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Summary: Solving word problems has never been easier than with Schaum's How to Solve Word Problems in Algebra! This popular study guide shows students easy ways to solve what they struggle with most in algebra: word problems. How to Solve Word Problems in Algebra, Second Edition, is ideal for anyone who wants to master these skills. Completely updated, with contemporary language and examples, features solution methods that are easy to learn and remember, plus a self-test....show more...070071343077 | 677.169 | 1 |
Microsoft® Mathematics for Educators
Step-by-Step
Microsoft® Mathematics for Educators
Step-by-Step
Familiarize yourself with the interface
When you first open Microsoft Mathematics, you'll see the following elements displayed:
1. The Calculator Pad which includes a number pad and the following button groups: Statistics, Trigonometry, Linear Algebra, Calculus, Standard, and Favorite Buttons.
2. The Worksheet tab is displayed by default, and is where you will do most of your numerical computing. This tab includes both an input and output pane. The input pane gives you the option of using the graphing calculator, keyboard or ink input. When you click buttons on the calculator pad, you construct a mathematical expression in the keyboard input pane.
3. The Graphing tab can be used to create most mathematical graphs. This tab includes an input pane to enter the function equation, inequality, data sets, or parametric equations that you want to plot.
4. Math Tools : On the Home tab, in the Tools group, you'll see buttons for additional math tools:
* Equation Solver to solve a single equation or a system of equations.
* Formulas and Equations to find frequently used equations from science and math, and explore them graphically or by solving for a particular variable.
* Triangle Solver to find the measures of the remaining sides and angles of a triangle when some sides and angles are known.
* Unit Conversion Tool to convert measurements in one system of units to another.
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Using the Graphing Calculator
The primary tool in Microsoft Mathematics is a full-featured scientific calculator with extensive graphing and equation-solving capabilities.
You can use it just like a handheld calculator by clicking buttons, or you can use your keyboard to type the mathematical expressions that you want the calculator to evaluate.
Solve an equation:
Our sample problem is to find the area of a walkway that surrounds a... | 677.169 | 1 |
ustafson and Frisk's Intermediate Algebra: Student Solutions Manual
This manual provides worked-out, step-by-step solutions to the odd-numbered problems in the text. This gives students the information as to how these ...Show synopsisThis manual provides worked-out, step-by-step solutions to the odd-numbered problems in the text. This gives students the information as to how these problems are solved | 677.169 | 1 |
Writing Math Research Papers: A Guide for Students and Instructors
Book Description: Students often need help learning to write well. This book serves as a student text and a resource for implementing a mathematics research program. The book details how to write a research paper, from pre-writing to presenting the paper. It provides interesting research topics, a bibliography of periodicals and problem-solving books and information about mathematics contests | 677.169 | 1 |
More About
This Book
Editorial Reviews
Booknews
Introduces elementary mathematics as it is used in engineering and science, keyed to intermediate and advanced GNVQ examinations in Britain, Australia, and former colonies in Africa. For such areas as algebra, geometry, trigonometry, calculus, and probability, briefly outlines the theory but counts on the examples and problems to codify it in the student's mind. Assumes no particular background in any area of mathematics. Two companion volumes continue the coverage through intermediate and advanced levels | 677.169 | 1 |
Linear Equations 6-9 - MAT-942 how to use engaging hands-on activities within the context of real-world situations to help students develop an understanding of linear function concepts. Through measuring and counting students discover patterns and relationships that they analyze, generalize, represent, and describe with tables, graphs, and rules that are expressed in words and with equations. This course requires student participation.
Connect With
Testimonial
"I enjoyed the opportunity to reflect after each lesson on how I would incorporate the new knowledge into my curriculum. I feel very confident that I'll be able to use this new technology with my students this year." | 677.169 | 1 |
Beginning Algebra - With Access - 6th edition
Elayn Martin-Gay's developmental math textbooks and video resources are motivated by her firm belief that every student can succeed. Martin-Gay's focus on the student shapes her clear, accessible writing, inspires her constant pedagogical innovations, and contributes to the popularity and effectiveness of her video resources. This revision of Martin-Gay's algebra series continues her focus on students and what they need to be successful.
......Used books do not include components such as Access Codes, CDs, DVDs, Study Guides/Readers, and one time use cards. Quality text from a reliable seller. Speedy service! Choose EXPEDITED for fast...show moreest shipping! ...show less
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S.O.S. MATHematics
S.O.S. MATHematics is your free resource for math review material from Algebra to Differential Equations!The perfect study site for high school, college students and adult learners. Get help to do your homework, refresh your memory, prepare for a test, ….Browse our more than 2,500 Math pages filled with short and easy-to-understand explanations. Click on one of the following subject areas: Algebra, Trigonometry, Calculus, Differential Equations, Complex Variables, Matrix Algebra, or Mathematical Tables.
This entry was posted on November 22, 2007 at 8:17 am and is filed under Curriculum, Mathematics | 677.169 | 1 |
Purplemath contains practical algebra lessons demonstrating useful techniques and pointing out common errors. Lessons are written with the struggling student in mind, and stress the practicalites over the technicalities. Links and other resources also ava | 677.169 | 1 |
Series has helped thousands of students succeed in developmental mathematics by providing the best learning and teaching support to students and instructors. The Lial Serieshas helped thousands of students succeed in developmental mathematics by providing the best learning and teaching support to students and instructors.
6.3 Using the Percent Proportion and Identifying the Components in a Percent Problem
6.4 Using Proportions to Solve Percent Problems
6.5 Using the Percent Equation
6.6 Solving Application Problems with Percent
6.7 Simple Interest
6.8 Compound Interest
7. Geometry
7.1 Lines and Angles
7.2 Rectangles and Squares
7.3 Parallelograms and Trapezoids
7.4 Triangles
7.5 Circles
7.6 Volume and Surface Area
7.7 Pythagorean Theorem
7.7 Congruent and Similar Triangles
8. Statistics
8.1 Circle Graphs
8.2 Bar Graphs and Line Graphs
8.3 Frequency Distributions and Histograms
8.4 Mean, Median, and Mode
9. The Real Number System
9.1 Exponents, Order of Operations, and Inequality
9.2 Variables, Expressions, and Equations
9.3 Real Numbers and the Number Line
9.4 Adding Real Numbers
9.5 Subtracting Real Numbers
9.6 Multiplying and Dividing Real Numbers
9.7 Properties of Real Numbers
9.8 Simplifying Expressions
10. Equations, Inequalities, and Applications
10.1 The Addition Property of Equality
10.2 The Multiplication Property of Equality
10.3 More on Solving Linear Equations
10.4 An Introduction to Applications of Linear Equations
10.5 Formulas and Additional Applications from Geometry
10.6 Solving Linear Inequalities
11. Graphs of Linear Equations and Inequalities in Two Variables
11.1 Linear Equations in Two Variables; The Rectangular Coordinate System
11.2 Graphing Linear Equations in Two Variables
11.3 The Slope of a Line
11.4 Writing and Graphing Equations of Lines
11.5 Graphing Linear Inequalities in Two Variables
12. Exponents and Polynomials
12.1 Adding and Subtracting Polynomials
12.2 The Product Rule and Power Rules for Exponents
12.3 Multiplying Polynomials
12.4 Special Products
12.5 Integer Exponents and the Quotient Rule
12.6 Dividing a Polynomial by a Monomial
12.7 Dividing a Polynomial by a Polynomial
12.8 An Application of Exponents: Scientific Notation
13. Factoring and Applications
13.1 Factors; The Greatest Common Factor
13.2 Factoring Trinomials
13.3 Factoring Trinomials by Grouping
13.4 Factoring Trinomials by Using the FOIL Method
13.5 Special Factoring Techniques
13.6 A General Approach to Factoring
13.7 Solving Quadratic Equations by Factoring
13.8 Applications of Quadratic Equations
14. Rational Expressions and Applications
14.1 The Fundamental Property of Rational Expressions
14.2 Multiplying and Dividing Rational Expressions
14.3 Least Common Denominators
14.4 Adding and Subtracting Rational Expressions
14.5 Complex Fractions
14.6 Solving Equations with Rational Expressions
14.7 Applications of Rational Expressions
14.8 Variation
15. Systems of Linear Equations and Inequalities
15.1 Solving Systems of Linear Equations by Graphing
15.2 Solving Systems of Linear Equations by Substitution
15.3 Solving Systems of Linear Equations by Elimination
15.4 Applications of Linear Systems
15.5 Solving Systems of Linear Inequalities
16. Roots and Radicals
16.1 Evaluating Roots
16.2 Multiplying, Dividing, and Simplifying Radicals
16.3 Adding and Subtracting Radicals
16.4 Rationalizing the Denominator
16.5 More Simplifying and Operations with Radicals
16.6 Solving Equations with Radicals
17. Quadratic Equations
17.1 Solving Quadratic Equations by the Square Root Property
17.2 Solving Quadratic Equations by Completing the Square
17.3 Solving Quadratic Equations by the Quadratic Formula
17.4 Graphing Quadratic Equations
17 | 677.169 | 1 |
Mathematical Symbols
Help
POV-Wiki supports the standard mediawiki math markup (available via the √n button on the edit toolbar). Additionally, it has an interactive TEX editor, called the 'TEX Box', which appears in a popup window when you click on the ∑ button at the left of the edit toolbar.
Inserting Formulas
Inserting TEX markup is done using <math>...</math> tags. For example, to display the following quadratic formula
<math>x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</math>
you could use the markup
<math>x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</math>
Consistent Use of <math>...</math>
It is strongly advised that <math>...</math> be used around all mathematics added to this wiki, even if the assistance of TEX is not required (e.g. if the formula could be displayed using standard HTML). This will assist when exporting the wiki into other formats, such as PDF. | 677.169 | 1 |
More Teaching Learning and Mathematics with ICT
This book contains a compilation of articles from Micromath, a journal of The Association of Teachers of Mathematics. The articles were published between Spring 1995 and Winter 1999. The articles have been selected to encourage and enable the reader to use ICT in their classroom. Their content ranges from primary, through secondary to higher education, with some articles encompassing more than one category.
They have been arranged into four main themes of logo, geometry and spreadsheets, and graphic calculators along with a miscellaneous section, which dips into different topics including, the internet. There is also a section of challenges. | 677.169 | 1 |
27,"ASIN":"156577034X","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":62.3,"ASIN":"1565775031","isPreorder":0}],"shippingId":"156577034X::nv33xl3%2F1T98UI5pH%2BTI8ML0jc7VLSN6T8AMz1Vgwz54O5F7tdEH9jtuJstwvDEOSDarup0BWuppN3mwxTBbIJRL64H6lTUs6HNWaR1gveqDUZcFzPs3Ig%3D%3D,1565775031::5bWYvMqyBTY%2F2QSRxqkCK8mVHsEwuODVeB7Fdy5fp2A4BrblNhicCkr4uRjPeX4aO4V%2BomN0E%2Fr5N119C9q3%2B%2BnA8PLg1LmQ0iqOE034V3 homeschooled our kids over a period of years, and Saxon Math, including Math 54, was always our choice for math texts. I also teach in a classical Christian school where we use Saxon Math as well. I find that for most students, if they will take the time to read the lesson well, do all of the problems, and then rework any problems they miss then they will achieve a high degree of mastery of the material at hand.
The greatest advantage of Saxon Math is that each lesson provides practice not only for the new problems but also built-in review for every kind of problem the student has previously encountered. Math 54 is no exception to the rule that Saxon Math texts help students learn math well. After Math 54, all of my kids who have taken it were definitely ready to move on to the next level.
In general, Saxon Math, including Math 54, is highly recommended. It is especially ideal for homeschooling families.
My kid does Saxon Math at her school. So decided to buy the same book and help her with exercises over the weekends. But while ordering, instead of ordering the Children edition, bought the teacher's edition. The book is exact same as Children's edition but answers in bold red next to the questions, making it totally unusable for children's homework.
I wrote the seller and requested to return it. The seller took few days to reply and those two days, I found how useful this book can be..Once my daughter finishes her exercise, check the answers in 30 seconds instead of 10-15 Minutes it takes everyday.
I did not return the book and instead ordered another book for Children .
As far as Saxon Math goes, it is a wonderful compliment for word problems.Tons of word problems alone makes it worth. The way exercises are built with couple of questions similar to those learnt in previous chapters is very well done.
I love this book and use it with the DIVE cd-rom. I highly recommend Saxon for lots of practice and building on concepts. There is much to be said for the DIVE program as well: It is awesome to have a computer tutor to teach each lesson! I love it!
I have used this book over and over again. After I give students the Saxon Math test, I can see which book the student needs to be put in. I have used the supplements in the books to bring students up to have basic skills in Math. This is a great book that reinforces adding, subtraction, multiplication, and division. This book is a tremendous help. | 677.169 | 1 |
This program consists of a developmental mathematics class that assists students with intermediate algebra (MAT 1010). Students enrolling in this option will form a learning community where they can help one another. To assist with this, the course will have a trained tutor who attends the class and then meets with students for supplemental instruction in the afternoons to help them progress daily. Taking this course during the summer will give students a strong academic foundation for course work in the fall semester, and will also fulfill developmental education requirements for those who test into these skills. The Summer Bridge Program will also help students become involved with university life as a whole, introducing them to many facets of belonging to a campus. | 677.169 | 1 |
This section contains free e-books and guides on Trigonometry, some of the resources in this section can be viewed online and some of them can be downloaded.
The first six chapters of this book give the
essentials of a course in numerical trigonometry and logarithmic computation.
The remainder of the theory usually given in the longer courses is contained in
the last two chapters.
Elementary trigonometry
is a book written by mathematicians H. S. Hall and S. R. Knight. This book
covers all the parts of Elementary Trigonometry which can conveniently be
treated without the use of infinite series and imaginary quantities. The
chapters have been subdivided into short sections, and the examples to
illustrate each section have been very carefully selected and arranged, the
earlier ones being easy enough for any reader to whom the subject is new, while
the later ones, and the Miscellaneous Examples scattered throughout the book,
will furnish sufficient practice for those who intend to pursue the subject
further as part of a mathematical education.
This book
covers elementary trigonometry. It is suitable for a one-semester course at the
college level, though it could also be used in high schools. The prerequisites
are high school algebra and geometry.
This note is focused on the
following subtopics: Trigonometric Functions, Acute
Angles and Right Angles, Radian Measure and Circular Functions, Graphs of the
Trigonometric Functions, Trigonometric Identities, Inverse Trig Functions and
Trig Equations, Applications of Trigonometry and Vectors. | 677.169 | 1 |
One of a set of three books for grades 10 – 12. A panel of senior subjects advisors and teachers with many years experience as examiners and sub-examiners wrote the books. A variety of different questions cover the syllabus fully and assist Maths students in the class and to prepare them for their exams. Both teacher and learners can use the explanatory examples with complete solutions fruitfully for continuous evaluation in the class. The last chapter consists of four exam question papers with complete memos.
Ook in Afrikaans beskikbaar as Ken & Verstaan Wiskunde Graad 10
Product details
Author:
Klarin Loots, E.A. Bester
Format:
Softcover
Imprint:
Cambridge University Press
Edition:
2nd revised edition
ISBN:
9780947465605
Series Title:
Study & Master
Audience:
Schools & Educational
Pages:
389
Width (mm):
245
Length (mm):
170 | 677.169 | 1 |
Math - Home
University Transfer
Learn more!
Sign up now for PierceConnect and keep up on the latest information about our courses, events and opportunities on campus.
In many disciplines, mathematics is used to help make sense of phenomenaobserved in the world. Math also can help us develop critical thinking and reasoning skills that can be used to solve problems in a variety of applications. Pierce College offers two sequences of math courses, pre-college and college-level, to meet the needs of the individual student and his or her goals.
Initial placement in a sequence of courses depends on COMPASS placement test scores. The choices and the number of courses a student takes depend on their chosen field of study and other factors. See a faculty advisor for help.
Pre-College Math
The Mathematics department offers a sequence of introductory courses that build the basic quantitative and symbolic reasoning skills needed in almost all fields of study and professional/technical training.
These pre-college mathematics classes accommodate students entering the college with a variety of math backgrounds. These courses are offered in the Math lab, online, and in traditional classrooms.
Math Lab
The Pierce College Math Labs try to meet different learning styles by providing pre-college level mathematics courses to students in a web-based format. Students take most of the responsibility for their own learning. Attendance is mandatory. There is a minimum pace requirement for the class but students may work ahead. Students who work ahead can be registered for the next class for NO additional costs (during the same quarter at the discretion of the instructor provided that the student has shown sufficient mastery by the 7th week). Class time is spent working exercises online, reading the book online, watching videos online and taking tests online. All tests and the final exam must be taken in the lab. An instructor or tutor will always be available to assist students.
The Fort Steilacoom Math Lab uses the web-based program ALEKS. The Puyallup Math Lab uses the web-based program MyMathLab.
Courses offered through the Math Lab:
MATH 051: Fundamentals of arithmetic
MATH 054: Pre-Algebra
MATH 060: Introduction to algebra
MATH 098: Intermediate algebra
When the lab is not being used for a class it is available for drop-in Math Lab student use. There will be a tutor available to assist students.
College-Level Math
Pierce College also provides a sequence of college-level math courses for students transferring to four-year colleges or pursuing technical vocational programs. These courses satisfy the math requirements for majors in mathematics, as well as business, accounting, economics, statistics, actuarial science, math education, engineering, and the sciences. These college-level courses include the math needed for the Associate in Science degree from Pierce College.
Each course includes examples of applications taken from many fields of study. Most of these courses require the use of graphing calculators, which may be rented for a nominal fee through the libraries.
College-level courses
The courses listed below satisfy the Quantitative Reasoning Skill (QS) requirement. The prerequisite for all these QS courses can be satisfied by MATH 098 with a grade of 2.0 or higher or placement above MATH 098 on the COMPASS placement test. MATH 095 with a grade of 2.0 or higher will serve as a prerequisite to MATH 107& and MATH& 146. Students unsure of their intended major are urged to take MATH 098 to allow for more options.
MATH& 107: Contemporary mathematics
MATH 114: Applied algebra, geometry, trig
MATH& 141: Pre-calculus I
MATH 147: Finite mathematics
MATH& 131: Structure of elementary mathematics I
MATH& 146: Intro to statistics
Mathematics major
The following courses should be taken,in addition to courses required for the AA degree:
MATH& 151-153: Calculus I-III
MATH 205: Linear algebra
MATH 224: Multivariate calculus
MATH 238: Differential equations
Courses in statistics and computer science are highly recommended for math majors. Math majors should also take one of the sequences of science courses such as physics or chemistry. See your advisor for specific recommendations. | 677.169 | 1 |
Mathematics has been coined as the queen of sciences. Mathematics is the purest and most profound of intellectual disciplines. What other discipline has a golden braid of "truth" reaching from Pythagoras, Euclid, and Archimedes to Fermat, Newton, Euler, Gauss, and Riemann.
Explore
Mathematics, like music, is a universal language. It's the language of the engineer, the biologist, the chemist and the physicist. Carl Sagan's classic novel "Contact" asserts that if there is extraterrestrial intelligence, the means of contact would be mathematics.
Mathematics is a human creative endeavor of understanding. It is the study of patterns in shape, time, distance and space through careful reasoning and rigorous deductions. Modern applications include Magnetic Resonance Imaging (MRI) which enables physicians to see more clearly. Other new mathematic discoveries include a 128-bit encryption for secure commerce on the World Wide Web (WWW), Global Positioning Systems (GPS), algorithms for speech recognition and canning spam by thwarting unwanted e-mail.
Experience
Men and women trained in mathematics are employed in a wide variety of fields where data analysis and logical thought processes are critical. Undergraduate training in mathematics trains students to organize their thought processes and hone their critical thinking skills.
Excel
Trine's program offers small classes taught by full-time professors who are committed to their professions and committed to the development of each student's full potential in an environment that is friendly and non-threatening. Every student is assigned a faculty adviser who will assist in designing an individual program of study. The faculty maintains regular scheduled office hours, as well as regular scheduled "math help" sessions eight hours per week. | 677.169 | 1 |
More About
This Textbook
Overview
MATLAB: An Introduction with Applications 4th Edition walks readers through the ins and outs of this powerful software for technical computing. The first chapter describes basic features of the program and shows how to use it in simple arithmetic operations with scalars. The next two chapters focus on the topic of arrays (the basis of MATLAB), while the remaining text covers a wide range of other applications. MATLAB: An Introduction with Applications 4th Edition is presented gradually and in great detail, generously illustrated through computer screen shots and step-by-step tutorials, and applied in problems in mathematics, science, and engineering.
