ecuaciones de Líneas
Chapter Outline
Loading Content
Chapter Summary
Description
This chapter covers solving one-step equations, solving two-step and multi-step equations, using ratios and proportions, solving problems using scale drawings, using similar figures to measure, and finding the percent of a number. |
Concepts in Geometry DVD Discover the role that math plays in the design, technology, and construction of modern skyscrapers, as it did in ancient Greek architecture.
9 - 12
DVD
$59.95
Patterns and Trends DVD From recognizing patterns of repeating events to determining rules for extending patterns, introduce young students to basic properties of functions and algebra.
K - 2
DVD
$39.95
Geometry Skills DVD Introduce elementary students to more advanced properties and concepts of geometry.
3 - 8
DVD
$39.95
Patterns, Symmetry, and Beauty DVD Beauty is in the eye of the beholder they say. So what do people find beautiful and why? Philosophers and mathematicians from the past and modern-day artists and scientists ponder this question.
6 - 12
DVD
$59.95
Coordinate Geometry DVD This video shows how coordinate grid systems have been used throughout history for navigation, archaeology, and space exploration. |
Precalculus: Functions and Graphs, CourseSmart eTextbook, 4th Edition
Description
Dugopolski's Precalculus: Functions and Graphs, Fourth Edition gives students the essential strategies they need to make the transition to calculus. The author's emphasis on problem solving and critical thinking is enhanced by the addition of 900 exercises including new vocabulary and cumulative review problems. Students will find carefully placed learning aids and review tools to help them learn the math without getting distracted. Along the way, students see how the algebra connects to their future calculus courses, with tools like Foreshadowing Calculus and Concepts of Calculus.
Table of Contents
P. Prerequisites
P.1 Real numbers and Their Properties
P.2 Integral Exponents and Scientific Notation
P.3 Rational Exponents and Radicals
P.4 Polynomials
P.5 Factoring Polynomials
P.6 Rational Expressions
P.7 Complex Numbers
Chapter P Highlights
Chapter P Review Exercises
Chapter P Test
1. Equations, Inequalities, and Modeling
1.1 Equations in One Variable
1.2 Constructing Models to Solve Problems
1.3 Equations and Graphs in Two Variables
1.4 Linear Equations in Two Variables
1.5 Scatter Diagrams and Curve Fitting
1.6 Complex Numbers
1.7 Quadratic Equations
1.8 Linear and Absolute Value Inequalities
Chapter 1 Highlights
Chapter 1 Review Exercises
Chapter 1 Test
Concepts of Calculus: Limits
2. Functions and Graphs
2.1 Functions
2.2 Graphs of Relations and Functions
2.3 Families of Functions, Transformations, and Symmetry
2.4 Operations with Functions
2.5 Inverse Functions
2.6 Constructing Functions with Variation
Chapter 2 Highlights
Chapter 2 Review Exercises
Chapter 2 Test
Tying it all Together
Concepts of Calculus: Instantaneous Rate of Change
3. Polynomial and Rational Functions
3.1 Quadratic Functions and Inequalities
3.2 Zeroes of Polynomial Functions
3.3 The Theory of Equations
3.4 Miscellaneous Equations
3.5 Graphs of Polynomial Functions
3.6 Rational Functions and Inequalities
Chapter 3 Highlights
Chapter 3 Review Exercises
Chapter 3 Test
Tying it all Together
Concepts of Calculus: Instantaneous Rate of Change of the Power Functions
4. Exponential and Logarithmic Functions
4.1 Exponential Functions and Their Applications
4.2 Logarithmic Functions and Their Applications
4.3 Rules of Logarithms
4.4 More Equations and Applications
Chapter 4 Highlights
Chapter 4 Review Exercises
Chapter 4 Test
Tying it all Together
Concepts of Calculus: The Instantaneous Rate of Change of f(x)= ex
5. The Trigonometric Functions
5.1 Angles and Their Measurements
5.2 The Sine and Cosine Functions
5.3 The Graphs of the Sine and Cosine Functions
5.4 The Other Trigonometric Functions and Their Graphs
5.5 The Inverse Trigonometric Functions
5.6 Right Triangle Trigonometry
Chapter 5 Highlights
Chapter 5 Review Exercises
Chapter 5 Test
Tying it all Together
Concepts of Calculus: Evaluating Transcendental Functions
6. Trigonometric Identities and Conditional Equations
6.1 Basic Identities
6.2 Verifying Identities
6.3 Sum and Difference Identities
6.4 Double-Angle and Half-Angle Identities
6.5 Product and Sum Identities
6.6 Conditional Trigonometric Equations
Chapter 6 Highlights
Chapter 6 Review Exercises
Chapter 6 Test
Tying it all Together
Concepts of Calculus: Area of a Circle and π
7. Applications of Trigonometry
7.1 The Law of Sines
7.2 The Law of Cosines
7.3 Vectors
7.4 Trigonometric Form of Complex Numbers
7.5 Powers and Roots of Complex and Numbers
7.6 Polar Equations
Chapter 7 Highlights
Chapter 7 Review Exercises
Chapter 7 Test
Tying it all Together
Concepts of Calculus: Limits and Asymptotes
8. Systems of Equations and Inequalities
8.1 Systems of Linear Equations in Two Variables
8.2 Systems of Linear Equations in Three Variables
8.3 Nonlinear Systems of Equations
8.4 Partial Fractions
8.5 Inequalities and Systems of Inequalities in Two Variables
8.6 The Linear Programming Model
Chapter 8 Highlights
Chapter 8 Review Exercises
Chapter 8 Test
Tying it all Together
Concepts of Calculus: Instantaneous Rate of Change and Partial Fractions
9. Matrices and Determinants
9.1 Solving Linear Systems Using Matrices
9.2 Operations with Matrices
9.3 Multiplication of Matrices
9.4 Inverses of Matrices
9.5 Solution of Linear Systems in Two Variables Using Determinants
9.6 Solution of Linear Systems in Three Variables Using Determinants
Chapter 9 Highlights
Chapter 9 Review Exercises
Chapter 9 Test
Tying it all Together
10. The Conic Sections
10.1 The Parabola
10.2 The Ellipse and the Circle
10.3 The Hyperbola
10.4 Rotation of Axes
10.5 Polar Equations of the Conics
Chapter 10 Highlights
Chapter 10 Review Exercises
Chapter 10 Test
Tying it all Together
Concepts of Calculus: The Reflection Property of a Parabola
11. Sequences, Series, and Probability
11.1 Sequences
11.2 Series
11.3 Geometric Sequences and Series
11.4 Counting and Permutations
11.5 Combinations, Labeling, and the Binomial Theorem
11.6 Probability
11.7 Mathematical Induction
Chapter 11 Highlights
Chapter 11 Review Exercises
Chapter 11 Test
Concepts of Calculus: Limits of Sequences
A. Appendix: Basic Algebra Review
A.1 Real Numbers and Their Properties
A.2 Exponents and Radicals
A.3 Polynomials
A.4 Factorials Polynomials
A.5 Rational Expressions
B. Appendix: Solutions to Try This Exercises
Credits
Answers to Selected Exercises
Index of Applications |
Math concepts is organized so that much of the differentiation for students is built into the design of the program. Ample practice is provided. Challenge exercises are included. Developing Concepts provide students with models for conceptual understanding of the mathematical reasoning behind each key concept. Mathematical reasoning is stressed. Vocabulary words, examples, and Guided Practice exercises are standard features throughout the course.