Related Subjects
Meet the Author
Amos Gilat, Ph.D., is a Mechanical Engineering Professor at the Ohio State University. Dr. Gilat's research has been supported by the National Science Foundation, NASA, FAA, Department of Energy, Department of Defense, and various | 677.169 | 1 |
Saxon students. Those students who have used the Saxon mathematics program are best ... 2000_HS_Catalog.pdf Author: Rick Yoesting Created Date: 8/22/2000 5:03:03 PM
ALEKS offers detailed PDF correlations with these standards. In addition, dynamic online reporting is available for all courses in all 50 states in grades 3-8 and in ...
2 Instructions: Click the Begin Quiz button before you begin your selections. For each question, click the checkbox containing the best answer to the ...
the students age, previous curriculum, and how quickly the student grasps math concepts. If you need more information from a qualified Saxon Math teacher about specific ...
The Numerical Skills/Prealgebra Placement Test includes items from more than a dozen content areas; however, a majority of the questions come from the following categories:
Saxon Publishers Placement Guide Saxon books are skill level books, not grade level books. It is essential that each student is placed in the text that meets the ... | 677.169 | 1 |
Videos on DVD for Elementary and Intermediate Algebra Concepts and Applications
Summary
This workbook provides one worksheet for each section of the text, organized by section objective. Each worksheet lists the associated objectives from the text, provides fill-in-the-blank vocabulary practice, and exercises for each objective. | 677.169 | 1 |
Find a Jeffersonville, PA AlgebraIt involves simplifying expressions, evaluating and solving equations and inequalities, and graphing linear and quadratic functions and relations. This course provides students with a framework for studying political, social, economic, and cultural issues, and for analyzing the impact these issu... | 677.169 | 1 |
State-of-the-art analysis of geological structures has become increasingly quantitative but traditionally, graphical methods are used in teaching. This innovative lab book provides a unified methodology for problem-solving in structural geology using linear algebra and computation. Assuming only limited mathematical training, the book begins with classic orientation problems and progresses to more fundamental topics of stress, strain and error propagation. It introduces linear algebra methods as the foundation for understanding vectors and tensors, and demonstrates the application of geometry and kinematics in geoscience without requiring students to take a supplementary mathematics course. All algorithms are illustrated with a suite of online MATLAB functions, allowing users to modify the code to solve their own structural problems. Containing 20 worked examples and over 60 exercises, this is the ideal lab book for advanced undergraduates or beginning graduate students. It will also provide professional structural geologists with a valuable reference and refresher for calculations. less | 677.169 | 1 |
Editorial Reviews
Using the simple conceptual framework of the Kolmogorov model, this intermediate-level textbook discusses random variables and probability distributions, sums and integrals, mathematical expectation, sequence and sums of random variables, and random processes. For advanced undergraduate students of science, engineering, or mathematics acquainted with basic calculus. Includes problems with answers and six appendixes. 1965 edition. | 677.169 | 1 |
15848847 Complex Analysis: Classical and Modern Approaches (Modern Analysis Series)
Like real analysis, complex analysis has generated methods indispensable to mathematics and its applications. Exploring the interactions between these two branches, this book uses the results of real analysis to lay the foundations of complex analysis and presents a unified structure of mathematical analysis as a whole.
To set the groundwork and mitigate the difficulties newcomers often experience, An Introduction to Complex Analysis begins with a complete review of concepts and methods from real analysis, such as metric spaces and the Green-Gauss Integral Formula. The approach leads to brief, clear proofs of basic statements - a distinct advantage for those mainly interested in applications. Alternate approaches, such as Fichera's proof of the Goursat Theorem and Estermann's proof of the Cauchy's Integral Theorem, are also presented for comparison.
Discussions include holomorphic functions, the Weierstrass Convergence Theorem, analytic continuation, isolated singularities, homotopy, Residue theory, conformal mappings, special functions and boundary value problems. More than 200 examples and 150 exercises illustrate the subject matter and make this book an ideal text for university courses on complex analysis, while the comprehensive compilation of theories and succinct proofs make this an excellent volume for | 677.169 | 1 |
0821833 comprehensive textbook on modern algebra written by an internationally renowned specialist. It covers material traditionally found in advanced undergraduate and basic graduate courses and presents it in a lucid style. The author includes almost no technically difficult proofs, and reflecting his point of view on mathematics, he tries wherever possible to replace calculations and difficult deductions with conceptual proofs and to associate geometric images to algebraic objects. The effort spent on the part of students in absorbing these ideas will pay off when they turn to solving problems outside of this textbook.
Another important feature is the presentation of most topics on several levels, allowing students to move smoothly from initial acquaintance with the subject to thorough study and a deeper understanding. Basic topics are included, such as algebraic structures, linear algebra, polynomials, and groups, as well as more advanced topics, such as affine and projective spaces, tensor algebra, Galois theory, Lie groups, and associative algebras and their representations. Some applications of linear algebra and group theory to physics are discussed.
The book is written with extreme care and contains over 200 exercises and 70 figures. It is ideal as a textbook and also suitable for independent study for advanced undergraduates and | 677.169 | 1 |
Edit by t9t.info: UltimaCalc - UltimaCalc is a scientific and mathematical graphing calculator. Always ready for use as it can stay on top of other windows, transparent when inactive. Type a calculation as plain text, evaluate it, maybe edit it and re-calculate, record all calculations. Has a comprehensive help system. Work with algebra. Simplify expressions, differentiate them. Integrate a wide range of expressions, and have the solution explained. Find Taylor series. Factorise polynomials, divide them, find their GCDs. Specialised tools run in their own windows, and can save their data for future reference. One tool performs a variety of least square fit methods ( including non-linear, polynomial, multivariate ). Another finds the minimum of a multi-variate expression. Others solve triangles, or find roots of polynomials up to tenth order, or solve simultaneous linear or non-linear equations. UltimaCalc includes logarithms to base 2, two-argument inverse tangent, greatest common divisor. Also floor and ceiling functions, absolute value, min, max, extract the fractional part of a number, find the value for which an expression is at its minimum. Find the slope of a line between two points. Calculate definite integrals. Define your own functions, variables and constants. UltimaCalc works to 38 digit precision. You can select the display precision and group the digits for readability. Two' scientific' view modes use exponent format. The' engineering' mode uses suffixes such as k ( kilo ) and M ( mega ). View results in hexadecimal and as ratios. Calculate the mean, median and standard deviation of a sample and its population. Use absolute deviation fit to minimise the distorting effects of outlying values. Plot functions: Specify starting and ending conditions and how the variables change. Combine multiple plots. Create charts. Add title, subtitle, labels. Adjust the layout, colours and hatching. Work with dates, future or past. Find Easter for any year. Simple navigational calculations. | 677.169 | 1 |
Functions Teacher Resources
Find Functions educational ideas and activities
Title
Resource Type
Views
Grade
Rating
When comparing pricing models, young mathematical consumers, create linear equations and analyzing them graphically and algebraically. They look at the meaning of slope and intercepts, as well as the intersection points of lines.
Students graph polynomials functions and analyze the end behavior. In this algebra lesson, student differentiate between the different polynomials based on the exponents. They use a TI to help with the graphing.
Here is an unexpected resource: chapter 1 of an Algebra textbook. You can use all or some of its contents to teach your Middle Schoolers all about algebraic expression, domain, function notation, linear equations, order of operations, input/output, ordered pairs, and variable expressions. This would be great for a substitute or newer teacher looking for reliable tools.
Use real world scenarios to facilitate discussion of the relationship between variables and how they are represented graphically and analytically. This can work in part as an introduction to functions, as a complete lesson, or as an extension to a unit on the library of functions.
Functions are on the move! This lesson plan provides an opportunity for learners to explore transformations of functions. The activity illustrates the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for both positive and negative values of k. Working in small groups, students complete a table of values for a parent function and an assigned transformation of that function. After sketching both graphs on the same coordinate plane, they analyze their results and write a conjecture about how the value of k affects the original function. Each group shares its findings with the class. The results of the activity are reinforced by using graphing calculators to graph the functions and comparing with the sketches done with pencil and paper. The activity concludes with learners applying what they have learned to write equations for functions when given their graphs.
Mathematicians study how algebra can tell the stories of linear growth and they develop problem solving skills in relation to linear growth contexts. In this lesson, students organize information to explain growth, they use algebraic equations to make connections between real life and linear change.
Exponential functions are the name of the game. Young mathematicians can work through each of the eight worksheets by evaluating functions, applying logarithms, completing logarithmic functions, and building inverse functions. This would be a great set of worksheets to accompany an entire chapter.
Middle schoolers describe plotting functions on the Cartesian coordinate plane. They solve functions on paper and using an online tool to plot points on a Cartesian coordinate plane creating lines and parabolasMiddle and high schoolers complete and solve 12 various types of problems. First, they express the output as a function of the input in each table. Then, pupils evaluate for the given variable when the value is as stated. In addition, they read the information provided and translate as much as they can into mathematical expressions.
This lesson has a number of fun worksheets for a pre-algebra or beginning algebra class. The main emphasis of this lesson is functions, formulas, and looking at square roots. It is the third lesson in a series on solving for unknowns, which you can find if you look first at the "Getting Started" link. This lesson, in particular, focuses on developing an understanding between the inverse relationship of squaring a number and taking its square root, finding probabilities, and creating linear equations and solving problems.
In this algebraic functions worksheet, learners write a function to determine the relationship between people and barrels of oil used. They research the population of the 10 largest cities in their state and use this functional relationship to calculate the number of barrels and gallons of oil used by each city.
Students solve formulas by using substitution. In this algebra lesson, students utilize formulas introduced in the lesson which apply to science as well as volume and area. The lesson gives detailed instruction for solving each type of problem. Detailed answers to all practice problems are provided with step by step solutions to assist.
Students explore the TI-92. In this secondary mathematics lesson, students examine the applications and functions of the TI-92. Students investigate symbolic manipulation, 2D and 3D graphing, the interactive geometry module and the programming and text editor.
High schoolers graph functions on their graphing calculators. They follow step-by-step directions to enter rational functions onto their calculators and then graph them. The worksheet includes nine questions
Pre-algebra pupils investigate linear equations and functions. In this algebra lesson, learners find the slope and identify the line as increasing or decreasing. They identify the x and y intercept given the equation in the form y= mx + b.
Examine multiple ways to solve algebraic equations. Pupils will generate a problem solving strategy that addresses the prompt given by the teacher. They will then share their problem solving strategy with the class. Graphic organizers, problem solving prompts, and tables are included.
Elementary schoolers use a function machine in order to help them look at the relationship between input and output, and to look at the rule for the change. The machine is actually a cardboard box, and it serves quite well for the lesson! One student takes the input numbers and creates an output number. After enough have been done, learners try to figure out the rule that is being used. A good teaching idea! | 677.169 | 1 |
Description: The purpose of this little book is to give the reader a convenient introduction to the theory of numbers, one of the most extensive and most elegant disciplines in the whole body of mathematics. The treatment throughout is made as brief as is possible consistent with clearness and is confined entirely to fundamental matters. | 677.169 | 1 |
Math for Merchandising : A Step-by-StepMerchandising Math: A Step-by Step Approach, Third Edition, takes users step by step through the concepts of merchandising math. It is organized so that the chapters parallel a career path in the merchandising industry. The text begins with coverage of fundamental math concepts used in merchandising and progresses through the forms and math skills needed to buy, price, and re-price merchandise. Next students learn the basics of creating and analyzing six-month plans. The final section of the text introduces math and merchandising concepts that ... MOREare typically used at the corporate level. New to this edition is a Student Resources CD packaged with the book that contains forms from the text, Excel templates, guided Excel exercises, and quizzes for each chapter in the book This book takes users step by step through the concepts of merchandising math. It is organized so that the chapters parallel a career path in the merchandising industry.The book begins with coverage of fundamental math concepts used in merchandising and progresses through the forms and math skills needed to buy, price, and re-price merchandise. Next readers learn the basics of creating and analyzing six-month plans. The final section of the book introduces math and merchandising concepts that are typically used at the corporate level.For individuals pursuing a career in merchandising. | 677.169 | 1 |
Facilities and Resources
Student Common Room
Equipped with sofas, desks, blackboards, a fridge and a microwave, this room is an ideal space for students to work collaboratively or take a break.
Labs
Mathematical Fluids Lab To model fluids more accurately, faculty and students use this lab to compare mathematical predictions, numerical simulations and experimental results.
Computational Algebra Lab To gain a deeper understanding of number theoretic and algebraic questions, faculty and students use this lab to generate numerical evidence for mathematical questions in number theory and abstract algebra.
Competitions
Putnam Exam More than 400 colleges and universities in the U.S. and Canada compete in the annual William Lowell Putnam Mathematical Competition. Bucknell often does well in this contest. In 2004 the Bucknell team placed 10th, higher than any other liberal arts institution in the nation. || LearnMore about the Putnam Exam.
John Steiner Gold Exam Bucknell students help to host this mathematical competition organized by the department in memory of a distinguished colleague. Students from public and private high schools as far as 100 miles away participate and compete for team and individual prizes. || LearnMore about the Gold Exam.
Mathematical Contest in Modeling The MCM is a nation-wide contest in which teams of undergraduates use mathematical modeling to present their solutions to real world problems. Bucknell often enters multiple teams. In 2010, the team of Dan Cavallaro, Bryan Ward, and Ryan Ward were one of only nine teams in the world to earn the highest designation of "Outstanding Winners" of the MCM. || LearnMore about the MCM.
The University supports Windows, Macintosh and Unix environments. Computationally intensive projects can be deployed on the 128-core Linux Computing Cluster.
Speakers and Events Mathematicians from academia and industry share valuable information about careers, and students gain exposure to the culture of mathematics and mathematicians. || Find out What's Happening
Math Education Tools The department owns a variety of mathematics manipulatives that assist in learning and teaching mathematics. These include items that can be used at the elementary and middle school levels (e.g., pattern blocks, base-10 blocks) as well as the high school and collegiate levels (e.g., Calculator Based Laboratory Units (CBL) with various probes).
Mathematical Treasures
at the Bertrand Library
During a recent visit to Bucknell, Ed Sandifer of Western Connecticut State University noted six mathematical treasures located in the Special Collections of the Betrand Library, including Blundevil's Exercises.
Off-campus Study in Math
About 45 percent of Bucknell University students take part in an off-campus experience while studying at Bucknell.
In recent years, several mathematics majors have participated in the highly prestigious Budapest Semesters in Mathematics program, which allows students from the United States and Canada to meet and engage in an intensive study of mathematics for a semester in Budapest.
Other mathematics students have spent semesters in Australia, Chile, England, Ireland, Italy, New Zealand, Scotland and Spain. | 677.169 | 1 |
Plenty of examples, practice problems, and learning tools provide the perfect math review for health professionals! With just the right level of content and highly illustrated example problems, this user-friendly worktext helps you learn and understand fundamental math principles and understand how they apply to patient | 677.169 | 1 |
Pre-AP: Strategies in Mathematics—Accumulation
Using a guided-exploration approach, teachers learn accumulation concepts for grades 6-12. Participants develop problems and learn instructional activities, assessment items, and cross-grade lessons for classroom use. They also learn diagnostic and assessment strategies that help teachers communicate with students and help monitor students' mathematical thinking.
Workshop topics include:
The concept of area
Accumulating distance when speed is constant, changes, or is a function
Agenda
Accumulation and the Concept of Area Accumulating Distance When Speed Is Constant Accumulating Distance When Speed Changes Accumulating Distance When Speed Is a Function Velocity Distinct from Speed The Big Picture of Accumulation
Workshop author
Jim Choike is a professor of mathematics at Oklahoma State University (OSU). He has been involved with the College Board for 20 years as an AP Reader, workshop presenter, curriculum developer, and professional development specialist. Mr. Choike has also worked on the College Board's: Pathways to Equity and Excellence, Pacesetter, CLEP, SAT, and SpringBoard programs. He teaches undergraduate and graduate mathematics courses at OSU and uses his summer months to work with middle and high school teachers and their students. | 677.169 | 1 |
Analysis Qualifying Exams
Syllabus Topics
This exam will test your working knowledge of basic real, complex and functional analysis. You will be required to demonstrate an ability to use standard results and techniques to solve problems, including special cases of standard theorems which do not require long arguments.
We will not emphasize the memorization of statements of theorems nor of long proofs of standard theorems.
The student is urged to work on the problems in the relevant sections and chapters in the reference books.
The syllabus is divided into the topics of Complex Analysis and Real and Functional Analysis.
Complex Analysis
1. Definition of Holomorphic fuctions with examples, including logarithms, roots, and Möbius transformations.
2. Cauchy-Riemann Equations.
3. Power Series Expansion and applications including the Identity Theorem.
Real and Functional Analysis
A. Real Analysis on the Real Line
σ-algebra, Borel sets, construction of Lebesgue measure, measurable sets, how to approximate a Lebesgue measurable set with positive measure from outside and inside, Cantor set, measurable functions, f(g(x)) is measurable if f is continuous and g is measurable.
Convergence a.e., convergence in measure, convergence in the mean and how they are related to each other, Egorov's Theorem, Luzin's Theorem. | 677.169 | 1 |
recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on fast inexpensive computers, has sparked a minor revolution in the study and practice of algebraic geometry. These algorithmic methods have also given rise to some exciting new applications of algebraic geometry. This book illustrates the many uses of algebraic geometry, highlighting some of the more recent applications of Grobner bases and resultants.In order to do this, the authors provide an introduction to some algebraic objects and techniques which are more advanced than one typically encounters in a first course, but nonetheless of great utility. The book is written for nonspecialists and for readers with a diverse range of backgrounds. It assumes knowledge of the material covered in a standard undergraduate course in abstract algebra, and it would help to have some previous exposure to Grobner bases. The book does not assume the reader is familiar with more advanced concepts such as modules. For this new edition the authors added two new sections and a new chapter, updated the references and made numerous minor improvements throughout the text. less | 677.169 | 1 |
CSET Math Exam
CSET Math Exam- a Brief Overview
If you are a potential Mathematics teacher and you are planning to take the California Subject Examinations for Teachers or CSET, then you have to first find out everything that you can about this examination so that you can prepare for the same in the most effective manner. The CSET math exam is not tough, not matter what you may have heard other people saying. As long as you study for it properly, there is no reason why you cannot score high in it. In this piece of writing, we will be discussing about the Mathematics portion of the CSET so that you will be able to get a clear idea of what it is before you start your preparation.
Sections of CSET Mathematics
It is important that you understand the subtests that will be included in this exam. You also need to make sure that you get a very clear idea of the subjects that will be tested on so that you can get a high score in this test. You will find that the CSET math exam has three subtests that you will need to take and these are as the following:
Subtest I: The questions that you will find here will be based on Algebra and Number Theory. You need to have a complete understanding of these topics so that you can answer the questions correctly. The areas that you should have a thorough understanding of in when it comes to this subtest are Linear Algebra, Functions, Polynomial Equations and Inequalities, Algebraic Structures and Natural Numbers.
Subtest II: This is the section of the CSET math exam where the questions will be based on Probability and Statistics and Geometry. You need to have a deep theoretical knowledge of the topics that will be tested so that you can get a high score in the examination. The areas that you should prepare for this subtest are Probability, Statistics, Transformational Geometry, Three-Dimensional Geometry, Plane Euclidean Geometry and Parallelism.
Subtest III: You will be tested on the History of Mathematics and Calculus in this CSET math subtest. The topics that you need to study in-depth to get a good score in this exam are Chronological and Topical Development of Mathematics, Series & Sequences, Integrals, Derivatives, Continuity & Limits and Trigonometry.
More on CSET Math
Here are some of the points that you should know about the CSET math exam:
This is a computer-based test where you will need to take the exam online. As such, it is essential that you have the basic skills to operate a computer.
The questions can be in the form of constructed-response and multiple-choice questions. In the multiple-choice questions, you will find four answer options for every question and you need to choose an option that you believe is the correct answer.
You will need to finish the exam within the time period that has been allotted to you, for there is no grace period. You will need to complete all the questions in Subtest I & II within 4 hours (2 hours for each section), and the time limit for Subtest III is 2.5 hours.
Each of the subtests will be scored individually and the result is generally available within four weeks from the date of the examination. You can find out more information on the result date by checking the official website of the examination at You can check the result online after it is released simply by signing into your account in this site. The report will be in PDF format and you can print it out within 45 days, after it has been released because after that the result will no longer be available online.
To Conclude...
You will be able to prepare for the test effectively when you know and understand it well. If you want to score high in the CSET math exam, make sure that you start your preparation | 677.169 | 1 |
Math 101 - Core Compentency in Mathematics
COURSE OBJECTIVES: The course helps the student develop the use of mathematics in the world in which we live.
It covers mastery of elementary skills and facts, understanding of logically correct arguments, learning to
think abstractly, and increasing problem solving capacity. Competency developed should be helpful in continued
learning, in setting and achieving goals, in personal decision-making, and in evaluating concerns in the community,
state, and nation.
CALCULATORS: You will need a hand calculator which can do basic arithmetic, square roots, and other exponents
(a y to the x key). Either a scientific or graphing calculator is acceptable. Standard calculators will be allowed
on all exams (laptops, calculators that access the internet, and calculators in cell phones are NOT allowed on exams -
calculators with memory may be subject to inspection and erasure of stored material). If you do not have a calculator,
the TI 30-series calculators are fine for this class - TI-34, TI-36, etc.
WITHDRAWAL: The last day for undergraduates to withdraw from a full-session course will be announced in class.
DRC STATEMENT: If you have specific physical, psychiatric, or learning disabilities and require accommodations,
please let your instructor know early in the semester so that your learning needs may be appropriately met. You will
need to provide documentation of your disability to the DRC (DisabilityResource Center)
the Health Services Building, 4th floor.
ACADEMIC CONDUCT: Academic honesty and mutual respect (student with student and instructor with student) are
expected in this course. Mutual respect includes being on time for class and not leaving early, being prepared to
give full attention to class work, not reading newspapers or other nonclass material in class, turning off phone
ringers and not using cell phones or pagers during class time, and not looking at another student'ÇÖs work during exams.
Academic misconduct, as defined by the Student Judicial Code, will not be treated lightly. | 677.169 | 1 |
MATH 255Vector Calculus•
5 Cr.
Department
Division
Description:
Course topics include multiple integration, line and surface integrals and the theorems of Green, Gauss and Stokes with applications. Related topics such as conservative vector fields, change of variables in special coordinate systems, the higher-dimensional Taylor's Theorem and constrained optimization will be considered. Prerequisite: Multivariable Calculus (MATH& 254).
Outcomes:
After completing this class, students should be able to:
Students taking this course will increase their understanding of the basic theory of functions of several variables, using vectors throughout.
They should be able to:
1. Demonstrate they understand the basic integration and differentiation theory for functions of several variables.
2. Perform calculations relating to double and triple integrals in cartesian, polar, cylindrical and spherical coordinates.
3. Demonstrate the ability to visualize vector fields in various dimensions.
4. Explain the basic theory of line and surface integrals and the theorems of Green, Stokes and Gauss.
5. Perform basic calculations relating to line and surface integrals and apply the theorems of Green, Stokes and Gauss.
6. Demonstrate understanding of basic applications of these additional topics. | 677.169 | 1 |
Earn College Credit with REA's Test Prep for CLEP* College Mathematics EverythingMore... for the CLEP* exam. What's best for you depends on how much time you have to study and how comfortable you are with the subject matter. Our test prep for CLEP* College Mathematics College Mathematics College Mathematics Our Author
About Research & Education Association
Acknowledgments
Passing the CLEP College MathematicsSets
Sets
Subsets
Union and Intersection of Sets
Laws of Set Operations
Cartesian Product
Drill Questions
The Real Number System
Properties of Real Numbers
Components of Real Numbers
Fractions
Odd and Even Numbers
Factors and Divisibility Numbers
Absolute Value
Integers
Inequalities
Drill Questions
Algebra Topics
Exponents
Logarithms
Equations
Simultaneous Linear Equations
Absolute Value Equations
Inequalities
Complex Numbers
Quadratic Equations
Advanced Algebraic Theorems
Drill Questions
Functions and Their Graphs
Elementary Functions
Translations, Reflections, and Symmetry of Functions
Drill Questions
Geometry Topics
Triangles
The Pythagorean Theorem
Quadrilaterals
Similar Polygons
Circles
Formulas for Area and Perimeter
Drill Questions
Probability and Statistics
The Fundamental Counting Principle
Permutations
Combinations
Probability
Probability Word Problems
Measures of Central Tendency
Measures of Variability
Data Analysis
Analyzing Patterns in Scatterplots
Drill Questions
Logic
Sentences
Statements
Basic Principles, Laws, and Theorems
Necessary and Sufficient Conditions
Deductive Reasoning
Truth Tables and Basic Logical Operations
Logical Equivalence
Sentences, Literals, and Fundamental Conjunctions
Drill Questions | 677.169 | 1 |
I am going to high school now. As math has always been my problem area, I purchased the course books in advance. I am plan studying a handful of chapters before the classes begin. Any kind of help would be much appreciated that could aid me to start studying f1 maths exercise download myself.
You might want to check out Algebrator. I bought it some time back to help me with my Remedial Algebra course and I can say that it was a wise decision. There are so many demos provided which you can go through. You can also try out the questions related to difference of squares and percentages by just typing them in. Algebrator provides complete description to the problems which helps to make difficult concepts understandable. I would say that this program is absolutely the best that money can buy.
I agree. Algebrator not only gets your assignment done faster, it actually improves your understanding of the subject by providing useful tips on how to solve similar questions. It is a very popular software among students so you should try it out.
least common denominator, proportions and graphing were a nightmare for me until I found Algebrator, which is really the best algebra program that I have ever come across. I have used it frequently through many algebra classes – Pre Algebra, College Algebra and College Algebra. Just typing in the math problem and clicking on Solve, Algebrator generates step-by-step solution to the problem, and my math homework would be ready. I really recommend the program. | 677.169 | 1 |
The fun and easy way to learn pre-calculus Getting.... more...
policy changes reduce political polarization? These questions may all seem very different, but they... more... current research. The five main parts of the book encompass... more...
Many students worry about starting algebra. Pre-Algebra Essentials For Dummies provides an overview of critical pre-algebra concepts to help new algebra students (and their parents) take the next step without fear. Free of ramp-up material, Pre-Algebra Essentials For Dummies contains content focused on key topics only. It provides discrete explanations | 677.169 | 1 |
Introduction
Welcome! This site has been designed to "assist you in your pursuit of increased mathematical
understanding," or whatever sounds good to you. The subjects covered range from Pre-Algebra
to Calculus.
First, a little background. As we worked our way through various math classes throughout the years, we
often became confused or lost. Instead of deciding that it might have something to do with all the sleeping
and talking we did during class, the teaching style, the pace of the class, or something like that, we figured that
it was probably because we were just
morons. So for those of you who are "morons like us," here's a site that will help you understand
math concepts better.
This site will hopefully clarify some of those confusing math concepts. You know -- the ones that have
been waking you up in the middle of the night for so long!
Learn
This is the largest portion of the site -- where you will find tutorials, sample problems, and quizzes. Here
are a few important notes about this section: Most other sites we've seen attempt to teach things "from the bottom
up." This site is designed under the assumption that you know some of the basic concepts but need some
reinforcement. Or, perhaps you want to review things you learned ages ago. Also, we have included a
short quiz after each tutorial so you can test yourself on what you've just learned or reviewed.
One other point of clarification: "Algebra" covers elementary algebra, "Algebra II" covers intermediate algebra as
well as basic trigonometry, and "Precalc" covers advanced algebra.
Interact
Interaction is what makes the Internet great, so we've provided a number of interactive resources to help you with
math.
Message Board
We have often found that many problems can be solved by simply asking someone else for some quick help, so we've
included a Message Board on the site where you can go communicate with others.
And for all the students out there who are suffering though calculus, we've set up a separate
Calculus Message Board for calculus students only. Don't you feel
special?
Formula Database
Have you ever needed to use a formula or equation, but couldn't quite
remember it? Now you can use our Formula Database. Commonly
used formulas have already been added to the database. You can
search the database as well as add new equations to the collection. Take
a look! And add your favorite equation -- we know you have one . . .
Quizzes
This page provides easy access to our JavaScript and text-only quizzes. That
way, if you want the quiz but don't want to wade through the lessons, you don't have to.
Math Links
There are a lot of great math sites on the Internet. This page has links to some of our favorites.
Educators
Teachers and educators are welcome to visit this section. Anyone else is forbidden! :-)
Feedback
Do you feel an intense need to send some feedback to the "morons" who created this
site? Here's your chance!
Credits
If you really care, you can look at all of our credits and acknowledgments. | 677.169 | 1 |
We provide FREE Solved Math problems with step-by-step solutions on Elementary, Middle, High School math content. We also...
see moreWeUseMath.org is a non-profit website that helps to answer this question. This website describes the importance of...
see more
WeUseMath.org is a non-profit website that helps to answer this question. This website describes the importance of mathematics and many rewarding career opportunities available to students who study mathematics. Includes a video and teacher resources.
A Singaporean Maths site catering to the cambridge A level H2 maths syllabus; it alsocontains two large question/solution...
see more
A Singaporean Maths site catering to the cambridge A level H2 maths syllabus; it alsocontains two large question/solution portals -״The Question Locker" and "Beyond H2 maths״which are relevant to the general high school and early college maths student.
PUMAS (poo' • mas) -- is a collection of brief examples showing how math and science topics taught in K-12 classes can be...
see more
PUMAS (poo' • mas) -- is a collection of brief examples showing how math and science topics taught in K-12 classes can be used in interesting settings, including every day life. The examples are written primarily by scientists, engineers, and other content experts having practical experience with the material. They are aimed mainly at classroom teachers, and are available to all interested parties via the PUMAS web site
A computational tool that runs the one-way ANOVA by the user inputing individual data or by copying and pasting a delimitted...
see more
A computational tool that runs the one-way ANOVA by the user inputing individual data or by copying and pasting a delimitted data set. This reference also includes description of what the ANOVA is and how it compares to the t-test. | 677.169 | 1 |
engrossing, how-to book designed to pique students' interest in the process of modelling in order to acquire both critical and creative modelling skills and the confidence to apply them. The author uses exercises, case studies and models, based on scientific literature, that are freely adaptable and presented in a fresh perspective as interlocking fragments of a mosaic. Examples are chosen from population dynamics, heat flow, optimal harvesting, traffic management and other areas that use models. Includes material for model builders.
Editorial Reviews
Booknews
A textbook that teaches both critical and creative modeling skills, primarily for a senior-level course that gives equal weight to deterministic and probabilistic modeling. It emphasizes both the validation of mathematical models and the rationale behind improving them. The approach embodies the belief that the three most fundamental ideas in mathematical modeling are transience, permanence, and optimality. The minimal mathematical prerequisites are the standard calculus sequence and first courses in linear algebra, ordinary differential equations, and probability and statistics. Probability and statistics are reviewed in an appendix | 677.169 | 1 |
Description: This is a modified Physics 30S course with emphasis on application of mathematics in real (Physics) situations. it will help prepare students for Applied Math 40S as well as Physics 40S. The math component will include algebra, equation solving, some graphing, vectors, and trigonometry. The Physics component will include motion (velocity, acceleration) or mechanics as well as gravity and friction. | 677.169 | 1 |
Mathematics for EveryDispelling some of the subject's alarming aspects, this book provides, in a witty and engaging style, the fundamentals of mathematical operations. Topics include system of tens and other number systems, symbols and commands, first steps in algebra and algebraic notation, common fractions and equations, irrational numbers, much more. 1958 edition. | 677.169 | 1 |
Online learning with math computer software is gaining in popularity among college students. Distance learning has become one of the most viable ways in which to get a college education. Many people have careers that require them to further their education. For instance, an employee in a company could be eligible for a promotion if he or she earns a graduate level degree. Most students who are taking online learning courses to advance their careers have to take complicated math courses. Math computer software is an innovative way to learn.
Many students who use math computer software demonstrate good problem solving skills, which is important in every career. Many students like to use math computer software because it stimulates their ability to recall what they have learned. Many students like to study with the help of math computer software. Math computer software is an effective tool for all students, whether they are young or old. Online learning software is more versatile and is less expensive than taking traditional classes.
Math computer software is designed to lead students from the beginning to the end of the math course. For instance, if you signed up for an online learning course, you would receive software to download into your computer. Some of the software may have some computer graphics and games. Learning software that employs the use of math games helps to reinforce your math skills. Many students take algebra, geometry, calculus, and many other math courses online with math computer software.
Distance learning makes it so much easier for working people to advance their careers through higher education. You save time and money by going to school online. There is individual help available for all courses, including math. Math computer software is a wonderful computer application, which helps with the students' time management. The time saved from commuting to classes can be used more efficiently for study and getting on with life, in general.
Most online learning classes have a forum where the students can chat about the issues they are having. They can talk about math problems they are having difficulty with on their math computer software program. The forum is a great support for all students who take college courses online. | 677.169 | 1 |
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In our standard Algebra 2 classes we don't do much with matrices, but I wanted my kids to see the power of matrices and their calculators for solving systems. This is step by step instructions and practice problems for the kids to work on individually, with a partner, or whatever you want. Sumbitted by MathTeacher44 | 677.169 | 1 |
Introductory Algebra - 2nd edition
ISBN13:978-0077281120 ISBN10: 0077281128 This edition has also been released as: ISBN13: 978-0073406091 ISBN10: 0073406090
Summary: Introductory Algebraoffers a refreshing approach to the traditional content of the course. Presented in worktext format,Introductory Algebrafocuses on solving equations and inequalities, graphing, polynomials, factoring, rational expressions, and radicals. Other topics include quadratic equations and an introduction to functions and complex numbers. The text reflects the compassion and insight of its experienced author team with features developed to address the specific needs of dev...show moreelopmental level students. ...show less
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COMAP, the Consortium for Mathematics and Its Applications, is an award-winning non-profit organization whose mission
is to improve mathematics education for students of all ages. Since 1980, COMAP has worked with teachers, students, and
business people to create learning environments where mathematics is used to investigate and model real issues in our world.
Featured Products
Against All Odds: Inside Statistics Updated
The new series features 32 10-minute videos showing people from all walks of life using statistics in their work, as well as interactive tools, and guides.
Picking up where the original Against All Odds left off in the 1980s, the new series maintains the same emphasis on "doing" statistics. Video modules take viewers on location to where people from all walks of life are using statistics in their work. Online materials allow viewers to practice and review what they've learned. To order, or for more information visit: Annenberg Media's Website.
Mathematical Modeling Handbook I & II
The Mathematical Modeling Handbook is intended to support the implementation
of the Common Core State Standards high school Mathematics Modeling
conceptual category. The CCSS document provides a brief description of mathematical
modeling accompanied by 22 star symbols (*) designating modeling
standards and standard clusters. The CCSS approach is to interpret modeling
"not as a collection of isolated topics but in relation to other standards."
The goal of this Handbook is to aid teachers in implementing the CCSS approach
by helping students to develop a modeling disposition, that is, to encourage
recognition of mathematical opportunities in everyday events. The Handbook
provides lessons and teachers' notes for thirty modeling topics together with
reference to specific CCSS starred standards for which the topics may be appropriate. Learn More
The Mathematics as a Second Language Glossary features mathematical terms defined in both English and Spanish
with accompanying examples and/or drawings and is now available in epub format for the Amazon Kindle and Apple EReaders.Learn More
Consortium Free Download Page
Consortium, published twice
a year and available electronically,
blends contemporary teaching activities with commentaries,
articles and contests to bring the excitement of mathematical
modeling to high school classrooms. Each issue contains
the Pull-Out
section, a reproducible classroom activity centered on a real-world
modeling problem. Recent Pull-Out
lessons have modeled a wide range of topics including the
genetics of sickle cell anemia and the accuracy of the Patriot
Missile System.
Starting with issue 104 COMAP has decided to make theConsortium available as a free download.Learn More
Mathematics: Modeling Our World (MMOW)
Course 1, 2 & 3
Based on feedback from users of the first edition, COMAP has completed a major revision of Courses 1-3, now available in both print and CD-ROM.
• Some chapters are completely rewritten (i.e., Pick a Winner and Landsat, which is now titled Scene from Above). Other chapters are streamlined while retaining the thematic, modeling approach. • Most chapters are shorter. The revised Course 1 has a total of 57 Activities— a 39% reduction from first edition's 93.
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NEW FREE course material A Course in Financial Mathematics
This is a free course in financial mathematics for upper high school and undergraduate students, with emphasis on personal finance. Teachers can make their own selections. Some of the lessons are articles published in various journals. Some are unpublished. This collection contains over forty lessons. A teacher can simply download and print a PDF, make copies, distribute them to students, and teach the lesson. Learn More | 677.169 | 1 |
Cliff Reiter, Lafayette College, Mathematics
J gives my students the computational and visual tools they need to explore linear algebra. They can create and observe the effects of transformations, use transformations to create fractals, implement error-correcting codes on real messages, and do curve fitting. | 677.169 | 1 |
Mathematics: A Brief Course
In this book, the author explains the history of mathematics by concentrating on the mathematics that was done and what it means in relation to other ...Show synopsisIn this book, the author explains the history of mathematics by concentrating on the mathematics that was done and what it means in relation to other mathematics and other areas of human endeavor. At all stages the reader will understand why people were interested in the problems that mathematicians were solving, and what consequences their solutions had for the further development of mathematics and its applications | 677.169 | 1 |
books.google.com - B... is for Googol
G is for Googol: A Math Alphabet Book
B or gift book for the budding young mathematician at home. Even the most reluctant math student will be drawn in by the author's trademark wit, Marissa Moss's quirky illustrations and funny captions, and the answers revealed in W is for " When are we ever gonna use this stuff, anyway?" Download the G is for Googol Teacher's Guide(300K)
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Review: G Is for Googol: A Math Alphabet Book
User Review - Emma - Goodreads
G Is For Googol is the quintessential reference book for STEM because it covers topics that are relevant to all of the STEM subjects. From abacus to zillion, this advanced ABC book conveys complex ...Read full review
Review: G Is for Googol: A Math Alphabet Book
User Review - ckodama152 - Goodreads
Great book to talk about different math concepts and vocabulary. There are some more complex math terms defined, so this book would be perfect for 5th graders and up. The pictures and examples used are also funny and help explain the concepts well.Read full review
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IS FOR OOGOL Based on the book G is for Googol: A Math Alphabet Book. by David M. Schwartz. Illustrated by Marissa Moss. 9. 781582 460567. 50295. ISBN 1-58246-056-6 ... tenspeedpress.com/ resources/ documents/ Googol_Guide.pdf
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math-mom.com: G Is for Googol: A Math Alphabet Book G Is for Googol: A Math Alphabet Book. by Schwartz David and Moss Marissa. Here'sa math dictionary you may not want to put down once you begin to look at it ... book-review/ g-is-for-googol/
David M. Schwartz the book G is for Googol: A Math Alphabet Book, by David M Schwartz to teach. probability. ... Alphabet Book, by David M. Schwartz and turned to p. 32. I .. ... unjobs.org/ authors/ david-m.-schwartz
C is for COUNTDOWN C is for COUNTDOWN. a worksheet to complement. G is for Googol, by David Schwartz & Marissa Moss. Make your own ABC math book by drawing a picture in each ... countdown.luc.edu/ pdfs/ Numbers_And_Operations/ N0027_Googol.pdf
G is for Googol: a math alphabet book. David Schwartz. How Much Is A Million. David Schwartz. Grandfather Tang' Story. Ann Tompert. Counting on Frank ... parents/ TurnUrdu.pdf.pdf.pdf
Less
About the author (1998)
DAVID SCHWARTZ is the author of 50 children's books, including G IS FOR GOOGOL and Q IS FOR QUARK. He is a frequent guest speaker at schools in the US abroad. He lives with his wife-and co-author-YAEL SCHY in Oakland, California. Marissa Moss was an honors math student and the only girl on her school math team. She is the creator of the Amelia's Notebook Series, RACHEL'S JOURNAL, and REGINA'S BIG MISTAKE, among others. She lives in Berkeley, CA. | 677.169 | 1 |
12, University Preparation (MCB4U) ... calculus. Students will investigate and
apply the properties of polynomial, exponential, and logarithmic .... communicate
the solutions with clarity and justification. 7.
Functions multiplied, or divided to form a new function. ... Find the first three
iterates of each function using the given initial vaiue. 12. Fitness ... Glencoe/
McGraw-Hill 5 Advanced Mathematical Concepts ... | 677.169 | 1 |
HiDigit is a new calculating software with extended capabilities. This is an essential application for math, algebra, calculus, geometry, physics and engineering students. The main advantage of the software is a simple input format even for the most complicated formulas. For example, you can enter 10pi instead of "10*pi". For complex numbers, you can use the following format - "1+2i". For percentages - "number + %". The other important feature of HiDigit is its high precision - up to 15 decimals. The program boasts an impressive number of built-in formulas, functions, constants and coefficients. Importantly, the users can customize all of them or add their own variables. Also, the history of all actions is kept, so the users can come back and undo/redo any action at any time. While HiDigit is a serious scientific software, it is extremely simple in use. No special skills or knowledge are required. The interface is straightforward and very easy to navigate through. The... | 677.169 | 1 |
Prealrealgebra, Second Edition, helps students not only learn but also retain, mathematical concepts - an important challenge that math instruction must meet in order to ensure the current and future success of mathematics students. A strong revision that includes a new design, a new art program, and key content enhancements, our text incorporates a careful development of mathematical concepts, a focus on the ""why"" behind the mathematics, and a problem-solving approach that can be applied in all math courses, as well as in everyday life. Refine p... MOREedagogy and an enhanced supplements package also provide maximum help and support for both instructors and students. Prealgebra, Third Edition, is a significant revision of the second edition, especially with respect to design, an all-new art program, pedagogy, and an enhanced supplements package. Its unique approach, which has been developed and refined over many years, is designed to help students both learn and retain mathematical skills. It is our belief that the third edition will continue to help today's students through pedagogical use of full color and updated applications. As part of MathMax: The Bittinger System of Instruction, a comprehensive and well-integrated supplements package provides maximum support for both instructor and student. MathMax: The Bittinger System of Instruction offers a completely integrated package of four-color text, multimedia CD-ROM, interactive tutorial software and videos that guide students successfully through developmental math. Key elements of the MathMax system include learning objectives keyed to the exposition, exercises, and examples; a hallmark five-step problem-solving process; and modern, interesting applications and problems. | 677.169 | 1 |
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I find these routine queries on almost every forum I visit. Please don't misunderstand me. It's just as we enter college, things change in a flash. Studies become challenging all of a sudden. As a result, students encounter problems in doing their homework. how to solve equations involving rational expressions in itself is a quite complex subject. There is a program named as Algebrator which can assist you in this situation.