Alebebra Ib is a continuation of the study of linear algebra concepts and
skills covered in Algebra Ia (eighth grade). You will review and refine
solving linear equations and inequalities, and linear functions. The study of
functions is expanded to include quadratic, exponential, radical, and rational
functions. Algebra is connected to data through the study of probability and
data analysis.
This is a college credit course. This course is an introduction to statistics. Topics
include data summary, frequency distributions, plots, graphs, and measures of
central tendency, variations, probabilities, probability distributions, and confidence
intervals. Hypothesis testing of means, proportions, and variances will be
conducted using z-test, t-test, chi-square test, f-test and Anova. |
WELCOME to the class! During your school career, you have probably asked at least one teacher, "When am I ever going to use this in real life?"Well, this course is about real life! Throughout the year, you will be doing different activities that use math and problem-solving skills, in order to help you become informed consumers and financially independent.
This class can be used as either a third science or third math credit. Although it may be used for a science credit, it is unlike most other science classes. There are no lab requirements or scientific terms. Students will inquire into topics and draw conclusions.The class incorporates basic math skills and uses them with real world problems.
»Consumer Jungle We've got information for you on everything you need to know to survive in the real world. Our content is packed with tips, advice and direction on how to navigate the "consumer jungle". |
Real-life focus - genuine economic applications and examples taken from a variety of areas of economic theory
Clear and user-friendly style
Pedagogy including detailed problems at the end of every chapter
Introductory Mathematical Economics, 2/e begins with an overview of necessary computational mathematics, then continues with a series of key economics problems using "higher mathematics." The book presents a mix of classical and contemporary economic theory, covering the problems of uncertainty, continuous-time dynamics, comparative statistics, and the applications of optimization methods to economics.
0: Review of Mathematics
1: Economic Applications of One-Variable Calculus
2: Economic Applications of Multivariate Calculus n 3Comparative Statics 1: One and Two Variables with and without Optimization
4: Integration, Time and Uncertainty in Economics
5: Introduction to Continuous-Time Dynamics in One and Two Dimensions
6: Matrices and Economic Theory
7: Comparative Statics 2: n Variables with and without Optimization
8: Comparative Statics 3: Optimization under Constraint
9: Inequality Constraints in Optimization Theory |
This introduction to probability theory transforms a highly abstract subject into a series of coherent concepts. Its extensive discussions and clear examples, written in plain language, expose students to the rules and methods of probability. Suitable for an introductory probability course, this volume requires abstract and conceptual thinking skills and a background in calculus. Topics include classical probability, set theory, axioms, probability functions, random and independent random variables, expected values, and covariance and correlations. Additional subjects include stochastic processes, continuous random variables, expectation and conditional expectation, and continuous parameter Markov processes. Numerous exercises foster the development of problem-solving skills, and all problems feature step-by-step solutions
Table of Contents for Introduction to Probability Theory with Contemporary Applications |
Secondary Mathematics Program Information
The Quebec Education Program at the secondary level is broken down into two Cycles:
Cycle One and Cycle Two. In addition, each Cycle is broken down into years. More specifically:
Secondary Cycle One, Year One
Secondary Cycle One, Year Two
Secondary Cycle Two, Year One
Secondary Cycle Two, Year Two
Secondary Cycle Two, Year Three
Secondary Cycle One is comprised of two years: Year One and Year Two. In Cycle
One, students complete the same mathematics program over the period of two years.
Secondary Cycle Two is comprised of three years: Year One, Year Two and Year Three.
In Secondary Cycle Two, Year One, students complete the same mathematics program over one year.
At the end of this year, they must select a mathematics option for the remainder of the Cycle
depending upon their personal interests, aspirations and skill set.
The three Mathematics Options for Cycle Two, Year Two and Three are:
Mathematics - Science Option
Mathematics - Technical and Scientific Option
Mathematics - Cultural, Social and Technical Option
A brief overview of the Mathematics Options for Cycle Two, Year Two and Year Three can be found
here. |
We don't try to teach you everything there is to know about calculus–only the strategies and information you'll need to get your highest score.
In Cracking the AP Calculus AB & BC Exams, we'll teach you how to·Use our preparation strategies and test-taking techniques to raise your score·Focus on the topics most likely to appear on the test·Test your knowledge with review questions for each calculus topic coveredThis book includes 5 full-length practice AP Calculus AB & BC tests: 3 for AB and 2 for BC.
All of our practice questions are just like those you'll see on the actual exam, and we explain how to answer every question..
For more information about the title Cracking the AP Calculus AB and BC Exams, 2006-2007 Edition (College Test PrepA "Unified Theory" For Calculus(January 29, 2003) — A University of Missouri-Rolla mathematician's research into a "unified theory" of continuous and discrete calculus is gaining the attention of mathematicians worldwide for numerous ... > read more
Math Goes Viral in the Classroom(December 11, 2009) — At least a dozen Alberta high-school calculus classrooms were exposed to the West Nile virus recently. Luckily, it wasn't literally the illness. Educators used the virus as a theoretical tool when ... > read more
Soap Films Help to Solve Mathematical Problems(January 27, 2011) — Soap bubbles and films have always fascinated children and adults, but they can also serve to solve complex mathematical calculations. This is shown by a study carried out by two professors who have ... > read more
Atoms Under The Mantle(March 14, 2007) — French CNRS scientists have succeeded in modeling the defects of the earth's mantle responsible for its deformation. These results, obtained using a novel approach which combines numerical calculus ... > read more |
... chapter and lesson, with one skills practice worksheet for every lesson in MathMatters 1. ... Use the graph to answer the questions. a. ... 1-8 B OX -AND-W HISKER P LOTS When you want ...
... Carolina HoltAlgebra 1 Practice Workbook is designed to provide additional practice of the skills taught in each lesson of ... in the Algebra 1Practice Workbook AnswerKey . ...
holtmcdougal.hmhco.com/../HRW_ALG1_PW.pdf |
II. COURSE DESCRIPTION
This course places as much emphasis on the modern mathematical ideas and their meaning as on computation. Topics included are set theory, logic, systems of numeration, mathematical systems, counting theory, probability, statistics, and geometry.
III. RATIONALE OF COURSE
The purpose of the course is to give insight into some of the more uncommon areas of mathematical thought. As many of these areas require the learning of methods of investigation rather than memorization, the main goal is that the student should be able to transfer his knowledge of logical investigation of mathematics to other fields of study.
IV. COURSE COMPETENCIES
Interpret mathematical language.
Judge an argument as to whether it follows the rules of deductive reasoning. |
Sign in to YouTube
This is the 6th lecture in this course on Linear Algebra. We review matrix arithmetic for 2x2 matrices and compare the main laws with the simpler case of 1x1 matrices. Then we apply 2x2 matrices to study transformations of vectors, with examples including reflections, rotations and dilations.
We visualize these with pictures using the standard Cartesian coordinate framework. The concept of a linear transformation is also introduced.
This is part of a series on Linear Algebra given by N J Wildberger, also the discoverer of Rational Trigonometry.
Two vectors define a lattice in 2D (lattices are extensively used in crystallography). Vectors can be packed into a matrix. An inverse matrix will be composed then from the transposed vectors of the primitive vectors of the reciprocal lattice. That could lead to a gentle introduction to the co- and contra- variant coords. |
TI Interactive Student Version
Student Edition TI Interactive Studio...Integrated learning software for math and science. A user-friendly, integrated computer learning environment that combines the functionality and familiarity of the TI83 graphing calculator with the desktop publishing capability of the computer.
TI InterActive! is the user-friendly, interactive computer software designed for teachers and students. TI InterActive! enables high school and college teachers and students to easily explore mathematics and science concepts on a computer. Teachers can enhance students' learning through interactive lessons that encourage exploration, visualization, data analysis and writing.
With over 125,000 items and parts in stock daily, TheNerds.net is sure to meet all your computer and electronics needs. This TI Interactive Student Version is factory fresh: We never sell refurbished products. The retail list price on this product is $60.89 |
Pre-Calculus Help
In this section you'll find study materials for pre-calculus help. Use the links below to find the area of pre-calculus you're looking for help with. Each study guide comes complete with an explanation, example problems, and practice problems with solutions to help you learn pre-calculus.
Introduction to Logarithms
A common question for investors is, "How long will it take for my investment to double?" If $1000 is invested so that it earns 8% interest, compounded annually, how long will it take to grow to $2000? To answer the question ...
Introduction to Simple Exponent and Logarithm Equations
Equations with exponents and logarithms come in many forms. Sometimes more than one strategy will work to solve them. We will first solve equations of the form "log = number" and "log = ...
Introduction to Exponents and Logarithmic Equations
For some logarithmic equations, a solution might be extraneous solution. That is, such a solution is a solution to the rewritten equations but not to the original equations. Some solutions to the rewritten ...
Introduction to The Change of Base Formula
There are countless bases for logarithms but calculators usually have only two logarithms—log and ln. How can we use our calculators to approximate log 2 5? We ...
Introduction to Applications of Logarithm and Exponential Equations
Now that we can solve exponential and logarithmic equations, we can solve many applied problems. We will need the compound growth formula for an investment earning interest rate r , ...
Introduction to Finding the Growth Rate
We can find the growth rate of a population if we have reason to believe that it is growing exponentially and if we know the population level at two different times. We will use the first population level as n
Introduction to Radioactive Decay
Some radioactive substances decay at the rate of nearly 100% per year and others at nearly 0% per year. For this reason, we use the half-life of a radioactive substance to describe how fast its radioactivity decays. For ...
Applications of Systems of Equations
Systems of two linear equations can be used to solve many kinds of word problems. In these problems, two facts will be given about two variables. Each pair of facts can be represented by a linear equation. This gives us a ...
Introduction to Graphical Solution to System of Equations
Two lines in the plane either intersect in one point, are parallel, or are really the same line. Until now, our lines have intersected in one point. When solving a system of two linear equations that are ... |
2007{"itemData":[{"priceBreaksMAP":null,"buyingPrice":50.02,"ASIN":"0387257659","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":70.12,"ASIN":"0387961712","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":53.2,"ASIN":"088385807X","isPreorder":0}],"shippingId":"0387257659::I7rPM7tSXJQC9Vl%2BXBQRCgiJuWVPm2rsYE%2Fx08%2BVFQk17FkbybHYIMoemUJ8xO%2BfAY%2BguGZTwkvMc%2BQ8oMk%2F3Q1NEF4VzzIcJWNTgzRJfFM15FUZNJh%2F1A%3D%3D,0387961712::djqJ%2FKTU349YD4m%2FAyNU6jbWYtyKS7fV5cAVy%2F697X5RP1H7CGHyLkKg6xbAPHWM3LEv7qoChTCe4Odetcdf7lXsZE5iIxViAgFBKrjExmM%3D,088385807X::BC6r4PCb3sHvDI49xr2wB9umsBbC%2FFVXKYeCTKZfPDzOGH203Ge%2BVLr2qSmdnbNCqsFHgZapdRfQe3eTbOUFMy9xAbNnRx6lCkEMsqJJH work contains carefully selected problems in Algebra, Real Analysis, Geometry and Trigonometry, Number Theory and Combinatorics and Probability. … The book is mainly intended to offer the principal skills and techniques for solving problems in elementary Mathematics. … The reviewer recommends this book to all students curious about the force of mathematics, especially those who are bored at school and ready for a challenge. Teachers would find this book to be a welcome resource, as will contest organizers." (Teodora-Liliana Radulescu, Zentralblatt MATH, Vol. 1122 (24), 2007) "I enjoyed this book … . Not just because of the collection of problems, but also because of their sheer scope and depth. This is a great collection which is extremely well-organized! … This extraordinary book can be read for fun. However, it can also serve as a textbook for preparation for the Putnam … for an advanced problem-solving course, or even as an overview of undergraduate mathematics. … it could certainly serve as a great review for senior-level students." (Donald L. Vestal, MathDL, December, 2007) "A 935-problem and almost 800-page super-problem book with solutions, whose reading would certainly challenge, attract, and keep really busy any undergraduate student interested in acquiring various problem-solving techniques. … the array of remarkable problem books has gained a new addition that could be really useful to undergraduate students. … a book about excellence in mathematics, coming from a long cultural tradition whose history and experience can only help us deepen our understanding of how mathematics could be taught in a more attractive and inquisitive way." (Bogdan D. Suceavă and Jack B. Gaumer, The Mathematical Intelligencer, Vol. 33 (2), 2011)
From the Back Cover Key features of Putnam and Beyond * Preliminary material provides an overview of common methods of proof: argument by contradiction, mathematical induction, pigeonhole principle, ordered sets, and invariants. * Each chapter systematically presents a single subject within which problems are clustered in every section according to the specific topic. * The exposition is driven by more than 1100 problems and examples chosen from numerous sources from around the world; many original contributions come from the authors. * Complete solutions to all problems are given at the end of the book. The source, author, and historical background are cited whenever possible. This work may be used as a study guide for the Putnam exam, as a text for many different problem-solving courses, and as a source of problems for standard courses in undergraduate mathematics. Putnam and Beyond is organized for self-study by undergraduate and graduate students, as well as teachers and researchers in the physical sciences who wish to expand their mathematical horizons.