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The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any CDs, lab manuals, study guides, etc.
Summary
Welcome toSingapore Maththe leading math program in the world! This workbook features math practice and activities for first and second grade students based on theSingapore Mathmethod. An introduction at the front of the book explainsSingapore MathandSingapore Mathand for those who just need extra math practice. | 677.169 | 1 |
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goals of senior secondary education and on other official documents related to
the curriculum and assessment reform .... (c) the ability to manipulate numbers,
symbols and other mathematical objects; ...
while providing the rigor and relevance needed in a high school senior math
course. AIM meets the ..... students to see the context of the detailed math
formulas. Contributing to their decision was their ...
The reference is made to Botswana senior secondary school syllabus where one
of the aims ... In this paper we consider mathematical problems involving linear
equations with two variables solved in a ...
in secondary schools for 22 years and was a head of faculty before taking up her
current post with MEI in 2006. ..... Mathematics, DE is Differential Equations, M is
Mechanics, S is Statistics, D is Decision ...
This book is based upon the original Free High School Science Text which was
entirely written by volunteer ..... The punctuation marks of mathematics are the
different signs and symbols that are used ...
Former Senior Advisor for Mathematics. Office of Elementary ... that 80% of the
1992 U.S. high school graduating class went on to college. Only about ... Terms,
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Street numbers, money in bank accounts, points on number lines, quantum particles
as contrasted with distinguishable manipulatives
For our purposes, infinity is not a number Permanent link
2
Algebra
Variables: At once arbitrary, yet specific and particular (a.s.a.p.)
Functions, composition, and inverse f(x) is not a function. f(x) is not the function f. f(x) is the particular value associated, in the big picture of the function f, with x, a number that is at once arbitrary, yet particular and specific
Inverse functions do not always exist
First glimpse at the complex plane and i := √ -1 Permanent link
3
Quadratic formula
Linear combination of terms in a polynomial
Zeroes or "roots" of a function
Completing the square Permanent link
Combinatorics b: Combinations
We obtain the famous (L + N)! / (L! N!) formula for counting the number of ways to arrange L indistinguishable objects and N indistinguishable objects together in a row. This is also the number of combinations of L objects that can be drawn from a container of L + N objects.
10
Combinatorics c: Binomial theorem
We use the formula for combinations from the previous video to write an expression for the binomial quantity (x + y)p. In some applications, only a small number of terms in the resulting sum are necessary for approximate calculations.
ε-δ definition of limit, notion of "arbitrarily close"
Example of calculating a limit
Limits do not always exist
For an example of a strategy for writing ε-δ proofs useful for plots of functions that have curvature, please see Yosen Lin's examples (example # 4 on p. 3-4). Permanent link
12
Differentiation
Differentiation a: Derivatives and differentials
We define the derivative, caution against interpreting differentials as numbers, and remark that derivatives do not always exist. It is important to become familiar with derivatives because they provide a basic vocabulary for talking about dynamical systems in the natural sciences (including in biology). Permanent link
13
Differentiation b: Power rule
We will later learn that many seemingly complicated functions can be approximated using sums of power law terms. To study the slopes of these terms, we use the power rule that we derive in this video, which is written d(xn)/dx = nxn-1.
14
Differentiation c: Chain rule (for composite functions)
One way to combine functions is to nest functions within each other. The chain rule is used to study the slopes of "composite" functions. The rule is written d(g(f))/dx = dg/df df/dx.
15
Differentiation d: Products and quotients
Another way to put basic functions together is to write their expressions next to each other as a product. In this video, we derive the product rule, which is used in such situations. The product rule is written d(fg)/dx = (df/dx)g + f(dg/dx).
16
Differentiation e: Sinusoidal functions
The derivative of sine is cosine, and the derivative of cosine is negative sine. This back-and-forth relationship is a hallmark of dynamical systems that might support oscillations. Thus, this pattern, which you will derive in this video, is important to keep in mind when you later study biological oscillations.
17
Partial differentiation
When a function depends on multiple independent variables, the curly-d symbol, ∂, denotes slopes calculated by jiggling only one independent variable at a time Permanent link
18
Power series representations
Power series representations a: Second derivative and curvature
Using a power series representation is like using decimal representation. Both techniques organize the description of the target object at levels of increasing refinement. In this first video, we show that the second derivative corresponds to the curvature of a plot. In this way, we strengthen intuition that higher-order derivatives can also have geometric interpretations. Permanent link
19
Power series representations b: Determining power series terms
We imitate a function by combining the descriptions of its geometric properties as embodied in its value and the values of its higher derivatives at an expansion point.
20
Power series representations c: Power series for sine
We obtain a power series representation for the sine function expanded about the point θ = 0.
21
Power series representations d: Decimal approximation for π
Using the first three terms of the power series representation for sine we obtained in the previous video, we iteratively approximate π to four decimal places.
22
Integration
Integration a: Area under a curve
In these four videos, we develop a familiar with integration that will later be useful for deducing functions of time (e.g. number of copies of a molecule as a function of time) using rates of change (e.g. the first derivative of the number of copies of a molecule with respect to time). In this first video, we develop the concept of the definite integral in terms of the area under a curve. Permanent link
23
Integration b: First fundamental theorem of calculus
In this video, we demonstrate that differentiation undoes integration. This is called the first fundamental theorem of calculus.
24
Integration c: Second fundamental theorem of calculus
We demonstrate that integration undoes differentiation. This is called the second fundamental theorem of calculus. This theorem allows us to construct a table of integrals using differentiation rules we previously learned.
25
Integration d: Change of variables rule
Sometimes, superficial differences can make it seem that a listing in an integration table does not match the integral we want to study. We develop a change of variables (also called a "u-substitution") rule that can sometimes help us to identify a match between an integral we want to study and a listing in a table.
26
Separation of variables
Two wrongs make a right
Tear two differentials apart as though they retained meaning in isolation
Slap on the smooth S integral sign as though it were a unit of meaning itself, even without a differential
You get the same integral expression you would obtain long-hand using u-substitution or "change of variables" in integrals Permanent link
27
Euler's number I
Euler's number 1a: Compound interest
Compounding interest with arbitrarily short compounding periods
Power series representation of ex Permanent link
This is a canonical worked problem from introductory systems biology. We will explain one way to fantasize about the classic protein dynamics equation dx/dt = β - αx and analytically demonstrate that protein "rise time" depends on degradation rate only.
EGT 1a: Population dynamics with interactions
Equations for collisional population dynamics using law of mass action
An outcome of the prisoner's dilemma is simultaneous survival of the relatively most fit with decrease in overall fitness
EGT 1b: Introduction to tabular game theory
Tabular game theory
An outcome of the prisoner's dilemma is simultaneous stability of D with, as a consequence, lower than maximum possible payoff for D
Our first verbal suggestion (1) that payoffs from tabular game theory can be associated with rate coefficients from the population dynamics in part 1a, and (2) that part 1a should be referred to as evolutionary game theory
41
Evolutionary game theory II
EGT 2a: Evolution resulting from repeated game play
In the previous slide deck, we noted similarities between population dynamics and business transaction payoff pictures. In this and the next video, we provide deeper understanding of these connections. In this video, we derive the population dynamics equations in such a way that it is natural to say that cells being modeled repeatedly play games and are subject to game outcomes. Permanent link
42
EGT 2b: Relationship between time and sophisticated computation
Repeated simple interactions in a population of robotic replicators can achieve results seemingly related to results obtained from sophisticated computations. The use of population dynamics and business transaction payoff matrix analyses from the previous slide deck to obtain this understanding is an example of quantitative reasoning.
Uncertainty propagation a: Quadrature
Quadrature formula is a result of Taylor expanding functions of multiple fluctuating variables, assuming that fluctuations are independent, and then applying the identity "variances of sums are sums of variances" Permanent link
Uncertainty propagation c: Square-root of sample size (√n) factor
Origin of the famous √n factor by which the standard deviation of the sample means is smaller than the standard deviation of the measurements (parent distribution)
52
Uncertainty propagation d: Comparing error bars visually
Are error bars non-overlapping, barely touching, or tightly overlapping? What p-value do people associate with the situation in which error bars barely touch?
53
Uncertainty propagation e: Illusory sample size "I quantitated staining intensity for 1 million cells from 5 patients, everything I measure is statistically significant!" It is quite possible that you need to use n = 5, instead of 5 million, for the √n factor in the standard error.
Poissonian copy numbers b: Stochastic synthesis and degradation
Model: RNA polymerase makes many (usually unsuccessful) independent attempts to initiate transcription. Once a mRNA strand is produced, it begins to make independent (usually many unsuccessful) attempts to be degraded.
Result: As in part a, mRNA copy numbers are Poisson distributed
DEs IIIb: Eigenvector-eigenvalue analysis
Determine the directions of "unbending" trajectories for a more precise hand sketch of the phase portrait
69
DEs IIIc: The cribsheet of linear stability analysis
Use eigenvalue-eigenvector analysis to find analytic solutions for linear systems and describe the qualitative features of trajectories approaching, side-swiping, or departing from steady state.
Additional activity: You may skim Ferrell, Jr., Tsai, and Yang, "Modeling the cell cycle: Why do certain circuits oscillate?" Cell, 144: 874-885 (2011)(online). Comment on how the positive-feedback term in Eqtn. 25 (pg. 882) contributes to the difference between the phase portraits in Fig. 4B (pg. 878) and Fig. 8B (pg. 883). The article describes the positive-feedback in terms of a time delay. Please describe the contribution of the positive-feedback term to stable oscillations instead in terms of "twisting nullclines" from the video tutorial.
Seeing what computers can do
In this activity, you will play against the computer in Blizzard's StarCraft for 2 hrs and in Sid Meier's Civilization for 2 hrs. WARNING: This activity might require rehabilitation and video game addiction treatment (PubMed).
74
Cellular automata
Cellular automata a
Deterministic cellular automata
In this video, we see that limiting dispersal of seeds of annual plants can increase the proportion of the copper-colored subpopulation, whereas thorough mixing instead allows the denim plant subpopulation to dominate quickly.
Additional activities: Refer to a similar model in Nowak and May, "Evolutionary games and spatial chaos," Nature359:826-829 (1992) (online). Watch Athena Aktipis talk about the walk-away model, which can contribute to the evolution of cooperation in highly-mobile populations (University of California, Los Angeles, Center for Behavior, Evolution, and Culture 2009, 1-hr video online) Permanent link
Cellular automata b
Stochastic cellular automata
Toy agent-based model
You will program a simple ABM
For more extensive discussion, see Athena Aktipis's page on agent-based modeling (online).
Statistical physics 101a: Fundamental postulate of statistical mechanics
Systems have states and energy levels
Energy can be exchanged between parts of a world
If the Hamiltonian of the world is time-independent, the overall energy of the world is conserved
Fundamental postulate of statistical mechanics: In an isolated system, all accessible microstates are accessed equally Permanent link
76
Statistical physics 101b: Notating configurations of a system with multiple parts
Direct product
77
Statistical physics 101c: Distribution of energy between a small system and a large bath
Bath: many parts
Number of ways to find the bath configured exponentially decays with increasing system energy
Boltzmann factor
78
Statistical physics 101d: Expressions for calculating average properties of systems connected to baths
The system energy most typically observed is the one that corresponds to the greatest number, W, of configurations of the world
Ways (W), entropy (sigma), free energy (F), probability (P), partition function (Z), taking derivative of Z
Maximizing ways of the world Maximizing entropy of the world Minimizing free energy of the system
79
Ideal chain
Ideal chain a: Introduction to model
A series of links pointed up or down Permanent link
Ideal chain c: Expectation of energy and elongation
For heavy weights, the chain tends to be found extended fully. For lesser weights, the chain can be found partially crumpled, with the weight lifted, and with energy given to the bath.
I take tonight's red eye to give a talk on quantitative biology in the morning. I haven't had time to learn this field. How can I learn to use buzzwords convincingly?
Download the videos in this digest (follow the vimeo links in the video lightboxes). The indicated segments can be viewed in under 2 hours, and even an hour's sample should offer an informative taste of reasoning styles and topics commonly encountered in introductory quantitative biology. Buzzwords are like salt. Avoid unconvincing overuse. Observe that the videos in the digest never use the words "complexity" or "emergence" even though both terms could be used repeatedly.
My institution already trains faculty in bioinformatics. How much of this website can I skip?
This is not a bioinformatics course (there's only a little bit of rudimentary probability). Going in the other direction, much of the content from this course might be missing from your bioinformatics training. To determine whether you are already familiar with styles of reasoning in quantitative biology, respond to the quiz questions below and view the accompanying videos that follow.
I just got funded to collaborate in quantitative biology. How do I find experts to coach me to understand the mathematical models I need to use?
You could test possible instructors by asking them to help you work through some of the quiz questions below. See how they answer (it's probably best to watch the corresponding video sections ahead of time).
Quiz 1: Protein level dynamics
In a toy model of a cell, protein X is produced according to a translation rate coefficient and eliminated according to a degradation rate coefficient. The protein copy number at which the rates for these processes balance is called the steady-state level. The time it takes for a cell initially containing zero copies of protein X to accumulate half the steady-state level is called the "rise time." Which statement describes the rise time?
Quiz 2: Law of mass action
In this course, we use "law of mass action" to refer to an idea that chemical reaction kinetics can be modeled using rate formulas containing products of abundances of reactants raised to exponents. Which statement is best?
Mass-action exponents and stoichiometric coefficients can be related using a probabilistic model of molecular collisions, so the stoichiometric coefficients of reactants in the proximate reaction that generates products under study can be deduced using the exponents in an equilibrium constant.
Instantaneous collisions of more than two hard-spheres are exceedingly rare, so mass-action rate formulas cannot be used to model reactions involving more than two reactants.
The warning against reading mass action exponents off of stoichiometric coefficients derives from the low likelihood of instantaneous collisions between more than two hard spheres. This warning can be relaxed when molecules have non-spherical geometries, and instantaneous collisions between three, or even four, molecules is common, as long as one of the reactants is not spherical.
Taylor expansion of complicated functions of reactant concentrations can produce sums of mass-action terms. In other words, stringing together mass-action formulas can produce experimentally accurate mathematical descriptions while concealing insight in the same way that epicycles permit accurate description of celestial motion while obscuring Kepler's laws.
Mass-action exponents must be empirically derived from time-course observations and cannot be deduced from stoichiometric coefficients.
Quiz 3: Evolutionary game theory
Evolutionary game theory is an example of a modeling framework used in the NCI Physical Sciences-Oncology Network to understand social aspects of biological systems. What statement about evolutionary game theory is best?
Evolutionary game theory refers to a collection of mathematical models in which organisms (e.g. cells) are modeled as automated, robotic replicators. The propensity with which a replicator generates progeny is modified by the time-frequency with which it encounters other replicators (e.g. through pairwise interactions).
In the prisoner's dilemma, defector population share and per capita fitness both increase. However, average fitness decreases because interaction between defectors and cooperators decreases the per capita fitness of cooperators more than enough to cancel out the fitness increase of defectors.
In normal tissue microenvironments, individual cells typically express rational behaviors (i.e. protecting long-term survival of the host). Following carcinogenesis, however, cells can also display irrational behaviors, such as circumvention of stress-related barriers. Because cells can now choose between two classes of strategies, it becomes necessary to employ evolutionary game theory to determine how individual cells might make these choices and alter overall tissue system dynamics.
John Maynard Smith understood the evolution of socially interacting biological individuals by describing the possible behaviors that individual agents could choose. The notion of choice in this context refers to the essential assumption that each individual organism expresses a strategy that maximizes its payoff, as computed using a payoff matrix. A startling result is the applicability of this kind of modeling, not just to organisms that perform advanced cognition, e.g. hawks and doves, but also, to individual cells, for which evolution had long been thought to proceed primarily in a Darwinian fashion.
In traditional models of population dynamics, cell numbers vary as though cells individually solved for anti-derivatives and then adjusted their behavior to obey governing equations. In evolutionary game theory, individual cells, instead, perform sophisticated computations using payoff matrices to decide among strategies so as to realize Nash equilibria.
Track
Topic
Slides
Video
Description
D5
Evolutionary game theory I
EGT 1a: Population dynamics with interactions
Equations for collisional population dynamics using law of mass action
An outcome of the prisoner's dilemma is simultaneous survival of the relatively most fit with decrease in overall fitness
Quiz 4: Poissonian copy numbers
Some quantitative biologists say that the copy numbers of mRNA in simple models of gene transcription are stochastic and Poisson distributed. Which of the following explains this claim?
The copy number of a species of mRNA can be small (~1 copy per cell or less). When a system is composed of a small number of parts, intrinsic stochastic fluctuations are generated. The copy number counts are Poisson distributed because the transcription machinery "forgets" whether it has previously generated a strand of mRNA in a time interval much shorter than needed to produce, on average, one copy of mRNA.
The copy number of a species of mRNA can be small (~1 copy per cell or less). This means that the molecule is "rare," so the limit of rare events, also known as the Poisson distribution, accurately models copy-number fluctuations.
If the transcription machinery for a species of mRNA "forgets" whether it has previously generated a copy of mRNA over a time scale much shorter than the duration that produces, on average, one mRNA strand, then the generation of mRNA is a Poisson process across time. The integral over an interval is a function evaluated on the boundary. As a rough example, the number of copies of a species of mRNA at a time of observation equals the number of copies produced up until that time since a reference time in the past (minus the number of copies generated up until a lifetime earlier than the time of observation). In this example of the second fundamental theorem of calculus, the number of copies of mRNA counted at a time is Poisson distributed because it inherits the statistical properties of the Poisson process across time described above.
A "Poisson distribution" refers to a distribution generated through natural random fluctuations. This is in contrast to fluctuations in engineered structures and circuits that use metabolic energy input to shape their distributions (i.e. the end products of biological signaling cascades can be log-normally distributed, rather than Poisson distributed). Hypothesizing a Poisson distribution for the copy numbers of a species of mRNA is equivalent to claiming that transcription occurs with minimal metabolic energy input.
Quiz 5: Quasispecies
Quasispecies models are used to understand the compositions of populations of cells in terms of mechanisms for genetic mutation. Choose the best statement:
The genotype that dominates a population does not necessarily correspond to the genotype underlying those cells that most rapidly produce offspring. The dominant genotype is not necessarily the genotype with greatest fitness.
Classical quasispecies models are sometimes referred to as mutation-selection models. A fundamental limitation of these models is an assumption of thorough mixture. The dynamics supported by cells undergoing mutation, selection, and spatial movement are examples of emergent phenomena because they are not easily predicted from models of mutation and selection alone.
A mutational meltdown in cancer occurs when a sudden accumulation of dangerous mutations in cancer cells threatens the host. Dangerous mutations can include, for example, mutations that increase the likelihood of survival cancer cells (e.g. increased proliferation, insensitivity to growth control signals, etc.). Analyzing quasispecies models, mathematicians recommend decreasing the mutation rates of cancer cells to reduce the chances of a mutational meltdown in a tumor.
Mutation leading away from the genotype of greatest fitness must be slow enough in order for this genotype to be dominant. Otherwise, this genotype will command only minority population share (in some models, no finite number will be small enough to represent population share). Condensation onto a dominant sequence at low mutation rates is often compared to the condensation of a population of bosons into the ground orbital at low temperatures because mutation is analogous with maximizing entropy of the thermal bath and selection is analogous with maximizing the entropy of the bosons.
Quiz 6: Adaptation
A gene-expression network composed precisely of nodes A, B, and C is said to exhibit adaptation. In the following, a step change in the level of node A is externally applied and maintained. Which one of the following is the best example for teaching how "adaptation" is achieved in systems biology?