There are many books on problem solving. The majority are aimed at junior high and high school students preparing for either the International Mathematical Olympiad or national IMO selection tests (the American Mathematics Contests in the United States, such as the USAMO). A select few, such as Problem Solving through Problems by Loren Larson, are aimed at university students preparing for university competitions. This book, as the title suggests, belongs to this latter category, and it has a particular emphasis on the sorts of problems that occur on the Putnam exams.
This book is generally written at a higher level than most other problem solving books. Many problem solving books place a great emphasis on geometry. Just as the Putnam exam generally replaces synthetic geometry with analysis and abstract and linear algebra (although there are exceptions), so this book replaces the traditional focus on geometry with a focus on analysis and algebra. That said, there is an entire chapter on geometry, but it does not discuss synthetic geometry, instead focusing on vectors, the geometry of the complex plane, analytic geometry, and some special topics that are especially relevant to college mathematics (integrals in geometry, some higher-level results such as the fact that all conics are rational curves, and a brief but still substantive survey of trigonometric substitutions).
Putnam and Beyond discusses many areas of college mathematics that are likely to appear on the Putnam exam but would never appear on the IMO, such as abstract algebra, linear algebra, and real analysis (with a very tiny bit of complex analysis).
That said, this book still does overlap a bit with many other problem solving books. It opens with a chapter on general problem solving strategies, but I feel that these sections are written with students who have encountered the basic methods before. For example, most introductions to induction demonstrate it by summing some series, but the authors here show that if finitely many lines divide the plane into regions, the regions can be colored with two colors in such a way that no two neighboring regions receive the same color. Another example they offer is a particularly difficult inequality from a past Putnam exam. So in a way the opening chapter is appropriate more as a *second* introduction to problem solving techniques than as a first introduction. This leads to my next point.
The book's exposition is generally written at a high level, and I'd say that to fully appreciate it would impose somewhat high prerequisites, including a good amount of mathematical maturity and a good knowledge of basic college mathematics up through first courses in algebra and analysis. For example, a problem in the very first section of the very first chapter on argument by contradiction requires one to be familiar with the density of rationals in the reals.
To anyone interested in beautiful proofs or in competition math, I would heartily recommend this book along with Problem Solving through Problems by Larson. I think Putnam and Beyond is written at a slightly higher level than Larson's book and many of the problems here are more difficult than those in Larson, but together both books provide a very thorough and strong review of undergraduate mathematics through problem solving.
Finally, full solutions to every single problem (and by "full" I mean complete proofs written out in detail, often with accompanying figures) are in the back of the book (in fact, a little more than half of the pages are devoted to these solutions).
This book consists of a very useful collection of Putnam-like math problems. Putnam and Beyond is organized for self-study by undergraduate and graduate students who wish to try a lot of competitive math problems.It is also useful for teachers who are preparing their bright students for IMO type (or higher) math competitions. However the book assumes a level of mathematical maturity and prior mathematical knowledge that not many college students possess. Another very useful book for math competitions is The IMO Compendium. |
Rates of Change for Algebra One Students
Pat Mauch
I. Introduction
One of the topics that is often addressed in a first year calculus course is the idea of related rates of change. The graphing calculator has now made it possible to study these kinds of change by collecting discrete data and fitting a curve to that data. This curve can then be used to approximate instantaneous rates of change. The following experiment and related activities could be used with first year algebra students.
II. The Balloon Problem
The following problem on related rates was taken from Calculus Volume One by Tom M. Apostol. "Suppose a gas is pumped into a spherical balloon at a constant rate of 50 cubic centimeters per second. Assume that the gas pressure remains constant and that the balloon always has a spherical shape. How fast is the radius of the balloon changing when the radius is 5 centimeters?" The solution involves derivatives and the chain rule with an answer of 1/2pi (approximately .159).
III. Collecting Data in Lab Situation
Equipment:
Graphing calculators (TI-82 was used for the example).
Spherical balloons.
Outside calipers.
Small hand pump of the type used to inflate air mattress (optional).
Data collection:
Divide the students into groups of three. One student will inflate the balloon by pumping or blowing uniform breaths into the balloon at five second intervals. One student will measure the diameter of the balloon at five second intervals. The third student will record the data of time and diameter for each interval. The diameter values should be converted to radius values before they are interred in the calculator.
Calculator modeling: (General instructions for the TI-82 calculator will be given. These can be modified to other graphic calculators.)
1.Enter the time units as the first set of data points in list one.
2.Enter the measured radius values in list two.
3.Use a scatter plot to plot the discrete values from the experiment.
4.Find the best fit regression line. (The students should find this to be the power regression.)
5.Trace the regression line to find the values on either side of y = 5.
6.Determine the rate of change by comparing the change in y with the change in x.