A step increase in node A is isolated. Nodes B and C are unchanged.
A step increase in node A leads to a temporary increase (followed by a return to steady state) in node C. Node B is unchanged.
A step increase in node A eventually leads a step increase in node C and a step decrease in node B. Both nodes C and B achieve new steady states, but with a delay so that no changes in node B and C are observed in the first moments after the increase in node A.
A step decrease in node A initially causes a temporary decrease in node C. Node C rises and returns to its initial steady-state level owing to variation in node B.
Track
Topic
Slides
Video
Description
D8
Differential Eqtns IV
DEs IVa: Adaptation Please see the excerpt from 19 min 14 sec to 21 min 27 sec. This video is inspired by Ma, Trusina, El-Samad, Lim, and Tang, "Defining network topologies that can achieve biochemical adaptation," Cell, 138: 760-773 (2009) (online). To view the short sequel to this video, jump to the Permanent link in main curriculum | Permanent link in digest
Quiz 7: Oscillations
Choose the best statement regarding oscillations in mathematical biological models.
Cyclic movement through phase space depends on deterministic, programmed behavior. Adding stochastic fluctuations to a deterministic system does not generate oscillatory trajectories. Instead, any oscillations originally present are damped out, if not completely eliminated.
Oscillatory circuits can generate a variety of kinds of signals. These need not resemble sines and cosines in time plots or perfect circles and ellipses in phase planes. For example, time courses can look like momentary spikes, and phase-plane trajectories could resemble rounded squares and triangles.
Oscillations correspond to loops in phase space. Such a structure is essentially 2-dimensional. Oscillations occur in high-dimensional phase spaces only when most of the degrees of freedom decouple from the pair that defines the phase portrait in which loops can be drawn.
Even though spiral and closed-loop trajectories qualitatively resemble each other in phase portraits, they correspond to different biological network topologies. In other words, it is usually not possible to construct a protein-interaction network that can support both kinds of trajectories with merely adjustments to numerical parameters. This implies that therapies that only mildly suppress or activate a network component are unlikely to change the qualitative form of system oscillations.
Oscillations are often visualized as loops in two dimensional slices of phase space. This kind of depiction is, in part, the consequence of arbitrary convention. Reversing one of the two axes by multiplying it by a negative sign reverses the orientation of its back-and-forth motion, and the motions along the two axes now synchronize in a way that traces cyclic motion along on a line, rather than a loop around a plane. Thus, oscillation can be represented in a 1-d "space."
Quiz 8: Phenotypic stochasticity
A cell can execute stochastic transitions between phenotypic states without need for gene sequence alterations or large-scale genomic rearrangement. This can lead to a type of cell individuality that has been called epigenetic or "non-genetic." Phenotypic stochasticity is actively studied in stem cell/developmental biology and cancer biology. Choose the best statement:
Whereas a genotype rigidly corresponding to one phenotypic state might be suited to one environment, but stressed under another, a genotype underlying a plastic collection of interconvertable phenotypes is protected from selection. Darwinian evolution occurs through selection on underlying genetic variation. For this reason, genetic evolution does not proceed in the presence of stochastic phenotypic fluctuations and non-genetic network adaptations.
Models based on phenotypic stochasticity and models based on cell-cycle phase specific therapeutic sensitivity both suggest adjusting dose timing according to the dynamics of non-genetic variation in the targeted cell population. However, models based on phenotypic stochasticity and cell-cycle specificity are distinct because stochastic transitions occur with fluctuating waiting times, whereas the cell-cycle proceeds in clockwork fashion through phases of well-defined duration.
Therapeutic failure is inevitable any time cells with a phenotype impervious to a therapeutic modality are present at the onset of treatment. Even if such a subpopulation is initially small, it will be selected for and eventually dominate. In a population regenerated by tumor [re]-initiating cells (TICs, cancer stem cells, CSCs), for example, therapy will eventually fail if the treatment modality cannot directly kill the TIC phenotype.
Drug-sensitive cells can enter relatively drug-resistant states through non-genetic mechanisms over time scales of days and weeks. Phenotypic stochasticity contributes to therapeutic failure.
Owing to the "non-genetic" character of the cell-cell individuality that phenotypic stochasticity can generate, the population dynamics resulting from phenotypic fluctuations cannot be described using principles of Darwinian evolution.
Quiz 9: Cellular automata and spatiality
Two populations of annual plants, "cooperators" and "defectors," are sown on a field. Prisoner's dilemmas describe the chemical and mechanical contact that occurs repeatedly between pairs of neighboring plants. These interactions determine the numbers of seeds that the plants contribute to the next generation. Which statement is true?
Increasing the spatial area over which offspring randomly disperse spreads the offspring of defectors too thin, making it more difficult for defectors to compete with dense pockets of cooperators. These pockets of cooperators survive and perpetuate heterogeneous co-existence.
Increasing the spatial area over which offspring randomly disperse promotes heterogeneous co-existence because survival of cooperators relies on their ability to move away from defectors in an ongoing cat-and-mouse chase.
Increasing the spatial area over which offspring randomly disperse makes it easier for defectors to take over the lattice and more difficult to realize heterogeneous co-existence.
Increasing the spatial area over which offspring randomly disperse promotes heterogeneous co-existence because defectors and cooperators both have increased chances of bumping into other cooperators. | 677.169 | 1 |
97808946459, Models and Algorithms: A First Course
The author presents his approach to how undergraduate students in mathematics, business, computer science, and engineering should be introduced to the science of decision making. The material is designed to prepare the student for more advanced topics. The level of mathematics required is deterministic mathematics at an elementary level, including linear equations and graphs. Introductory probabilistic notions are assumed, but they are not used extensively and can be introduced by the instructor. The target audience is juniors, seniors, and advanced lower-division students. The text is for a one-semester course | 677.169 | 1 |
"Math Connects: Concepts, Skills, and Problem Solving" was written by the authorship team with the end results in mind. They looked at the content needed to be successful in Geometry and Algebra and backmapped the development of mathematical content, concepts, and procedures to PreK to ensure a solid foundation and seamless transition from grade level to grade level. The series is organized around the new NCTM Focal Points and is designed to meet most state standards. "Math Connects" focuses on three key areas of vocabulary to build mathematical literacy, intervention options aligned to RtI, and a comprehensive assessment system of diagnostic, formative, and summative assessments.
Description:
This is the first systematic exposition of random sets theory
since Matheron (1975), with full proofs, exhaustive bibliographies and literature notesInterdisciplinary connections and applications of random sets are emphasized throughout the bookAn extensive bibliography in the book is available ...
Description:
NoteablesTM Interactive Study Notebook with FoldablesTM is a complete note
taking system with guided note taking for every lesson in a workbook format. Plus, vocabulary builder and a chapter test preparation section are included for every chapter.Book Format: Paperback. Number ...
Description:
Elementary Algebra, 6/e is part of the latest offerings in
the successful Dugopolski series in mathematics. Given the importance of examples within a math book, the author has paid close attention to the most important details for solving the ... | 677.169 | 1 |
The Importance of Mathematics to ConstructionPosted: Fri, 23 Dec 2011 17:13:00 +0000Imagine you building your first home or making your first set of cabinets without ever having to know how to read a tape measure. "Well, you've over slept and need to be wakened". Just the very thought of building or making anything requires that you completely understand how to properly read a standard tape measure which includes a combination of whole numbers, fractions,decimals and equivalents.
Reviews:
5.0 out of 5 stars Very Useful, October 30, 2011
By
E. Stole "Me" (LV usa)
(REAL NAME)
This review is from: Applying Mathematics to Construction: Carpentry Mathematics & Estimating (Paperback)
I've read many construction books and math text books that do a pretty good job at enhancing my understanding of carpentry mathematics, but I must say this book tops them all. The methods used in the mathematical sense will blow your mind away. Lot's of times I found myself saying, "Wow I didn't even know it could be done this way" , or "That made it so much easier".
This book will definitely help you in many areas, even if you think you know it all, you don't. It takes a gifted mind to be able to come up with these formulas that no one else really uses. I recommend this book to anyone seeking to better themselves in estimating, framing, exterior AND interior finish and trim work. instead of beating yourself up trying to figure out the math part of a project, take a moment and go through this book and you will be amazed at how much easier things can be done.
"... | 677.169 | 1 |
Publisher's Description
From simple calculator operations to large-scale programming and interactive document preparation, Mathematica is the tool of choice at the frontiers of scientific research, in engineering analysis and modeling, in technical education from high school to graduate school, and wherever quantitative methods are used.
- Powerful symbolic mathematics - Extensive built-in numerical routines - Easily handles day-to-day mathematical tasks for me. I work for NASA as an experimental cosmologist. - For me, this is a game changer. Had mathematica been available when I was a Ph.D. student in the 1980's, my career might have taken a different path.
Cons
- Mathematica is very good, but it is not as good as a good human. It does not "see" symmetries in systems of equations. Sometimes I have to go in by hand and solve things that Mathematica cannot. When this happens, the problem at hand is usually postgraduate level or higher. - Mathematica is clumsy with tensors. When doing tensor computations, I often have to trick it to get it to do what I want. I admit that more expert users might be able to get it to work straight away.
Summary
I use Mathematica every day in my work as an experimental cosmologist at NASA. I use it for designing scientific instruments and for solving many statistical problems. I tend to use IDL for numerical computation, but for symbolic work Mathematica is unparalleled in my experience. Yes, I still occasionally have to call on the standard post-gradualte level texts, but Mathematica is indispensable | 677.169 | 1 |
The best way to study mathematics is to do as many problems as possible. However, it is often the case where a student doesn't completely understand the steps to solve a problem, or there are certain nuances which only someone who has been doing mathematics for years would pick up. That is what I am here for. | 677.169 | 1 |
Math Forum provides cadets an opportunity to explore math concepts and applications beyond the academic program. The intent is to foster interest in mathematics as an art and a science, and provide an arena for the exchange of ideas among individuals and organizations within and outside of the Academy. Club activities include monthly meetings at which guest speakers present topics ranging from math history to modern applications. Members have participated in national math modeling competitions and traveled to other service academies and universities to observe their math programs. Trips to research labs allows cadets to see the application of mathematics in defense and advanced technology | 677.169 | 1 |
In Math C257 students are expected to consistently write the derivative
of expressions that contain the inverse trigonometric, logarithmic,
exponential, hyperbolic, and inverse hyperbolic functions; evaluate
integrals (definite and indefinite) by using fundamental integral
formulas, partial fractions, integration by parts, and substitutions,
trigonometric substitutions; expand skills with limits, including
l'Hôpital's Rule and improper integrals; identify the conic section
represented by a second degree equation and give the foci, vertices,
and directricies; use polar coordinates to graph equations and to find
area, arc length, and intersection of curves; use the tests for
convergence and divergence of sequences and series; write infinite
series representations of various functions; and use the fundamental
concepts of vectors including sums, dot product, and projection.
Students successfully demonstrating these Math C152 skills will be
prepared for Math C257. | 677.169 | 1 |
ALGEBRATOR
ALGEBRATOR Description
Detailed Features
Algebrator step-by-step math problem solverAlgebrator software is your 24/7 math tutor. You can literally type in your homework assignment and see it solved step-by-step (just like your teacher would solve it on the board, only more patient!). When a particular step is not clear, Algebrator will explain it in an easy to understand way. It will not only tell you what rule is applied, but also how and why it is applied in your particular problem. Not only will your homework assignment be done in minutes, but you will learn the important math concepts while observing Algebrator at workWhat does Algebrator cover?ALgebrator covers every important math concept starting with pre-algebra, all the way to college algebra. Here are some feature highlights:simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic and long division ...), exponential expressions , fractions and roots (radicals) , absolute values)factoring and expanding expressionsfinding LCM, GCFoperations with complex numbers (simplifying, rationalizing complex denominators...)solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations)solving a system of two and three linear equations (including Cramer's rule)graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions)graphing general functionsoperations with functions (composition, inverse, range, domain...)simplifying logarithmsbasic geometry and trigonometry (similarity, calculating trig functions, right triangle...)arithmetic and other pre-algebra topics (ratios, proportions, measurements...)linear algebra (addition, subtraction and multiplication of matrices, matrix inverse, determinants) | 677.169 | 1 |
This webinar offers educators a quick and easy way to learn some of the fundamental concepts of Maple. Learn a few simple techniques that will allow you to use Clickable Math™ features to compose, visualize, and solve a wide variety of mathematical problems without commands. This webinar will also provide an introduction to some of the technical documentation features in Maple, including the use of interactive components such as buttons and sliders.
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. | 677.169 | 1 |
Mathematics
- Edexcel
Who is this course for?
Mathematics at AS and A Level is a course worth studying in its own right. It is challenging but interesting. It builds on work met at GCSE, but involves new ideas that some of the greatest minds of the millennium have produced. During AS, we offer options in Statistics and Mechanics, for those of you who have particular degree courses in mind.
AS in Mathematics is very valuable as a supporting subject to many courses at A Level and degree level, especially in the sciences, Geography, Psychology, Sociology and medicine. A Level mathematics is a much sought after qualification for entry to a wide variety of full-time courses in Higher Education. There are also many areas of employment that see Mathematics A Level as an important or vital qualification.
Formal Entry Requirements
All students studying for A Level would be expected to have five GCSEs A*-C in academic subjects (of which two must be B grades) including GCSE English Language. We will count Level 2 Btec Diplomas towards this total, but only merits and distinctions will be counted and each diploma will count as one GCSE. Additionally, you will need GCSE Maths at B or above in the higher paper.
What does the course involve?
Mathematics at AS and A level is divided into three branches:
Pure Mathematics (Modules C1, C2, C3, C4)
Pure Mathematics at AS and A level extends your knowledge of topics such as algebra and trigonometry as well as introducing new ideas such as calculus. If you enjoyed the challenge of problem solving at GCSE then you should find this course very appealing.
Mechanics (Modules M1, D1)
Mechanics describes the motion of objects and how they respond to forces acting upon them, from cars in the street to satellites orbiting a planet. You will learn techniques of mathematical modelling by turning a complicated problem into a simpler one that can be analysed and solved using mathematics. Many of the ideas you will meet form an essential introduction to modern fields of study such as cybernetics, robotics, biomechanics and sports science, as well as the more traditional areas of engineering and physics.
Statistics(Modules S1, D1)
Statistics covers the analysis of numerical data in order to arrive at conclusions about it. Many of the ideas met have applications in a wide range of other fields: from assessing what car insurance costs to how likely the Earth is going to be hit by a comet.
In order to get an AS Level, you will need to take three modules. For a full A Level, you will need to take three further modules. We offer two options:
Pure and Mechanics: This option is usually taken by students studying Science (especially Physics), Engineering or Construction.
Pure and Statistics: This option is usually taken by students studying Business (Economics, Accounting or Business Studies), Psychology or Biology.
How will I be assessed?
Both AS and A level Mathematics are assessed through a series of written examinations. If necessary, students can retake any module. There is no course work involved in assessing mathematics.
Where can I go next?
Most A level students go on to study at university. Some have used Mathematics to go directly into a career in accountancy.
The study of mathematics opens the door to many varied professions. Obvious choices would be in the area of Science and Finance. To see the many varied careers that a student of mathematics and statistics may follow, from games programmer to weather forecasting, go to | 677.169 | 1 |
This booklet contains a number of case studies of lessons that emphasise working with what students already know and working from concrete ideas to the abstract. Each case study explains the task, contains examples of students' work and explains how the lesson was followed up.
The function game is one way in which algebra game from the Contemporary School Mathematics collection published by Edward Arnold, was written in the belief that there is still value in the examination of Euclidean geometry as a logical system, whatever other approach may be used to increase the students' spatial perception.
The topics covered are:
What is… | 677.169 | 1 |
Math 521 ``Graduate Algebra I''
Fall 2011
Introduction:
Abstract Algebra is the branch of pure mathematics
that tries to reduce mathematical questions to symbolic manipulation.
Here is an example. Consider a cube, an object most
people feel they understand. 6 congruent square faces,
12 congruent edges, 8 vertices.
How much symmetry does it have? This question seems to
make sense already, but it is hard to quantify until we define
``symmetry''.
In algebra, a symmetry of a geometric object
is a bijection of the object to itself that preserves the object's defining
properties.
That is an algebraic formulation of
a geometric concept.
``Preserving the object's defining properties'' in this case means
preserving the cube's shape (metric) and its orientation in space.
So, how many geometric symmetries does the cube have?
Our position in this class is that
we don't really understand the cube
if we cannot answer this question.
Our collective mind will fester around this problem,
until we have built up the machinery necessary to answer it.
We will see that not only can we count the symmetries,
we can describe the structure of this set, using the algebraic
notion of group. We will name the symmetry
group of the cube.
For the last few hundred years,
algebra has developed mostly around attempts to
solve specific math problems, mostly in number theory and geometry.
For example, algebra was used to solve the
ancient problem
of determining which polygons can be constructed using only a
straight edge and compass.
Gauss solved this problem in 1796, when he was five years old.
We'll try to solve some of these types of problems.
``Abstract'' means, ``disassociated from any specific instance''.
In the 20th century, certain basic algebraic objects were isolated
and abstracted to form the core of abstract algebra:
groups, rings, fields, and modules.
These abstract objects appear in practically every area of pure mathematics.
We'll start with groups, then start on rings.
We'll do modules and fields in Math 522. | 677.169 | 1 |
Key To… When it comes to higher math, if either you (teaching) or your student (learning) lack confidence, then this curriculum may be your answer.
Key to Algebra offers a unique, proven way to introduce algebra to your students. New concepts are explained in simple language, and examples are easy to follow. Word problems relate algebra to familiar situations, helping students understand abstract concepts. Students develop understanding by solving equations and inequalities intuitively before formal solutions are introduced.
These | 677.169 | 1 |
TEACHINGpoint authors are master teachers with a degree in their content specialty. They are veteran instructors with classroom-tested labs and activities, and exceptional skills in developing dynamic daily lesson plans that work with a wide range of student learning styles and academic skills. Additionally, these materials are designed to work well with any textbook you choose (if necessary) for the course as the lesson plans refer to topics to read vs. specific page numbers.
The course materials are aligned to standards and reviewed by an Academic Review Board composed of content specialists and veteran teachers to ensure both accuracy, "teachability," and to support the implementation of best practice in classroom instruction.
MEET OUR AUTHORS - In Alphabetical Order by Last Name
Cathleen Alexander, author of Pre-Algebra, has taught Mathematics at the elementary, middle school and high school levels in both public and private schools for over 14 years. In the California public schools, she has taught Pre-Algebra, Algebra and Geometry. In addition, she has taught Algebra in the Pre-College Program at Sonoma State University, and was an elementary and middle school principal. Ms. Alexander a U. California Davis Ph.D in Math candidate, also has a background developing Science curriculum, most recently "Inventions Plus" for Upward Bound Math and Science students. She has also contributed Mathematics and Science curriculum to academic journals. For 8 years, she has been an annual speaker at state and national education conferences, presenting numerous workshops such as "Geography Long Jump! And A Math Activity That Sneaks in Negative Numbers" and "Chess and the Mathematics Classroom." Ms. Alexander says: "My philosophy of education is to teach students in a way that they will understand and remember. My method combines direct teaching, observation, student discovery and practice. I also weave in brain research, multiple intelligence theory and inquiry-based techniques. I am passionate about my teaching, and try to impart the importance and relevance of the subject to students' real lives. I incorporate advanced concepts into simple exercises and authentic activities."
Ruth Antmann is the author of the Elementary Music Series for Grades K-5 (links for levels K, 1, 2, 3, 4, 5). She graduated from Florida State University with her Bachelor's degree in Music Education in 2001, and her Master's degree in Music Education in 2004. She began her teaching career at Holy Comforter Episcopal School in Tallahassee, Florida, teaching elementary and middle school instrumental music. During her five years there, the middle school band consistently earned Superior ratings and performed at Magic Music Days at Walt Disney World. In 2007 she moved with her family to the Orlando area, where she began teaching elementary general music in the Orange County Public Schools. She has supervised the production of numerous musicals and concerts. Ruth Antmann has presented lesson plan ideas at workshops for the Orange County Elementary Music Educators and at curriculum fairs for the Florida Music Educators Conference in Tampa, Florida
George Burson, author of Advanced United States History and IB History of the Americas, is a long-time teacher and Woodrow Wilson Fellow who has authored a dozen articles on history and history education. He served five years on the Advisory Board of the Magazine of History. He has an M.A. in history and completed two years of post-graduate work at Vanderbilt University. As a National Endowment for the Humanities Teacher-Scholar, he spent the 1992-1993 school year at the University of North Carolina, Chapel Hill conducting historical research. In 2001 he was awarded the Aspen, Colorado School District Distinguished Teacher Award.
George Cassutto, author of Civics, is an award-winning author who developed curriculum for the PBS Series "The Democracy Project," consulted on the PBS "Thomas Jefferson" documentary and has developed curriculum for the Discovery Channel and U.S. News & World Report.
Veronique Cheniaux, author of IB FrenchB is a native French speaker from Visé, Belgium, and a long time language educator at the college and high school level. With a European degree to teach French as a foreign language and a BA in French and Francophone studies, she has also collaborated in the publication of a video tape program to teach French to young children. Her experience encompasses a teaching assignment with the US army intelligence in Germany, adjunct professorships in several US colleges, free –lance translation and editing work and curriculum LOTE development. She is currently teaching at the Canandaigua Academy in the NY state.
Dave Conarroe, author of Confronting Drug Use, has been teaching at Aspen High School since 1976. During that time he was the athletic director 1989 to 1998; the girls basketball coach 1976 to 1991 and 2004-2006; the boys basketball coach 1992 to 1998; the head track coach 1978 to 1986; an assistant football coach 1977-1985; co-founder of Aspen's youth football team in 1998 as a member of Three Rivers Youth Football; a member of Colorado High School Activities Association Board of Control 1995-1998; Fulbright teacher of A-Level Business Studies at Victoria College Belfast, Northern Ireland 2001-2002; AHS teacher of the following courses: IB/AP Economics, IB Business and Management, Marketing, Intro to Finance, Business Law, Accounting, Sports and Entertainment Marketing, MS Office, Journalism, Psychology, Physical Education, Web page development, Career Planning, and Drug Education. His graduate assistantship at Northern Arizona University was in the University Advisement Center.
Zora Dougherty deGrandpre, author of AP Chemistry and co-author of AP Biology, has been a high school science teacher of biology, chemistry and physics. She holds a B.S. degree in Medicinal Chemistry from SUNY and an MS from the Department of Natural Science, Roswell Park Cancer Institute, where her thesis was entitled "The Development of an ELISA for Anti-lymphocyte Antibodies in Plasmapheresis Donors and Recipients." Her doctoral thesis at Roswell is entitled "Anti-idiotypic T-suppressor Cells in Response to Bacterial Dextrans." Her educator responsibilities have included involvement in outcomes-based curriculum development as well as laboratory exercise development using standards developed in conjunction with the NYS Department of Education and as a member of curriculum development committees responsible for the creation of outcomes-based standards and Regents test development, with a particular emphasis in laboratory science.
Kerry Doll, author ofInterior Design, graduated from California Polytechnic State University, San Luis Obispo in 1979 with a Bachelor of Science degree in Home Economics and received a Master's degree in Teaching in 2003. She has been a Home Economics teacher for 22 years, 16 of them at Fountain Valley High School. About nine years ago, she and another teacher co-wrote Environmental Design, which meets the a-g requirements for the UC/CSU systems in California. This class is a mix of Interior Design and Architecture and the lessons have been included in this course. She has worked with the California Dept of Education, Home Economics Careers and Technology Unit on the last two revisions of the Interior Design standards including the last alignment for the Common Core standards, and CTEonline supervising and writing lessons for Interior Design. The Environmental Design class has been articulated with Orange Coast College for their entry level Interior Design class. She is currently a member of the Orange County Professional Learning Community for Fashion and Interior Design, and a Community Group Leader for Fashion and Interior Design Career Pathways for CTEonline.
Joseph Enge, author of World History: Early Man to the Age of Discovery, and World History: Early Man to the Age of Discovery was a Fulbright teacher in the former Soviet Union, a history columnist, and an internationally published journalist in addition to being a history teacher since 1988. Enge has mentored teachers in the United States and abroad as well as being one of the writers of Nevada's history standards. He and his students just received an award from U.S. Senator John Ensign, Nevada, for utilization of technology in education and his teacher Web site has received a number of educational awards. Peter Farrands, PhD, is the author of IG History 0470 and IG Literature 0486 (in development), both for the Cambridge Curriculum. After securing an Honours degree in Literature and Humanities from Middlesex University in the United Kingdom, Peter began teaching Cambridge IGCSE O' Levels in Zimbabwe in 1984 in one of the new rural government secondary schools. He returned to the UK in 1987 for the one-year Post-Graduate Teachers Certificate at Westminster College. While writing his thesis he headed the new Media Studies department at The Sixth Form College Farnborough. He was awarded his doctorate from Southampton University (UK) in 1994 while teaching at Molepolole Teachers College in Botswana. Building on his experiences in Zimbabwe, his PhD thesis focussed on Southern African Literature and Politics. Since then he has worked for the University of Mobile (USA) at their Central American campus, the University of the Witwatersrand in South Africa and as a writer of adult Literature courses for the University of South Africa. His areas of academic expertise are History and Literature at pre-University Advanced level. He has published numerous articles and academic courses including studies in seventeenth century Cavalier poetry and nineteenth century Russian Realism.
Randolph Femmer, author of Honors Chemistry and Ecology, has taught high school science in such diverse subjects as A.P. Biology, Ecology, Marine Biology, and Honors Chemistry for twenty-five years. His classroom presentations and curricula include such exceptional labs, units, and demonstrations as Observing the Invisible, Measuring the Invisible, and "What Every Citizen Should Know about Our Planet." He has written three books and a variety of articles and digital presentations on topics as diverse as Telomeres and Telomerase, DNA Sequencing, and the Photoisomerization of Retinol. His web presence includes three educational web pages and his classes conduct computer activities utilizing Molecular Visualization, Rasmol, Stella computer modeling, and Scion imaging software. He has also conducted a variety of district workshops for new teachers, including molecular visualization using Rasmol, exceptional labs and demonstrations for new teachers, and 21st century science for the high school classroom. He and his wife Carol attended the University of Miami and reside in Florida.
Dom Festante, author of Computer Applications and the Internet, started his career as a middle/high school English teacher in New Jersey. He was a founder of a computer consulting company and then he returned to the field of education as director of an Educational Technology Training Center (ETTC), a unique concept developed by the New Jersey Department of Education. The ETTCs were created to offer workshops that assisted educators in the seamless integration of technology in the district and in the classroom. He has authored two workbooks designed and written for students and adults possessing little or no knowledge in the process of creating databases using Microsoft Access. Dom has also served as a middle school principal, Director of Curriculum, Dean of an academy devoted to mathematics and science, supervisor of mathematics and science departments, supervisor of staff development and a member of the adjunct faculty of several colleges and universities teaching both graduate and undergraduate courses. He holds a B.A. in English from Seton Hall University, a MA in Education from Kean University and an M.Ed. in Educational Leadership from William Paterson University Thoroughly enjoying leading workshops, Dom has presented such workshops as Recognizing Hate on the Internet, Differentiated Instruction, Multiple Methods of Assessment, So You Want to use the Internet in Your Classroom?, and Middle School Concepts and Practices and Technology in the Classroom.
Caroline Goode, author of Grade 5 Science, has taught fifth and sixth grade middle school science in Rockland Public Schools, Rockland, MA for 20 years and is a professional development presenter specializing in STEM (Science, Technology, Engineering, Mathematics) education, inquiry across the curriculum, 21st Century Skills, and standards-based learning. Currently, she works as an independent consultant working with pre-service teachers and classroom teachers at the K-8 grade level. She has a BA, MA (K-8 Elem. Ed.) and MAT (Physical/Earth Science) from Bridgewater State College, MA.
Since 1989, she has logged over 1,200 hours of personal professional development to build her content knowledge and pedagogical strategies for effective teaching. Caroline has been a National Science Teachers Association (NSTA) presenter, curriculum writer, reviewer, and author of their SciGuides online packets, and now is the MA State Coordinator for the NSTA Science Matters in the Massachusetts online dissemination network reaching over 1,200 K-16 science educators with her two weekly e-blasts on Professional Opportunities and K-16 Resources at the national, state, and local level helping teachers overcome the isolation of their classrooms. She is a NEA/NFIE Christa McAuliffe fellow, a recipient of the 2005 MA Christa McAuliffe Teacher of the Year Award and the 2006 National Challenger Center for Space Education Turner N. Wiley Award. She has been an online mentor of the New Teacher Center's National Electronic Mentoring for Student Success (eMSS) since 2005, and is an education consultant for the National Institute of Health's Office of Science Education and the U.S. Department of Energy Office of Science Education. In 2010, Caroline was appointed to the MA Governor's STEM Advisory Council serving on the Teacher Development sub-committee.
Louis Guglielmo, author of Sociology, and Model U.N., is a veteran teacher and National Endowment for the Humanities Scholar. He spent the summer of 1999 as a visiting scholar at Douglas College working under Dr. Bonnie Smith studying Gender from a Global Perspective; He received his Masters in Education from Rutgers University Graduate School of Education in 1994, and holds a B.A from Temple University (1992). He has been teaching at Franklin High School in Somerset, NJ his entire career. A selection for Who's Who in Education the past two years, Louis has been nominated for Disney Teacher of the Year, and numerous other accolades by his former students. In addition to his teaching experiences, Louis is also a copyrighted screenwriter, softball coach, advisor to the Model UN and Model Congress clubs, and roommate with his two tabby cats--Linus and Lucy. Susan Henson, author of Advanced Language & Composition, has taught all levels of high school English, including honors and college-level classes. Both an SAT essay reader and Advanced Placement® Language reader, Susan specializes in teaching advanced rhetoric to high school juniors. She has also served as a founding member of a campus vertical alignment team, as an English department chair, and as a member of a core curriculum development team. In addition, Susan regularly delivers presentations on the teaching of English and the use of technology in the classroom setting at local, state, and national conferences. Most recently, she presented the session, "The Rhetorical Triad: The Foundation of a the Advanced Placement Language Course" at the 2013 AP National Convention. Susan has established and directed two secondary writing centers and was the founding faculty sponsor of her campus student art and writing magazine. In addition to her current work in the classroom, Susan also directs an academic advancement center and facilitates student and teacher publications and collaborative projects.
Art Hovey, author of Advanced Physics, earned a B.A. in physics and mathematics in 1964 and a Master of Arts in Teaching in 1965, both from Yale University. He taught physics and mathematics at New Haven's Hillhouse High School from 1965 to 1967, and then taught physics at Amity Regional High School in Woodbridge, CT from 1967 until his recent retirement. While at Amity he had the pleasure of seeing the physics enrollment grow from two classes to more than a dozen. He received a "Celebration of Excellence" award in 1987, CT State Department of Education CORE training for master teachers in 1989, and attended MIT's Science and Engineering Program for Teachers in 1992. In 1999 his student team won first place in Yale's state-wide Physics Olympiad competition. He is a member of American Association of Physics Teachers, New England Science Teachers and Connecticut Association of Science Teachers. He is also active as a musician, playing tuba in the Galvanized Jazz Band, the Connecticut Symphonic Band, and many other groups.
Chad Husting, author of Chemistry, has attended several colleges and universities. He graduated from Dominican University (Rosary College) in 1989 with a B.A. in Chemistry. He then went on to graduate from Indiana University in 1991 with a M.S. in Physical Organic Chemistry. Post graduate credit has been earned at University California Berkeley, Wright State University, University of Dayton, Elmhurst College, Miami University, University of Cincinnati and Boston University. Mr. Husting has published papers on topics such as organic chemistry, using Examview as an assessment tool, pre and post testing and has published two books with Teaching-Point. He also was awarded a grant from the American Chemical Society to study the use of using professional digital assistants in the classroom and at Miamisburg High School he was one of three recipients that were awarded a $10,000 grant to study the effects of global warming and have students put their information on a web site. He currently teaches chemistry at Sycamore High School in Ohio and was just named as an adjunct professor with Ashland University of Ohio where he teaches teachers about using BlackBoard to create classroom web sites.
Rosa Mª Iglesias (Traviesas), author of IB Spanish Ab, graduated in 1996 from Oviedo State University in Asturias, Spain, with a Bachelor's degree in English Language, and Teaching Training Certificate from Oviedo State University, Asturias, Spain in 1997. She began her teaching career in state secondary schools in Asturias 1999. She teaches A2 to B2 CEF levels in state language schools and serves both as an IB Spanish Ab SL paper two Examiner and IB Spanish Ab SL internal assessment (oral) moderator. She is also member of the supervising group for the English A2 language Examinations administered by Asturias Department of Education, Spain.
Helen Joyce, author of Elections,Using Film in the Social Studies: World, and Using Film in the Social Studies: Government, served over 30 years as a middle and high school classroom teacher, Social Studies Department Chair and high school administrator. She has taught AP® Government, World History, AP® US History, and interdisciplinary courses in both World and American Studies at the high school level for most of her career. She completed her undergraduate studies in History/ Education at City University of New York (Hunter / Herbert H. Lehman College) where she earned the Kappa Delta Pi Award for Academic Achievement and Professional Promise in 1974. She earned a Masters Degree in Educational Administration at Plymouth State College in New Hampshire in 1981. In 1993, Mrs. Joyce was named the New Hampshire Assistant Principal of the Year by the NH Association of Secondary School Principals. She has supervised her Elections program in a number of high schools since 1980 and both she and her students have gained statewide attention and recognition by the media as a result of their work.
Thomas Joseph Kaup, along with Dianne Smith, is the co-author of Middle School Journalism Semester 1 and Semester 2. Mr. Kaup has been an educator for over twenty years, as a high school English teacher and English Department Chairman, Adult Education Coordinator, and a middle school language arts and journalism teacher. He completed his undergraduate studies in English at the University of St. Thomas in St. Paul, Minnesota, and received a Canonical European Masters Degree, S.T.L., in English Literature and Theology from the University of St. Mary of the Lake, in Mundelein, Illinois, affiliated with the Archdiocese of Chicago, in 1986. He is a National Board Certified Teacher and is a Master Journalism Educator with the Journalism Education Association. Mr. Kaup has been listed in Who's Who among America's Teachers, was the 1998 St. Albert Teacher of the Year. Mr. Kaup's middle school and high school yearbooks have won national recognition from the National Scholastic Press Association and the Columbia Scholastic Press Association. Kaup recently presented at the Magnet Schools of American National Conference and most recently taught middle school journalism at Alice Buffett Magnet Middle School in the Omaha Public School district in Omaha, Nebraska.
Olga Kokino, author of Journalism, has served as president of the Los Angeles Journalism Teachers Association for the last eight years, coordinating regional write-off competitions with the California State University at Northridge. She has also served as a judge for the Journalism Educators Association, the California Association of Teachers of English, and has critiqued student newspapers and literary magazines JEA and the National Council Teachers of English. She received her B.A. in English from the University of California at Santa Barbara in 1977, M.A. in Education and Reading Specialist Credential from UC Riverside in 1981, Certified Journalism Educator, 2000, and National Board Certification in 2001. She is a fellow of the UCLA Writing and Literature Projects, and has developed curriculum for the Institute of Standards, Curriculum and Assessment, as well as contributing to standards-based assessments for the WestEd research and consulting firm. Kokino served on the California Department of Education Recommended Literature Committee and has mentored beginning teachers and NBC candidates. She has been a frequent conference speaker in the past for ISCA, CATE, NCTE, JEA, and the International Reading Association. Her journalism students have won prestigious internships and assignments from Highwired.com, the LA Times, the CSUN Sundial, the Harvard Crimson, as well as the Hispanic Heritage Award, the KTLA Stand Chambers Journalism Awards, and the Beverly Hills Friar's Club First Place Award in Screenwriting for high school students, among other honors. In 2003, she was recognized for outstanding classroom achievement with a Los Angles Educational Partnership Award, and in 2002 she received the Excellence Award for contributions to the teaching profession presented by the Southland Council Teachers of English. Presently, she is serving as journalism adviser, English teacher, and Title 1 Compliance Coordinator at University High School in Los Angeles. She also serves as the Staff Officer, Publications, for the USCG Auxiliary Flotilla in King Harbor. She has lessons online with the American Society of Newspaper Editors (ASNE), the Los Angeles County Office of Education, the California Technology Assistance Program, and the Teach the Teachers Collaborative.
James Kovalcin, author of Honors Physics, Volumes 1 & 2, has been teaching all levels of high school physics for over 33 years. He graduated with a B.S. in Physics from the University of Pittsburgh in 1971 and completed his MAT in December 1972. After a brief sojourn into research, he moved into the public school classroom and has been there ever since. For the past 15 years he has been teaching a combination of Lab Physics and AP Physics C Mechanics and Electricity and Magnetism. During the 2002-2003 school year, 29 of his students took the physics C exam with 25 receiving 5's and the remainder receiving 4's. Over the last decade he has had four students become member of the US Physics Team. In the international competition, one student received a Bronze medal and another received a silver medal. The silver medalist also came in 2nd in the experimental section of the international competition. David Lovell, author of U.S. History through 1988, Survey of U.S. History to 1945 and Contemporary U.S. History 1945-1988, currently teaches U.S. History and Honors U.S. History at Father Ryan High School in Nashville, Tennessee. He received his Bachelor of the Arts in Education, History, Theology and Philosophy from St. Ambrose University in Davenport, Iowa. He went on to do his graduate studies at the state university in Louvain, Belgium. While studying in Europe he did a stint with the Marine Corps in the Middle East. David has given seminars on the Civil War and The Battle of Nashville to various groups including at the SACS convention and at Vanderbilt University. He maintains his award winning web site to assist his students in their academic pursuits, and he has twice been named to Who's Who among America's Teachers. In addition to his work in the high school classroom, Mr. Lovell has taught many adult classes on American History and the Civil War.
Jim Matiya, author of Psychology and Advanced Psychology, has taught Psychology, Psychology II and Advanced Psychology at Carl Sandburg High School, in Orland Park, Illinois. In addition, he has taught psychology at the junior college, university and, even, the post graduate level. Jim Matiya was the recipient of the American Psychological Association's Moffett Award winner (high school teacher of the year) in 2003. He even taught a course titled "Teaching High School Psychology" to prospective teachers at Lewis University. He has authored and/ or co-authored twenty articles about high school psychology. He is the author of two books; one is called Creating a Psychology Fair and has written student workbooks for three different high school psychology books. In addition, he has written material for an Advanced Psychology Guide website and created PowerPoint presentations for another psychology text as well as chapter readings. He has also been a writer/editor/consultant for twenty different high school and college textbooks. Matiya is a regular contributor at national and local social studies meetings and has been an invited speaker at several workshops. Jim's students annually participate in a Psychology Fair and some of their studies have been replicated in other books, many others have pursued psychology or in related fields. Furthermore, Jim also makes materials for psychology classes, and he is best known for his goggles that are used in the unit of vision. The goggles can be found in high schools, hospitals, and universities around the world. Above and beyond all these honors, he treasures his wife's and children's love for him and, especially, their tolerance for all the time he devotes to make high school psychology a fun and interesting course.
Carol Matthews is the author of five TEACHINGpoint course materials, including Advanced (AP) Environmental Science (Winner of the Text and Academic Authors Association TEXTY Award for the best text in the Physical Sciences), Environmental Science (regular/honors version), Marine Biology and Oceanography,Freshwater Science and Aquatic Science (a one year combination of Marine, Oceanography and Freshwater to be released summer 2013) has been an active classroom teacher for over 30 years specializing in these subjects and has spent more than a decade committed to protecting and restoring natural habitats and mentoring teachers in her field. Since 1998, she has led AP™ Environmental Workshops to prepare teachers for their new assignments and is an AP Environmental Exam Reader for the College Board. Matthews received her M.Ed from the University of Delaware Sea Grant College. She served for 10 years as Chairman of the Stewards of the St. John's River, an environmental organization with the mission to protect and restore the St. John's River in northern Florida. In 2002, has been a Board Member of the Falorida Assn. of Teachers (FAST), a Board Member of the Florida Marine Science Educator's Assn. (FMSEA) and was named the Jacksonville, Florida Environmental Citizen of the Year.
Amy McCracken, author of English 11 and Honors English 11, is a 1994 graduate of Indiana University of Pennsylvania, receiving a B.S. in Education and Secondary English concentration. Since 1996, she has been teaching English 9, 10, and 11; grammar and composition; photojournalism; and drama in the state of Virginia. In 1999, she became the chair of her English department, and she was included in the 2002 edition of Who's Who of American Teachers. Since she began teaching for the English 11 SOL exams in the state of Virginia, her class pass rate has an average of 98%, and her department has risen from a 66% pass rate in 1998 to a 98% pass rate in 2004. Amy is currently working on her Master's Degree in Literature, with a concentration in American literature, at George Mason University.
Nancy Montgomery ED.D, author of Elementary ESL, and Middle School ESL and also High School ESL, has her doctorate from Texas A&M. She brings more than 20 years of classroom experience from Southeast Asia to the United States at the elementary, college and secondary level. She is working as a Senior Consultant for Education Service Center in Richardson, TX and providing assistance to the Russian Reading Project in Moscow and the South Africa Farm School Project.