Example data:
L(1) L(2)
(time) (radius measured)
_____ _____
5 4
10 5
15 5.5
20 6
25 6.75
30 7
35 7.5
40 7.75
45 8
50 8.5
Using the power regression y = axb a = 2.34201560 and b = .3243611769. Near y values yield y = 4.9848088 with x= 10.265957 and y = 5.0736281 with x = 10.840426. The resulting rate of change is approximately .155. If you zoom in on the curve, the result can be improved to approximately .157.
This particular experiment is hands on and should be fun for the students. The resulting curve is very "friendly" and small errors in the lab should still produce results that are reasonably good.
IV. Revisiting the Problem
The students should keep the results of this experiment in their portfolios. After the class has covered isolation of variables in an equation, the problem can be approached in a different way.
1. Enter the values from 1 to 10 in list 1.
2. Enter the values ( 50*L(1)) in list 2.
3. Enter the radius values () in list 3.
4. Plot L(1) and L(3).
5. Plot the regression line.
6. Trace the regression line to find the rate of change.
Example data:
L(1) L(2) L(3)
(time) (volume) (radius)
_____ _______ ______
1 50 2.2854
2 100 2.8794
3 150 3.2961
4 200 3.6278
5 250 3.908
6 300 4.1528
7 350 4.3718
8 400 4.5708
9 450 4.7538
10 500 4.9237
Since the regression line is a perfect fit, the answer can be determined to whatever degree of accuracy is needed by zooming in on the graph. I feel it is important to plot and find the regression line rather than simply graph the equation. This reinforces the idea of working from discrete values to the continuous and keeps a strong link with the previous lab work. This may be a good time to discuss the relationship between the a and b values in the regression equations (lab and revisit ) and the value of .75pi and 1/3. The idea of inverse functions, curve fitting, and residuals can also be explored at this time.
V. Extensions of the Problem
Perhaps the original problem is incomplete or doesn't address some of the more interesting situations involved with balloon inflating. Here is a short list of other ideas that can be explored.
1. How fast is the surface area of the balloon changing at a particular time?
2. How fast is the radius and surface area of the balloon changing at the time when it bursts?
3. How long will it take the balloon to burst?
4. If we experiment with spherical balloons of different sizes (masses), can we predict when it will burst? ( Determine a constant that can be used, in conjunction with volume or radius, to predict bursting.)
5. Find the mass of the balloon and, assuming that it is filled with He rather than air, determine the size of the balloon required for it to rise.
6. How high will the balloon rise? How fast will it rise? Will it burst?
7. Explore all of these ideas with a balloon that is in the shape of a cylinder.
8. Others?
VI. Conclusion
The concept of change and rates of change is one that is very important to the study of mathematics, and its application to real life situations. In the past these ideas were not explored, to any great extent, with students in junior high or beginning high school. Now, with the graphing calculator and computer spreadsheets available to most classrooms, the instructor has the opportunity to explore these topics with students much earlier in their mathematical development. The work in this paper is simply an example of the type of work that can be done to explore change. |
Practical Problems in Mathematics for Manufacturing, 4th Edition
ISBN10: 0-8273-6710-4
ISBN13: 978-0-8273-6710-4
AUTHORS: Davis
This workbook/textbook has been newly updated to supply the basic mathematical skills and applications encountered in the workplace by manufacturing technicians. Practical exercises are presented in clear, easy-to-follow steps, offering a systematic approach to mastering essential mathematical skills. This new edition highlights critical thinking, to train students on the "how tos" of problem solving.
ALSO AVAILABLE
INSTRUCTOR SUPPLEMENTS CALL CUSTOMER SUPPORT TO ORDER
Instructor's Guide, ISBN: 0-8273-6711-2 |
polynomial
polynomial, In algebra, an expression consisting of numbers and variables grouped according to certain patterns. Specifically, polynomials are sums of monomials of the form axn, where a (the coefficient) can be any real number and n (the degree) must be a whole number. A polynomial's degree is that of its monomial of highest degree. Like whole numbers, polynomials may be prime or factorable into products of primes. They may contain any number of variables, provided that the power of each variable is a nonnegative integer. They are the basis of algebraic equation solving. Setting a polynomial equal to zero results in a polynomial equation; equating it to a variable results in a polynomial function, a particularly useful tool in modeling physical situations. Polynomial equations and functions can be analyzed completely by methods of algebra and calculus |
I recall the days when studying Simple Harmonic Motion in Physics A-Level, one would need to solve differential equations. Later, a topic called Kirchoff's Laws was removed from the syllabus because it was deemed too difficult to solve three simultaneous equations.
There are a lot of A-Level students of late studying what I would class as "unrelated" subject combinations such as Maths, Biology and History as opposed to standard Maths, Physics and Chemistry or English, History and Latin.
To answer your question, maths is the common language that binds everything. In order to make progress, mastery of it is unavoidable, rather like proofs, which I agree, is not to everyone's tastes but is necessary.
Is Further Maths necessary to get into reasonable unis for economics? Non of the websites seem to suggest FM is required but everyones always telling me that FM and economics is a must to get into a uni like LSE or Oxford etc?Economics at university is very different from economics at A-level. It is a lot more formal. Everything you study starts with the building of a mathematical model, which you use mathematical techniques to analyse. If I recall correctly (although I only did AS-level economics), the concept of utility, which is really the foundation of choice theory and economics, is not introduced. But at university level, most things start with analysing a consumer's utility function, which then must be maximised subject to some constraints. This is a mathematical problem.
For example, you might use optimisation techniques to answer the questions:
"What bundle should a consumer choose to maximise his utility subject to his budget constraint?"
"What inputs should a firm choose to minimise its cost subject to producing amount x?"
"How should an owner write a contract that incentivises his employee to work hard, despite the fact that the owner cannot observe the employee's efforts?"
You might use integrals to answer the question:
"How does the consumer's surplus from this transaction vary with price?"
You might use differential equations in macroeconomics to answer:
"Does this economic system converge to a steady-state?"
Then, of course, there is the whole branch of econometrics, which prima facie is closest to the statistics component of maths A-level.
If you want to get an idea for the mathematical level, I would take a look at Varian's Intermediate Microeconomics (make sure you don't look at his Microeconomic Analysis as that is a graduate textbook and a lot more formal).The issue is, economics as a discipline at A-Level is nothing like its university counterpart. At A-Level, economics is very discursive and requires you to write essays, and dare I say involves a bit of normativeness and politics. At university, however, economics really does become a 'science' and is empirical based; that is to say, you study a whole host of abstract economic models, look at how changes in certain variables affect the outcomes of the model, and then use econometrics to analyse whether or not the model is reflective of reality.