Barbara Moran has taught Creative Writing since the 1980's. In 1994, the Michigan Council of Teachers of English named her Creative Writing Teacher of the Year. She advised the school literary magazine, Voices, which was recognized by state and national organizations. Hundreds of individual student writers have won honors in local, state, and national writing contests, including publication in national magazines such as Writing! . Creative Writing contains lessons that foster the crafts of poetry, fiction, and drama in a format accessible to both teachers and students.
Naemah Morris, author of Advanced European History has been teaching since 2000, serving as a high school classroom teacher, social studies department chair and director of forensics. She has taught World Civilizations I, World Civilizations II, AP® European History and International Relations. She received her undergraduate degree from Wheaton College in Norton, MA, graduating Suma cum Laude and earned her Masters Degree in Education from Loyola Marymount University Ms. Morris' sophomore students have, on average, a 95% pass rate on the AP® European History exam. In addition, as the Speech and Debate coach she has led students to success at the local, state and national levels. She enjoys coordinating faculty in-services and aspires to work as a mentor to new teachers.
Elizabeth Morse, author of IB English B, is both an IB examiner and a workshop leader for IB Diploma Group 2. She served as IB Online Curriculum Centre Faculty Member for Diploma English A2 and English B for three years. She started her teaching career at Tokyo Friends School and later taught IB Diploma English B and English A2 at United World College-USA for seven years. She now serves as Director of Development and Communications at United World College-USA. She earned her MA TEFL from University of Reading (England), and her BA from Smith College.
Eudeen Mott, author of 4th Grade Language Arts, is a veteran elementary school teacher who is currently active in the Orange County Public Schools, Orlando, Florida. She was awarded Teacher-of-the-Year at her school in Broward County, FL in 1984 and again in Orange County in 1993. She has been a three-time Disney Teacheriffic Award winner for her innovative ideas in the classroom. She has recently published a children's picture book about her two dogs--"The Antics of Addison and Winston from A to Z." She attended Purdue University and Indiana University respectively. She also attended the University of South Florida for Library Science. She recently completed coursework at The Institute for Children's Literature to become a more proficient writer for children. She knows how to make teaching simple for the children but also wonderful. Her motto is, "Children are people too, and learning can be fun."
Laura K. Negri, author of Scholastic Yearbook, has taught journalism, photojournalism, newspaper, yearbook and technology classes for 18 years in Texas public schools. Negri graduated from the University of Texas at Austin where she majored in the Plan II Honors Liberal Arts program. Prior to becoming an educator, she was a newspaper reporter, photographer and editor. She evaluates yearbooks for several state organizations and has been a speaker at state and national conventions. She is a Certified Journalism Educator by the Journalism Education Association, a 2002 Reynolds High School Journalism Institute participant, a 2005 Radio Television News Directors Foundation Teacher Ambassador, and a 2012 Fund For Teachers Fellow.
John B. Nici, author of Advanced Art History, Great Books, and Advanced (AP) Literature and Composition, has taught Advanced Placement Art History and Great Books for thirty years at Lawrence High School in Cedarhurst, New York, and Forest Hills High School in Forest Hills, New York. Additionally, he teaches art history as an adjunct professor at Queens College in Flushing, New York. In that capacity he has taught such diverse subjects as Medieval Art, Art of Renaissance Italy: 16th Century, Art of England, American Art, Romanticism and Impressionism. Queens College has recently honored him as the 2004 recipient of the President's Award for Excellence in Teaching by Adjunct Faculty. He has delivered scholarly papers at symposia held at Indiana University, Western Michigan University and Siena College. His recent article, "Delacroix's Portrait of Chopin as a Surrogate Self-Portrait," appeared in the book The Age of Chopin (Indiana University Press, 2004). Forthcoming is "The Most Perfect Picture in the World: Raphael's Sistine Madonna" which will be included in the volume The Masterpiece Effect. In 1997 he began his association with the College Board, first as a reader and table leader of the Advanced Placement Art History examination, and then as a consultant holding workshops for teachers new to the field. He has contributed questions to the Praxis Art Content Examination, used for teacher certification in many states. He has also been active in his high school community, working as advisor to the school yearbook for twenty years. This yearbook has won several distinguished awards including being selected as the best in New York State by Syracuse University. He has lectured on yearbook methodology and published in yearbook trade magazines. He has also functioned as senior advisor, organizing events like the senior prom and graduation. In addition to Great Books and Art History he has taught a full complement of English courses from Advanced Placement English Literature to remedial writing workshops.
Betsy Norris, author of 5th Grade Language Arts, has served as Supervisor of Grants and eLearrning for Bedford County Schools since 2006. She serves her 14 school district as grant writer and grant supervisor obtaining and managing 2.5 million dollars of grants. She is currently implementing grants for history, counseling, telemedicine, distance learning, and afterschool programs for K-12. She also serves as the Moodle administrator overseeing the district's 49 virtual courses with 33 online teachers. She was selected Wal-Mart Teacher of the Year in 2001, as well as the district and school Teacher of the Year. She received her B.S. in Elementary Education from Middle Tennessee State University, her Masters in Administration and Supervision from Tennessee State University, and her Ed.S. in Curriculum and Supervision from Middle Tennessee State University in 1984. Betsy taught ELA for 26 years with experience in public and private schools with experience in grades 1-12. She also taught adults for English GED courses and technology courses in the local technology center. She has served on the advisory board of both Technology and Learning Magazine and the PBS (Public Broadcasting System) TeacherSource. Some of her developed curriculum for PBS includes "Newshour Extra Poetry" and "Circle of Stories." She also served to develop curriculum for the PBS series "The Children's Hospital." In 2000, she was named Technology and Learning magazine's Southeast Teacher of the Year. That same year, she traveled to California to accept the National Business Week Award for Instructional Innovation for her school at the time. She has done consulting work and technology presentations both locally, nationally, and internationally. Recently she presented at NECC and iNACOL. Beside her writing for Teaching Point, she has done freelance writing for Technology and Learning, PBS, Teacher Created, PC Create It.
Steve Pellegrini, author of Botany and Zoology is a thirty-four year veteran of the secondary science classroom. He has taught biological science to students of all levels from seventh grade through college. He has published numerous papers and articles including a booklet on traditional uses of plants by Native Americans in the Great Basin. He earned an M.S. from the University of Nevada in Reno. The recipient of Nevada's first Presidential Award for Excellence in Science Teaching, his achievements have also been recognized with numerous awards including the McAuliffe Fellowship, Milken Award, National Association of Biology Teachers "Biology Teacher of the Year" and NASCD Conservation Teacher of the Year for the Pacific Region. The author has also been widely recognized as an authority on feral horses.
Jean Potter, author ofPre-School(Pre-Kindergarten), has been a kindergarten teacher and the Director of Early Childhood Education for the West Virginia State Department of Education. She was appointed by President Ronald Reagan as Deputy Assistant and Assistant Secretary of Education for the U.S. Department of Education. At the U.S. Department of Education, she was responsible for the overall management of the elementary and secondary education programs at several colleges and universities. Jean is the recipient of numerous awards for outstanding achievement in the field of education. She continues to write and consult in the early childhood education field.
W. Jason Reagin, author of IB MYP Technology Volume 1 (grades 6-8), and Volume 2 (grades 9-10) graduated from the University of Georgia with a MEd in Technological Studies. He has 15 years of teaching experience in US as well as Bermuda and China. Mr. Reagin has taught a wide spectrum of students from age 3 to 83. For over 10 years he has been working in 'IB' schools and has served IB as a workshop leader, site visitor and consultant to candidate schools. Mr. Reagin is currently Head of Design at the Suzhou Singapore International School in Suzhou, China just west of Shanghai.
Eric Sapp, author World Geography, has been teaching social studies since 1995 and is the school department chair. Eric has twice been nominated for Who's Who Among America's Teachers. Eric Graduated from Central Missouri State University with a B.S. in Education and has a Masters degree in technology in education from Lesley University.
Pamela Schnell has been teaching high school science for since 1986, and is an adjunct professor for Western Nebraska Community College. After working with a student teacher, she started documenting ideas that worked well in establishing positive interactions with students. She compiled these ideas into a book, 50 Strategies to Improve Instruction and Classroom Management, as a project for a Master's Degree in Science Education from Chadron State College, Chadron, Nebraska, where she earned her Bachelor of Science in Education Degree as well. Pamela is a member of the National Biology Teachers Association, Alpha Delta Kappa, and a participant of the Howard Hughes Medical Institute for Science Teachers.
Michael Scott, PhD, author of Applied Jazz Theory was awarded the "Jamey Abersold Scholarship Award" to attend the Jazz Clinic hosted by the University of Massachusetts, Amherst where he studied with such renowned jazz artists as Ted Dunbar, Max Roach, Dr. Billy Taylor and selected members of the "Saturday Night Live Orchestra" including Steve Turre in 1986. Dr. Scott received his Bachelor's Degree in Music Education from Mansfield University and has held full Pennsylvania State Certification since 1991. He was then hired under full contract to serve as Director of Instrumental Music and Drama at the Wilmington Friends School in Delaware until 1995. Dr. Scott achieved his Master's Degree in Saxophone Performance at The New England Conservatory of Music in 1997 where he performed with conservatory ensembles and professionally throughout the Boston Metropolitan area including regular engagements at New England Conservatory's Main Stage at Jordan Hall the Boston Hard Rock Café. Dr. Scott is the published author of both the Instrumentalist Accreditation Program and the Jazz Instrumentalist Accreditation Program which are performance programs designed to motivate music students to advance through four levels of achievement based on specific measurable performance criteria. The IAP's have been published by the Emelior Publishing Corporation since 2001 and 2002. Dr. Scott received his Ph.D. in 2004 from Century University for his coursework in education and his dissertation on The Development and Analysis of a Performance Based Assessment Model for the Formal Study of Instrumental Music. His most recent publication, Applied Jazz Theory is a complete course of study which couples the theoretical foundations of music with the practical applications of improvisational performance. Dr. Scott is proud to have been the Director of Instrumental Music for the Morrisville School District since 1998.
Dianne Smith, author of Introduction to Journalism and Scholastic Newspaper Production, was the 2003 Texas Journalism Teacher of the Year, selected by the Texas Professional Communicators. She is also co-author ofMiddle School Journalism 1 and 2 with Tom Kaup. She is a 2000 recipient of the Edith Fox King Award for outstanding contributions to Texas scholastic journalism, and was awarded the status of Certified Journalism Educator (CJE) in 2000 and Master Journalism Educator (MJE) in 2001 from the Journalism Education Association. She was selected as a Dow Jones Newspaper Fund Special Recognition Adviser in 2001. She is listed in Who's Who among America's Teachers. In 2002, Dianne was named a First Amendment Mentor Teacher by the Freedom Forum. Vitally interested in First Amendment rights for student journalists, Dianne serves as chair of the First Amendment Issues Committee of the Texas Association of Journalism Educators and is a member of the Scholastic Press Rights Commission of the Journalism Education Association. She established and maintains the first independent web site dedicated to scholastic journalism at and serves as Webmaster for TAJE. She teaches journalism, photojournalism, and desktop publishing and advises the student newspaper in the Houston, Texas area.
Susan Stein, author of Elementary Poetry and Grades K-5 First Year Teacher's Guide to Survival has taught for 34 years. She has been retired since 2003. Susan's passion for writing is exhibited in the two books that she has written. In the Survival Guide she has given first-year teachers the best advice for getting through the year filled with successes and failures reflected by her own experiences. Some of the challenges for the year are classroom management, parent involvement, homework, spelling, planning lessons, report cards, writing, reading, journals and plenty of helpful hints and things to avoid. Susan has always mentored new teachers and helped them adjust to the first year of their career. So, in reading this book, get ready to spread your wings and soar! In the Elementary Poetry book Susan has shown her desire to teach poetry to her students and share her techniques with teachers so they too can be successful in this area. Many of her students have won poetry contests; had their work published, while still others became something in the writing field. Kelly, a student she had many years ago, is working at a publications company writing for their website. When asked what teachers were inspirational to her she responded, "Mrs. Stein, because she encouraged me to write and instilled in me a love for poetry." Susan has an award winning website ( which encompasses a variety of educational themes, poetry, and literacy. There are over 200,000 visitors to her many pages since 2000. Susan's most prestigious award was winning USA Today Education Best Bet Web Site, which she has won twice. Fewer than 150 sites are selected each year as USA Today Education "Best Bets."
Renee L. Stroh-McClurg, author of Anatomy and Physiology, has taught high school science in Tomah, Wisconsin, since 1990. Subjects taught include biology, general science, and anatomy/physiology. Her undergraduate life science degree was earned at Winona State University in Winona, MN in 1990 and she completed her masters in education at the University of Wisconsin, La Crosse in 2000.
Paul Syme, author of Art 3: Multimedia Art and Design, has taught art and design in a high tech environment for seven years. Before teaching, Paul earned a Specialized Honours Bachelor of Arts Degree in Fine Art from the University of Guelph; a Baccalaureate of Education from the University of Ottawa; and, an Masters of Art in Art Education from the Nova Scotia College of Art and Design University. In 1997, Paul was appointed to design a new art education facility and curriculum for a new high-tech high school with aims to meaningfully integrate computer related technologies in the visual arts. In this capacity, he designed outcomes and strategies for teaching and learning art and design through a wide range of traditional and new media. Since his program opened in 1998, Paul created a dynamic web site for teaching and learning art and design, and with his students, he created several. Paul has earned recognition from Apple Computers for his innovative use of technology within the English Language Arts. Paul has written curriculum for the Province of Nova Scotia and advises teachers and school administrators on effective strategies for teaching through computer-related technologies in several key subject areas. Paul has been able to advance his program and gain notoriety by demonstrating how the potential of computer related technologies, when recognized and employed through experientially grounded learning strategies, can enhance the breadth, depth, and enjoyment of lifelong learning in any discipline. Paul also continues to serve on the E-Learning company, Adaptive Tutoring Systems Inc.'s, Advisory council as he has since 2000.
Olga Tcherviakova, author of Spanish 1 has taught Spanish at levels One, Three, Four, and Five at Nazareth Area High School in Nazareth, Pennsylvania for five years. As an author of the Spanish 1 book, Ms. Tcherviakova intends to equip teachers with a clearly structured material covering all the beginner grammar topics in depth and allowing for the immediate development of speaking skills. Originally from Minsk, Belarus, Olga taught English at the Suvorov Military School and two public schools in Minsk for two years and tutored Spanish and English privately for five years. She is a graduate of the Minsk State Linguistic University. She majored in Spanish, while earning her Master's Degree in Teacher Education. While a student at the university, Olga spent her summer 1997 in Andalucia, Spain in the capacity of a monitor, translator, and interpreter for the children from radiation contaminated regions near Chernobyl. Olga is fluent in four languages other than Spanish. These languages are Belarusian, English, French, and Russian. Along with being fluent in five languages, Olga is capable of comprehending six other languages. Olga utilized her multilingual skills in 2001 – 2003, when she taught English to adult immigrants at the Adult Literacy Center of the Lehigh Valley at the beginner and advanced levels. Ms. Tcherviakova was acknowledged in the 2003, 2004, and 2005 editions of Who's Who among America's Teachers and featured in local TV and newspaper editions several times. Olga Tcherviakova is dedicated to her work and devotes a lot of her free time to students. She encourages her students to work to their maximum potential, just as she does.
Marsha Tisdale, author of Keyboarding and Office Procedures, has been teaching since 1972. She has a Bachelor of Arts from Brigham Young University in French with a Business Education minor and a Master of Arts in Teaching Business Education from Portland State University. She has taught in junior high, high school, junior college, and vocational college. Subjects taught has included accounting, business law, career exploration, computer programming, drama, desktop publishing, economics, English, French, keyboarding, marketing, math, office procedures, portfolios, middle-school projects, speech and debate, and word processing. In addition, she has developed and supervised numerous portfolio processes, remained active in a site-based committee for school improvement, served as a computer technology and software coordinator, acted as an advisor to the National Honor Society chapter, served as foreign language and business education chairs, participated in the regional business management cadre, and helped organize a regional student organization (Business Leaders of Tomorrow). She helped supervise student teachers, acted as mentor teacher to new staff, and developed an on-going staff training on the Oregon Certificate of Initial Mastery (CIM) and state curriculum/portfolio requirements. She also participated in the US West "Train the Trainer" Program teaching staff the use of technology in classrooms. Professional involvement has included regional, state, and national associations in business, English, and foreign language. She's a multi-faceted person who loves to teach.
Dan Tompkins, author of Essay Writing, has taught literature and writing in Naperville (IL) District 203 since earning his B.A. in English and Philosophy from Wheaton College (1998). Dan researched the most effective strategies for teaching grammar and convention skills, earning his Master of Arts in Teaching in 2000. Additionally, since 2001 Dan has taught philosophy of education as an adjunct professor at his alma mater. He is a National Board Certified Teacher who also enjoys coaching the boy's tennis team. In 2002 and 2007 he was named a "Those Who Excel" award winner in Naperville (IL) District 203. In 2004 he and his students were chosen to present at TECH 2004 for their utilization of technology in education.
Judy Turner, author of 9th Grade English, is a 33-year-English-teaching veteran. She completed her undergraduate work at Colorado State College (now the University of Northern Colorado) and finished her Master's degree at The Citadel. Her experience at all secondary levels of English teaching from grade 7 to grade 13 has been strengthened over the years through her association with the Kern/Eastern Sierra Writing Project (3 time fellow, '81, '84, '87), NEH Summer Seminar (fellow, 2000) and professional organizations including NCTE, CATE, IATE, and NCEA. A favorite presenter at professional conferences since the early 1980's and a contract staff development coordinator for individual schools in both California and Illinois, she has focused on topics such as "Prewriting: The Key to Good Writing" and "The Writing Process." Her nominations for Illinois Teacher of the Year and Disney Teacher of the Year and her award as Part Time Faculty Member of the Year at Cerro Coso Community College (Ridgecrest, CA) and Teacher of the Year at Schlarman High School (Danville, IL) all demonstrate the support of administrators, parents and students throughout her career. Committed to the principle that good teachers of writing model writing for their students, she has published articles in the journals of both CATE and IATE, a monograph for the Kern/Eastern Sierra Writing Project, and is presently editing a student-written publication about an important senior citizen whose influence on her present high school has been inspirational to alumnae and present students. With no plans to even consider retirement, she hopes to continue both writing and publishing while pushing her students to use their high school education for lifetime success.
James Wenk, author of Algebra 1, was honored as Teacher of the Year in the Downey, California Unified School District for his work as a District Math Mentor Teacher. He has been selected GATE Lead Teacher for the past 5 years, math department co-chair at Griffiths Middle School and received the Outstanding Achievement Award from Mobile Oil Corporation.
Jennifer Williams, author of Art 2, is the Idaho Teacher of the Year (2002). She has twice been a semi- finalist to the National Teachers Hall of Fame, received the Horace Mann National Education Association Award for Teaching Excellence (2002), the Idaho Education Association Marsha Nakamura Teaching Excellence Award (2002), teacher of the year three times for her school district, the Idaho Art Teacher of the Year (2001), national finalist, the 1st place National Unsung Heroes Award (2000), the Governor's Award in the Arts for Idaho (2000). She has also been the US West Teacher of the Year for Idaho (1992), named as honorable mention in USA Today's 2004 All-USA Teacher Team, Woman of the Year, Who's Who among America's Teachers, and Outstanding Young Woman of America. She has taught high school Art for 32 years in Mountain Home and Nampa, Idaho. In addition, she has been an Adjunct Professor at Boise State University for a number of years and Albertson College, teaching art classes at all levels and supervising student teachers. She is the creator of "Project Van Go," an art outreach to rural schools. She has been actively involved in writing State Humanities Standards, speaking to the Legislature and teacher rallies on behalf of Education and as a representative for all children. Many of Jennifer's students have continued their education to become professional artists or art educators. Jennifer believes that art should be taken "beyond classroom walls" and into other curriculums, and shared in the community and beyond state lines.
Deborah S. Wilson, author ofGrade 1 Science, has taught first grade, second grade, sixth grade, K-6 Learning Disabilities and K-6 Remedial Reading. She holds a BS from Missouri State University in K-8 Elementary Education with a minor in Early Reading as well as an MS from MSU in Reading. Wilson has written numerous grants to get needed hands-on materials into her primary classroom. She has received numerous awards and grants that play a role to her belief that Hands-on/Minds-on learning contributes to increased reading and math scores. She has completed over 1,000 hours of professional development as she models her belief in the importance of being a lifelong learner. She is a NASA NEWEST Team member, a national judge for the Young Inventors, and helped write authentic Amazon Rainforest Curriculum from her personal explorations. As a small group state team member she helped develop grade level curriculum and train regional trainers and teachers to improve the science instruction within her state. In 1994 she received the Presidential Award for Elementary Math and Science. Serving on the National Science Teachers Association Pre-school and Elementary Committee and the Board for the Council of Elementary Science-International she organized many Elementary Extravaganza workshops enhancing the professional science learning opportunities for elementary teachers and emphasizing the importance of science in the primary grades.