The most important mathematical tool in economics is optimization, as constantly you are trying to minimize costs subject to some constraint or maximise profits subject to some constraint. Further, game theory becomes quite technical when dealing with oligopolies and firm behaviour in uncertainty (asymmetric information), especially when you come onto Pure Bayes Nash Equilibrium, which in addition makes extensive use of probability theory.
Otherwise, econometrics, or statistics, is vital. Hence you will need to have a solid working knowledge of calculus, linear algebra, and probability theory.
(Original post by placenta medicae talpae)But a lot of the applicative math models for economics are simply not realistic nor are they up to date.
Tell me what are the examples of uncooperative games, some inane Jack and Jill example ? Why use some real world examples like from the fighting sports ?
Cause let's face it , most academics know jack about real world economics o/w they wouldn't be in a university - they'd be chief economist @ GS.
Lot of the maths is chucked in to make it look good. i'm not vs maths in economics but I am when it distorts the subject to something unreal and inapplicableEconomics at a high level requires a level of precision that can only be achieved through Mathematics. At BSc level, you don't write essays.
(Original post by screenager2004)
Because lots of people like to believe that the infinite and subjective complexity of human competition, risk and sense of value can be reduced down to little numbers.
(Original post by dugdugdug)I may be mistaken, but doesn't pretty much every BSc Physics programme require A-Level Maths?
(Original post by dugdugdug)Economics at university is still a mathematical discipline, and very rigorous and proof based at the top universities. Extensive use of calculus is used as well as linear algebra and probability theory. |
201795116 / ISBN-13: 9780201795110
Mathematics All Around
"Tom Pirnot" believes that conceptual understanding is the key to a student's success in learning mathematics. He focuses on explaining the thinking ...Show synopsis"Tom Pirnot" believes that conceptual understanding is the key to a student's success in learning mathematics. He focuses on explaining the thinking behind the subject matter, so that students are able to truly understand the material and apply it to their lives. This textbook maintains a conversational tone throughout and focuses on motivating students and the mathematics through current applications. Ultimately, students who use this book will become more educated consumers of the vast amount of technical and mathematical information that they encounter daily, transforming them into mathematically aware citizens.Hide synopsis
...Show more difficult" for liberal arts students. As a result, students end up with an understanding of and positive attitude toward many different and often challenging mathematical topics Mathematics All Around
I cannot believe that all of this was crammed into ONE 8 week college course. I'm still getting over the stress of trying to make it through this course. The book is ok if you understand math, but if you don't, you're just going to be more lost than you were before you started. Very confusing stuff |
Mathematics Coursetaking and Achievement at the End of High School: Evidence from the Education Longitudinal Study of 2002 (ELS:2002)
Description:
This report documents and examines the relationship between the number and types of math courses taken in the 11th and 12th grade and growth in mathematics proficiency over the same time period. Using data from the Education Longitudinal Study of 2002 (ELS:2002), the analysis identifies the coursetaking sequences most prevalent among contemporary high school students in their junior and senior years, sociodemographic characteristics of the students who follow these course sequences, and the association between specific courses and course sequences and mathematics gains over the last two years of high school. Because most students (94 percent) entered the second half of high school with a mastery of basic mathematics skills such as simple arithmetic and operations, most learning during this time was in intermediate-level mathematics skills and concepts. For example, the percentage of students with an understanding of simple problem solving skills grew from 53 to 65 percentage points over the two year period. In terms of learning in specific content areas, the largest gains in intermediate skills such as simple operations and problem solving were made by those who followed the geometry–algebra II sequence. The largest gains in advanced skills such as derivations and making inferences from algebraic expressions were made by students who took precalculus paired with another course. The smallest gains were made by students who took one mathematics course or no mathematics courses during their last 2 years. |
Hoschton Physics fundamental to most physical sciences. As a geologist, I have taken courses in advanced math up to differential equations, and have used math extensively in my research modeling carbon dioxide diffusion through the soil. Algebra I and 2 are fundamental to all advanced mathematics.
...Algebra is a very powerful tool in multiple situations, so it's well worth the effort to make it work for you. Repeat - work for you - not scare you. Algebra 2 kicks in with much more powerful analysis tools to describe and evaluate real-life situations in hundreds of scientific disciplines |
College Algebra
9780618643103
ISBN:
0618643109
Edition: 7 Pub Date: 2006 Publisher: Houghton Mifflin College Div
Summary: This market-leading text continues to provide students and instructors with sound, consistently structured explanations of the mathematical concepts. Designed for a one-term course that prepares students for further study in mathematics, the new Seventh Edition retains the features that have always made "College Algebra" a complete solution for both students and instructors: interesting applications, pedagogically ef...fective design, and innovative technology combined with an abundance of carefully developed examples and exercises."New!" "Side-by-side Example Solutions" for select examples include multiple problem solving approaches--such as algebraic, graphical, and numerical--to appeal to a variety of teaching and learning styles."New!" "Checkpoints" after each Example/Solution refer students to similar problems in the Section Exercises, giving students the opportunity to practice and reinforce the concepts they just learned. Answers to Checkpoint exercises are included at the back of the book."New!" "Vocabulary Checks" open every set of Section Exercises. This review of mathematical terms, formulas, and theorems provides regular assessment and reinforcement of students' understanding of algebraic language and concepts."Exercise Sets" have been carefully analyzed and revised to improve the grading of problems from "basic skill-building" to "challenging;" the pairing of similar odd- and even-numbered exercises; update all real data; and add real-life and real-data applications."New!" "Make a Decision" applications--presented throughout the text at the end of selected exercise sets--are based on large sets of real data. These extended modeling applications give students the opportunityto use all the mathematical concepts and techniques they've learned and apply them to large sets of real date--analyzing it, graphing it, and making conjectures about its behavior. These applications are featured in Eduspace and the Online Learning Center in an interactive format."Eduspace, powered by Blackboard," Houghton Mifflin's online learning environment, brings your students quality online homework, tutorials, multimedia, and testing that correspond to the "College Algebra" text. This content is paired with the recognized course management tools of Blackboard.For copyright 2007, two titles have been added to the Larson/Hostetler "Precalculus Series: Precalculus with Limits" and "Precalculus: A Concise Course." These textbooks enhance the scope of the series, making it even more flexible and adaptable to a variety of learning and teaching styles |
Mathematics
In Years 8 and 9, there are three different syllabuses, Course 1, Course 2 and Course 3. Course 1 is studied by the top 40% of Maths students, Course 2 by the next 40% of students and Course 3 by the next 20%. Course 3 is designed for students who experience difficulties with mathematical concepts and places emphasis on practical, life skill topics.
In Year 10 there are four courses. Course 1 in Year 9 is split into two courses in Year 10, Course 1A and Course 1B. The extra course is designed to give students greater opportunity in studying a course that meets their needs and abilities. Course 1A is designed for students who wish to study at the highest level in Years 11 and 12.
In Years 11 and 12, there are four courses, Specialist Maths, Mathematical Methods, Mathematical Applications and Maths General. The first three are tertiary type 2 courses. Specialist Maths is designed for the top 10% of our Maths students and can be studied as a double major, major minor or major. Mathematical Methods is a theoretical tertiary course while Mathematical Applications is an applied tertiary course. Both these courses can be studied as majors and are considered to be of equal academic rigour. Maths General is an accredited course which can be studied as a major.
Student assessment is varied. Besides the more traditional tests and assignments, students attempt open ended assignments, oral presentations and group work tasks.
Students in tertiary Maths courses in Years 11 and 12 must sit moderating tests so that marks from the three different courses can be equated on a common scale. |
Unit specification
Aims
The programme unit aims to introduce the algebraic structures of rings and fields; describe the quotient structure and its connection with homomorphisms of rings; present important examples rings and develop some of their properties with particular emphasis on polynomial rings and factorisation in rings.
Brief description
This course builds on Algebraic Structures 1, which is a prerequisite, and continues the strong emphasis on examples.
The algebraic structures of rings and fields will be introduced. The construction of quotient rings and the relationship with homomorphisms is one of the main themes. These ideas will be used to construct roots of polynomials in extension fields. Factorisation in polynomial rings and rings of integers of number fields will also be studied.
Intended learning outcomes
On completion of this unit successful students will be able to:
demonstrate their knowledge of the definition of a ring and important examples;
demonstrate their understanding of the quotient construction in theoretical terms and also in particular contexts;
demonstrate their understanding of how to produce roots of polynomials in extension fields and be able to compute in such fields;
solve a range of problems which require understanding of rings and fields;
apply theoretical results to computations in particular examples of rings.
Future topics requiring this course unit
Most, possibly all, algebra courses in years 3 and 4.
Syllabus
Definitions and examples of rings (rings of numbers, rings of matrices, quaternions, rings of endomorphisms, group rings, rings of polynomials, subrings); [4 lectures]
Domains, fields and division rings; nilpotent and idempotent elements, products of rings; (many) examples; with students gaining familiarity with the ideas and examples through attempting exercises. [4]
Isomorphisms and homomorphisms (of rings): what is preserved and reflected; kernel of a homomorphism, ideals; principal ideals, operations on ideals. [4]
The quotient construction (for rings): the construction and connection with homomorphisms; maximal ideals; ideals of the quotient ring; examples. [3] |
Differential geometry has a wide range of applications, going far beyond strictly mathematical pursuits to include architecture, engineering, and just about every scientific discipline. John Oprea's second edition of Differential Geometry and Its Applications illuminates a wide range of ideas that can be beneficial to students majoring not only in mathematics but also in other fields.
Differential Geometry and Its Applications was written to help students adapt to "a type of mathematics that is a unified whole," one that mixes together geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and various notions from the sciences. The textbook touches on many different mathematical concepts, including aspects of linear algebra, the Gauss-Bonnet Theorem, and geodesics. It also encourages students to visualize and experiment with the ideas they are studying through their use of the computer program Maple. This allows students to develop a better understanding of the mathematics involved in differential geometry. The book is full of exercises that challenge students to combine concepts from different areas of mathematics to obtain solutions. |
In this course, students will study the branch of mathematics that deals with rates of change in continuous and varying quantities. The class will include exercises in the graphical, numerical, analytical and verbal representation of functions; derivative rates of change and the use of derivatives to solve a variety of problems; and derivative and definite integrals as expressed in both parts of the Fundamental Theorem of Calculus. Students will communicate mathematical solutions both orally and with the written word; use technology to help solve problems, interpret results, and verify conclusions; and determine the reasonableness of solutionsCalculus Materials
**Materials will be sent automatically if you have not previously received them from us. |
Add New Comment
In calculus power rule is one of the most important rule that is defined for
differentiating the linear or polynomial terms. It is denoted as the differentiation of the terms d
(x n) / d x = n x n - ...
8th grade math helpprovides students with all the support required with solving problems. Grade 8 Math help
has this representative list of topics covered in our help list - however all programs will ...
Get 4th grade math help from expert tutorvista online tutors and make your math easy. It is always necessary
to have a clear basic knowledge about everything, sign up for 4th grade Math help from our ...
Get 4th grade math help from expert tutorvista online tutors and make your math easy.
It is always necessary to have a clear basic knowledge about everything, sign up for 4th
grade Math help from our ...
The objectives of my curriculum unit are aligned with the objectives from the Texas Essentials Knowledge and Skills in Social Studies and Music for grade 8 (Texas Education Agency Curriculum Codes). ... |
Each student will receive a concept list and assignment sheet for each unit. We will cover a conceptevery day or so. Students will be:
expected to complete the practice problems as directed
given opportunities to ask questions and gain additional clarification on concepts
given the answers to the practice problems on the day the problems are assigned
given the opportunity daily to show me what they have completed of the practice problemsand I will note this appropriately
given a quiz after approximately 3 concepts are taught
given an opportunity to evaluate their understanding of the concepts and given feedback as totheir grasp of the concept using the scale below:No answer orno work shownI know youdont know itI think youdont know itI think youknow itI know youmostly know itI know youknow it0 1 2 3 4 5We will repeat this process (teach a few concepts, quiz, and get feedback) until we reach the end of aunit. At the end of each unit, each student will receive scores for each concept that was tested usingthe same scale from the quizzes. These scores for each concept will be entered into the gradebook asfollows:No answer orno work shownI know youdont know itI think youdont know itI think youknow itI know youmostly know itI know youknow it0 1 2 3 4 55/10(50%)6/10(60%)7/10(70%)8/10(80%)9/10(90%)10/10(100%)Understand that these are the only scores that will be entered into the gradebook. There will be noscores entered for practice problems and quizzes I will note what practice problems have beencompleted and I will use the information from the homework and quizzes to help determine whattopics the class needs more time and help learning. Students are expected to use the practiceproblems to help them to grasp the concepts and to use the feedback from the quizzes to gauge wherethey are at in their understanding and prepare accordingly for the test.If a student is not satisfied with his or her understanding of a concept, he or she may choose toreassess that concept. In order to reassess, the following must occur:
The student must have completed the practice problems for the concept prior to the unit test. Iwill have already noted what was completed as mentioned above.
After the unit test, the student needs to have done some additional practice or gotten helpfrom either myself or another student or tutor. |
West Chicago Excel, speaking in front of an audience is a fairly important skill to have! I have also spoken several times at history colloquiums during college. I use this program a LOT for my job.
...Following style guidelines is also critical. English writing can be difficult for ESL students, as they need to learn the meanings of homophones--words that sound the same, but are spelled differently--and homonyms (words that are spelled the same but have different meanings). Good writing also ...Calculus is the mathematics of change and variation which is fundamental to Physics, Chemistry, Biology, and Engineering. It is also fundamental to a deeper understanding of finance, marketing, and economics. Differential Calculus leads directly into Integral Calculus and eventually to the Differential Equations which can be used to model just about any continuous function or process |
Math software for students studying precalculus. Can be interesting for teachers teaching precalculus. Math Center Level 1 consists of Graphing calculator 2D, Advanced Calculator, Simple Calculator, Simple Calculator, Simple Rational Calculator, and Simple Integer Calculator called from the Control Panel. Simple calculator is a general purpose calculator which combines can enter any number or formula which contains numbers. In the f(x) window you can enter formulas containing numbers and formulas containing x. First, x will be calculated. Then the result for x will be substituted into the formula for f(x). The presence of two editing windows demands switching between windows. You can do it by clicking buttons "go to x" and "go to f(x)", or by clicking inside the window. If you forget to enter x, then the x=1 will be assumed. If you forget to enter f(x), then f(x)=x will be assumed. Advanced Calculator works in scientific mode. All numbers in internal calculations are treated in scientific format. Graphing Calculator 2D has two panels. The Left Panel has the Magnifying Square represented by Small Square with gray border on the Left Panel. It is 16 times smaller than the Left Panel. The Right Panel shows content of the Magnifying Square magnified 16 times. You can press button "zoom +". Then the Left and Right Panels will be zoomed twice each. Maximum zoom is 8 (tree clicks of "zoom +"). Clicking button "C" (for Center) on Zoom returns picture to starting position with no zoom and Magnifying Square at the center of Left Panel.Users need to be aware that whereas Romaco Calculator does not support decimal input, it can...Math workpad - Math workpad is a programmable workpad for mathematics.Math workpad is a programmable workpad for mathematics. This widget lets you evaluate complex mathematical expressions. All results are displayed, and you can use the answer from the previous...
Java's Calculator - Java's Calculator is a simple, easy-to-use and accessible instrument that allows you to perform various math calculations.Java's Calculator is a simple, easy-to-use and accessible instrument that allows you to perform various mathFASTT Math - FASTT Math ensures that all students, regardless of their fluency level, build the long-lasting fluency they will need to tackle higher-order math.FASTT Math ensures that all students, regardless of their fluency level, build the long-lasting...
ScientificCalculatorDecimal - Scientific Calculator Decimal is programmed in C# and is similar to Scientific Calculator from Math Center Level 2 except that all calculations are done in decimal data type instead of double.Scientific Calculator Decimal is programmed in C# and...
Math Stars Plus - Math Stars Plus is an educational application which includes a series of games that will help kids improve their Math skills.Math Stars Plus is an educational application which includes a series of games that will help kids improve their Math |
In this tutorial we explain what a "normal" is and the math behind calculating them. Math topics include the cross product, magnitude and normalizing of vectors. Normals are used for many things, lighting and collision for example. |
Al It has a practice and a game area. It has a great help system that makes it easy for the beginner to do and understand algebra. It also has a "Einstein" level that even algebra experts will find fun and challenging. You can choose
Master Algebra in 24 hours. This Tutorial. intended for mature students, covers the Algebra Topics taught in School and required for College - Numbers, Fractions, Linear Equations, Simultaneous Equations, Exponents, Quadratic Equations, Graphs and Polynomials. It makes Algebra easy by carefully explaining the Rules and providing examples showing how to apply them. Many people have trouble with Algebra because when it was taught in school, they weren't ready to absorb the abstract Rules. And The complete set of A-PDF Screen Tutorial Maker features include Simple, Fast, Effective: YouThe best algebra calculator there is.It is not just a calculator you can write your own programs on it. > Can store up to 15 functions at run time. Can give these functions names > Can write your own programs that manipulate functions and can use these programs on different sets of data. You can write as many programs as you need. > Shows the past history of manipulations on functions with their results > Can save, edit, and update the work on functions. > Can do integration and...
...
started.
Mavscript allows the user to do calculations in a text document. Plain text and OpenOffice Writer files (odt,sxw) are supported. The calculation is done by the algebra system Yacas or by the Java interpreter BeanShell. Mavscript runs on LINUX, Windows, Mac OS X and other platforms. How it works ----------- Mavscript reads the calculation commands in the template. These commands start with the control characters $m and end with one of the following control characters: $i, $o, $io und LSP is powered by the powerful and light weight programming language Lua and is comparable to the speed of a compiled language such as C++. As an example,... The lessons are designed for guitar enthusiasts with no prior musical knowledge. All lessons are written in both tablature and Volume II is for beginning and intermediate musicians. Its 23 lessons cover guitar skills, technique, and musical theory. It uses both tab and standard musical notation to teach students to master the pick,... action with what the program would do in the same...
A Chinese Typing Tutorial in the form of Slide-Show Presentation, based on the popular HanWJ Chinese Input Software. It demonstrates the most-commonly used PinYin input method, plus advanced Chinese input techniques.
Algebra Vision is a unique educational software tool to help students develop algebraic problem solving strategies. It provides an environment to play and see algebra in a more tangible light. You can literally move expressions around! Draw lines connecting distributive elements!
Interactive biquadratic, reciprocal, cubic and fractional algebraic equations. Each solution step is provided with its objective, related definition, rule and underlying math formula or theorem. A translation...
You can use it for any kind of numeric or exact symbolic computation (Polynomial arithmetic, Linear algebra and matrix arithmetic, Derivivative and Integrals, Ordinary differential equations, Limits, series expansion, Probability and statistics). It is just like having a mathematical lab right into your pocket!. . |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.