Robert David Wright, author of Learn Logic, studied philosophy and logic at the University of Arizona, where he earned his degree. Robert also studied at the University of Maryland, Wichita State, and in Europe, where his concentration was on mathematics and languages. Robert has been writing professionally for more than 20 years and has taught logic to small groups as well as tutoring/mentoring individuals. In addition to writing on the subjects of philosophy and logic, he has written several essays, fiction novels, and screenplays. Naturally inquisitive about our world and universe, Robert continues to study, write, and teach logic and other subjects. His students have progressed to become honor students and earn scholastic recognition.
Jon Yeyna, author of Elementary Math – Level 4, has been teaching at Colton Joint Unified School District's Grant Elementary in Colton, California since 1999. In 2010, he was one of 38 individuals, businesses and organizations who were nominated for the annual San Bernardino County Education Medal of Honor because of his innovative style of teaching. He is a graduate from California State Polytechnic University in Pomona, California and received his Masters of Arts in Teaching from Grand Canyon University in Phoenix, Arizona. He has done numerous workshops and presentations that focus on his successful Four Step Language Math, a homework and teaching tool that helps all students develop a strong math foundation. He has also authored "A Science Fair Workbook-Step-by-Step Instructions on How to Plan and Write a Winning Science Fair Project".
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MINISTRY OF EDUCATION MALAYSIA
Inttegratted Curriicullum ffor Secondary Schoolls
In egra ed Curr cu um or Secondary Schoo s
SYLLABUS
SYLLABUS
MATHEMATICS
Curriculum Development Centre
Ministry of Education Malaysia
2004
PREFACE their proficiency in English; and thus make the learning of
mathematics more interesting and exciting.
Science and technology plays a critical role in realising Malaysia's The development of this Mathematics syllabus is the work of many
aspiration to become a developed nation. Since mathematics is individuals and experts in the field. On behalf of the Curriculum
instrumental in the development of scientific and technological Development Centre, I would like to express much gratitude and
knowledge, the provision of quality mathematics education from an appreciation to those who have contributed in one way or another
early age in the education process is thus important. The Malaysian towards this initiative.
school curriculum offers three mathematics education programs,
namely Mathematics for primary schools, Mathematics and Additional
Mathematics for secondary schools.
The Malaysian school mathematics curriculum aims to develop
mathematical knowledge, competency and inculcate positive attitudes
towards mathematics among pupils. Mathematics for secondary
schools provides opportunities for pupils to acquire mathematical
knowledge and skills, and develop higher order problem solving and
decision making skills to enable pupils to cope with daily life (MAHZAN BIN BAKAR SMP, AMP)
challenges. As with other subjects in the secondary school curriculum,
Director
Mathematics aims to inculcate noble values and love for the nation in
Curriculum Development Centre
the development of a holistic person, who in turn will be able to
Ministry of Education
contribute to the harmony and prosperity of the nation and its people.
Malaysia.
Beginning 2003, English is used as the medium of instruction for
Science and Mathematics subjects. The policy to change the medium
of instruction for Science and Mathematics subjects follows a phased
implementation schedule and is expected to be completed by 2008.
In the teaching and learning of Mathematics, the use of technology
especially ICT is greatly emphasised. Mathematics taught in English,
coupled with the use of ICT, provide greater opportunities for pupils to
improve their knowledge and skills in mathematics because of the
richness of resources and repositories of knowledge in English. Pupils
will be better able to interact with pupils from other countries, improve
RUKUNEGARA
DECLARATION
OUR NATION, MALAYSIA, being dedicated
• to achieving a greater unity of all her peoples;
• to maintaining a democratic way of life;
• to creating a just society in which the wealth of the nation Education in Malaysia is an ongoing effort
shall be equitably shared; towards further developing the potential of
• to ensuring a liberal approach to her rich and diverse individuals in a holistic and integrated
cultural traditions; manner so as to produce individuals who are
• to building a progressive society which shall be oriented intellectually, spiritually, emotionally and
to modern science and technology; physically balanced and harmonious, based
on a firm belief in God. Such an effort is
WE, her peoples, pledge our united efforts to attain these
ends guided by these principles: designed to produce Malaysian citizens who
are knowledgeable and competent, who
• BELIEF IN GOD
possess high moral standards, and who are
• LOYALTY TO KING AND COUNTRY responsible and capable of achieving a high
• UPHOLDING THE CONSTITUTION level of personal well-being as well as being
• RULE OF LAW able to contribute to the betterment of the
• GOOD BEHAVIOUR AND MORALITY family, the society and the nation at large.
INTRODUCTION The general Mathematics curriculum has often been seen to comprise
of discrete areas related to counting, measurement, geometry, algebra
A well-informed and knowledgeable society well versed in the use of and solving of problems. To avoid the areas to be continually seen as
mathematics to cope with daily life challenges is integral to realising separate and pupils acquiring concepts and skills in isolation,
the nation's aspiration to become an industrialised nation. Thus, efforts mathematics is linked to everyday life and experiences in and out of
are taken to ensure a society that assimilates mathematics into their school. Pupils will have the opportunity to apply mathematics in
daily lives. Pupils are nurtured from an early age with the skills to different contexts, and see the relevance of mathematics in daily life.
solve problems and communicate mathematically, to enable them to
make effective decisions. In giving opinions and solving problems either orally or in writing,
pupils are guided in the correct usage of language and mathematics
Mathematics is essential in preparing a workforce capable of meeting registers. Pupils are trained to select information presented in
the demands of a progressive nation. As such, this field assumes its mathematical and non-mathematical language; interpret and represent
role as the driving force behind various developments in science and information in tables, graphs, diagrams, equations or inequalities; and
technology. In line with the nation's objective to create a knowledge- subsequently present information clearly and precisely, without any
based economy, the skills of Research & Development in mathematics deviation from the original meaning.
is nurtured and developed at school level.
Technology in education supports the mastery and achievement of the
As a field of study, Mathematics trains the mind to think logically and desired learning outcomes. Technology used in the teaching and
systematically in solving problems and making decisions. This learning of Mathematics, for example calculators, are to be regarded as
discipline encourages meaningful learning and challenges the mind, tools to enhance the teaching and learning process and not to replace
and hence contributes to the holistic development of the individual. To teachers.
this end, strategies to solve problems are widely used in the teaching
and learning of mathematics. The development of mathematical Importance is also placed on the appreciation of the inherent beauty of
reasoning is believed to be closely linked to the intellectual mathematics. Acquainting pupils with the life-history of well-known
development and communication ability of pupils. Hence, mathematics mathematicians or events, the information of which is easily available
reasoning skills are also incorporated in the mathematics activities to from the Internet for example, will go a long way in motivating pupils
enable pupils to recognize, build and evaluate mathematics conjectures to appreciate mathematics.
and statements.
The intrinsic values of mathematics namely thinking systematically,
In keeping with the National Education Philosophy, the Mathematics accurately, thoroughly, diligently and with confidence, infused
curriculum provides opportunities to pupils from various backgrounds throughout the teaching and learning process; contribute to the
and levels of abilities to acquire mathematical skills and knowledge. moulding of character and the inculcation of positive attitudes towards
Pupils are then able to seek relevant information, and be creative in mathematics. Together with these, moral values are also introduced in
formulating alternatives and solutions when faced with challenges. context throughout the teaching and learning of mathematics.
Assessment, in the form of tests and examinations helps to gauge • representing and interpreting data;
pupils' achievement. The use of good assessment data from a variety
of sources also provides valuable information on the development and • recognising and representing relationship mathematically;
progress of pupils. On-going assessment built into the daily lessons • using algorithm and relationship;
allows the identification of pupils' strengths and weaknesses, and
effectiveness of the instructional activities. Information gained from • solving problems; and
responses to questions, group work results, and homework helps in • making decisions.
improving the teaching process, and hence enables the provision of
effectively aimed lessons. 4 communicate mathematically;
5 apply knowledge and skills of mathematics in solving problems
AIM and making decisions;
6 relate mathematics with other areas of knowledge;
The mathematics curriculum for secondary schools aims to develop
individuals who are able to think mathematically, and apply 7 use suitable technologies in concept building, acquiring skills,
mathematical knowledge effectively and responsibly in solving solving problems and exploring the field of mathematics;
problems and making decisions; and face the challenges in everyday
8 acquire mathematical knowledge and develop skills effectively
life brought about by the advancement of science and technology.
and use them responsibly;
9 inculcate a positive attitude towards mathematics; and
OBJECTIVES 10 appreciate the importance and beauty of mathematics.
The mathematics curriculum for the secondary school enables pupils
to:
1 understand definitions, concepts, laws, principles, and theorems CONTENT ORGANISATION
related to Number, Shape and Space, and Relationship; The content of the curriculum is presented in three areas that are
2 widen the use of basic operations of addition, subtraction, interrelated, that is, NUMBER, SHAPE and SPACE, and
multiplication and division related to Number, Shape and Space, RELATIONSHIP. In everyday situations, an individual generally
and Relationship; needs the following:
3 acquire basic mathematical skills such as: • knowledge and skills related to numbers such as counting and
computing (NUMBER);
• making estimation and rounding;
• knowledge and skills related to shapes and space such as
• measuring and constructing; recognising the properties of shapes and working with
• collecting and handling data; measurements (SHAPE and SPACE);
• knowledge and skills related to patterns, rules, general 1. NUMBER
principles, laws, relations and others for the purpose of
recognising and understanding relationships involving The understanding of numbers enables pupils to make calculations and
numbers and shape (RELATIONSHIP) estimates, and analyse and solve related problems. This area is a
continuation of the primary school mathematics curriculum. The scope
The teaching and learning of mathematics put emphasis on the of this area is as follows:
understanding of concepts and the mastery of skills in the three areas
stated above, as well as the use of mathematics to solve problems in
various situations. As such, the following areas require attention during 1.1 Whole Numbers
the teaching and learning process: (a) Place value of digits in whole numbers.
(b) Rounding whole numbers.
• development of problem solving skills that involves four main (c) Addition, subtraction, multiplication and
steps namely interpreting the problem, planning the strategy, division involving whole numbers.
carrying out the strategy, and reflecting on the solution
obtained so that pupils can effectively solve problems in daily 1.2 Fractions
life; (a) Equivalent fractions.
(b) Proper and improper fractions.
• development of logical, systematic and creative thinking skills (c) Mixed numbers.
together with reasoning skills so as to produce an individual (d) Addition, subtraction, multiplication and
who is able to think logically and rationally; and division involving fractions.
• inculcation of the intrinsic value of mathematics and the values 1.3 Decimals
of Malaysian society which include being systematic, accurate, (a) Conversion of decimals to fractions and vice
diligent, confident, not wasteful, moderate and cooperative, all versa.
of which contribute towards becoming a responsible citizen. (b) Place value of digits in decimals.
(c) Rounding decimals.
(d) Addition, subtraction, multiplication and
CONTENT division involving decimals.
This section outlines the important elements in each area, namely
NUMBER, SHAPE and SPACE, and RELATIONSHIP followed by a 1.4 Percentages
list of topics that defines the scope for each area. (a) Percentage and symbol.
(b) Increase and decrease of a certain quantity in
terms of percentage.
(c) The use of percentages in comparison.
1.5 Negative Numbers 2. SHAPE and SPACE
(a) The + and − signs in numbers.
(b) Integers. Shape and space is an important component in the secondary school
(c) Negative fractions and negative decimals. mathematics curriculum. Knowledge and skills in this area and their
(d) Addition, subtraction, multiplication and application in related topics is useful in everyday life. Improving
division involving negative and positive understanding in this area helps pupils to effectively solve problems in
numbers. geometry. At the same time, pupils can also improve their visual skills
and appreciate the aesthetic value of shapes and space. The scope is as
1.6 Multiples and Factors follows:
(a) Prime numbers.
(b) Multiples.
(c) Common multiples and the lowest common 2.1 Basic Measurements
multiple. (a) Length.
(d) Factors and prime factors. (b) Mass.
(e) Common factors and the highest common factor. (c) Time.
1.7 Squares, Square Roots, Cubes and Cube Roots 2.2 Lines and Angles
(a) Squares. (a) Angles.
(b) Square roots. (b) Unit of measurement of angles.
(c) Cubes. (c) Types of angles.
(d) Cube roots. (d) Intersecting lines.
(e) Properties of angles related to intersecting lines.
1.8 Standard Form (f) Parallel lines.
(a) Significant figures. (g) Properties of angles related to parallel lines.
(b) Numbers in standard form.
(c) Addition, subtraction, multiplication and 2.3 Polygons
division involving numbers in standard form. (a) Types of polygons.
(b) Line symmetry.
1.9 Number Bases (c) Types of triangles.
(a) Numbers in base 2, 5 and 8. (d) Properties of angles related to triangles.
(b) Place value of digits in numbers in base 2, 5 and (e) Types of quadrilaterals.
8. (f) Properties of angles related to quadrilaterals.
(c) Conversion of numbers in base 2, 5, 8 and 10 (g) Regular polygons.
from one base to another. (h) Properties of angles related to regular polygons.
2.4 Perimeter and Area 2.9 Pythagoras' Theorem
(a) Perimeter. (a) Pythagoras' theorem.
(b) Area of triangles and quadrilaterals. (b) Converse of the Pythagoras' theorem.
2.5 Geometrical Construction 2.10 Trigonometry
(a) Construction of a line segment, a triangle, a (a) Measurement of angles in degrees and minutes.
perpendicular bisector, a perpendicular to a line, (b) Sine, cosine and tangent of an angle.
an angle, an angle bisector, parallel lines and a (c) Solution of triangles (based on the solution of
parallelogram. right-angled triangles)
(b) Scale drawing.
2.11 Bearings
2.6 Loci in Two Dimensions (a) Compass directions.
(a) Locus of a moving point satisfying a condition. (b) Bearings.
(b) Two-dimensional locus of a point satisfying
more than one condition. 2.12 Angle of Elevation and Angle of Depression
(a) Angle of elevation.
2.7 Circles (b) Angle of depression.
(a) The circle and its parts.
(b) Circumference and arc length. 2.13 Lines and Planes in Three Dimensions
(c) Area of a circle and area of a sector. (a) Normal to a plane and the projection of a line
(d) Properties of angles related to circles and cyclic onto a plane.
quadrilaterals. (b) Angle between a line and a plane.
(e) Tangents to a circle. (c) Angle between two intersecting planes.
(f) Properties of angles related to tangents to a
circle. 2.14 Plan and Elevation
(g) Common tangents to circles. (a) Orthogonal Projections.
(b) Plans of solids.
2.8 Geometric Solids (c) Front and side elevations of solids.
(a) Types of geometric solids.
(b) Nets. 2.15 Earth as a Sphere
(c) Surface area of geometric solids. (a) Longitudes and latitudes.
(d) Volume. (b) Distance along a meridian and along a parallel
of latitude.
(c) Shortest distance on the earth's surface.
(d) Nautical mile and knot.
2.16 Transformation 3.3 Algebraic Formulae
(a) Types of transformations − translation, (a) Variables and their representations by letters of
reflection, rotation and enlargement. the alphabet.
(b) Isometry and congruence. (b) Algebraic formulae.
(c) Similar shapes. (c) Subject of a formula.
(d) Combination of transformations.
3.4 Linear Equations
(a) Linear equations in one unknown.
3. RELATIONSHIP (b) Simultaneous linear equations in two unknowns.
The relationships between several quantities can often be found in 3.5 Linear Inequalities
daily life. Therefore, the handling of relationships such as recognizing (a) The symbols <, <, > and >.
a formula or a law and making generalisations of a situation becomes a (b) Linear inequalities in one unknown.
basic necessity. A relationship can be expressed in the form of a table, (c) Simultaneous linear equations in one unknown.
a graph, a formula, an equation or an inequality. The expression of the
relationship in these forms becomes useful and an effective tool in 3.6 Quadratic Expressions and Equations
problem solving and communication. The scope of learning is as (a) The expression ax2 + bx + c.
follows: (b) Factorisation of a quadratic expression.
3.1 Indices (c) Quadratic equations.
(a) Introduction to indices.
(b) The laws of indices. 3.7 Coordinates
(a) The Cartesian coordinate system.
3.2 Algebraic Expressions (b) Distance between two points.
(a) Representation of unknown by a letter of the (c) Mid-point between two points.
alphabet.
(b) Addition, subtraction, multiplication and 3.8 The Straight Line
division involving algebraic terms. (a) The gradient of a straight line.
(c) Algebraic expressions. (b) The intercepts on the x-axis and the y-axis.
(d) Addition and subtraction involving algebraic (c) The equation of a straight line y = mx + c.
expressions. (d) Parallel straight lines.
(e) Expansion and factorisation.
3.9 Graphs of Functions
(f) Algebraic fractions.
(a) Functions.
(g) Addition, subtraction, multiplication and
(b) Graphs of functions.
division involving algebraic fractions.
(c) The solution of an equation by graphical 3.15 Mathematical Reasoning
method. (a) Introduction to logic.
(d) The region representing an inequality in two (b) Statements.
variables. (c) Quantifiers - "all", "some".
(d) Operations on statements - "and", "or", "not".
3.10 Gradient and the Area under a Graph (e) Implications - "if", "if and only if".
(a) Quantity represented by the gradient of a graph. (f) Arguments - syllogism, modus ponens and
(b) Quantity represented by the area under a graph. modus tollens.
(g) Deduction and induction.
3.11 Ratios and Proportions
(a) The ratio of two quantities. 3.16 Statistics
(b) The ratio of three quantities. (a) Collection of data.
(c) Direct proportion. (b) Frequency, frequency tables and class intervals.
(d) Rate. (c) Pictograph, bar chart, pie chart and line graph.
(d) Histogram and frequency polygon.
3.12 Variations (e) Cumulative frequency and the ogive.
(a) Direct variation. (f) Measures of central tendency: mode, mean and
(b) Inverse variation. median.
(c) Joint variation. (g) Measures of dispersion: range and inter-quartile
range.
3.13 Matrices
(a) Introduction to matrices. 3.17 Probability
(b) Equal matrices. (a) Sample spaces.
(c) Addition, subtraction and multiplication (b) Events.
involving matrices. (c) The probability of an event.
(d) The 2 × 2 identity matrix. (d) The probability of complementary events.
(e) The 2 × 2 inverse matrix. (e) Combined events.
(f) Solution of simultaneous linear equations in two (f) The probability of combined events.
unknowns by the matrix method.
3.14 Sets
(a) Introduction to sets.
(b) Equal sets, the empty set, subsets, the universal
set and the complement of a set.
(c) Operations on | 677.169 | 1 |
after its initial publication, this volume continues to rank among the field's most-cited references. One of the largest and finest available collections, the catalog covers general properties of curves and types of derived curves. The curves and the values of their parameters are illustrated by nearly 90 images from a CalComp digital incremental plotter. Suitable for students and researchers in geometry and computer science, the text begins by introducing general properties of curves and types of derived curves. Subsequent chapters apply these properties to conics and polynomials, cubic and quartic curves, algebraic curves of high degree, and transcendental curves. A total of more than 60 special curves are featured, each illustrated with one or more CalComp plots containing curves in up to eight different variants. Indexes provide tables of derived curves, curve names, and a 95-item guide to further reading | 677.169 | 1 |
COURSE FACILITATOR
Mrs Kumar has taught Mathematics for 2 decades! Her wealth of experience in teaching & her fun n lively personality will make learning a worthy & meaningful experience! Very difficult concepts are made easier with great clarity! What's more....she has made learning affordable at a relatively lower cost!
PROGRAMME For Day 1 & 2
Day
Topic s Covered
Details
Day 1
Indices & Surds
üTesting the Laws of Indices & its relevance to everyday maths
üApplication of surds using =,=
üWhat is meant by conjugate surds to rationalize the surd
üSolve simple equations involving indices & surds.
üApply the rules of indices to simple problems.
üSolve exponential equations of the form ax= b where b = an
üSolve exponential equations using substitutions.
Quadratic Expressions
and Equations
üWhat is meant by roots and how it is interpreted in graphs
üUse of Discriminant (b2-4ac) to find if equation has roots
üDetermining the turning point using completing the squares
üSolving complex problem sums
Logarithm
üUsing the laws of Logarithm to solve complex problem sums
üUnderstanding the logarithmic principles and being able to solve complex problem sums
üExponentials functions & its relevance to logarithmic functions
üPlotting lg & ex curves with confidence
Day 2
Remainder & Factor Theorem
üThe difference between Factor & Remainder Theorem.
üSolving cubic equations by factorization.
ü
Partial Fractions
üExpress a rational expression in partial fractions
üApplication of Partial Fractions
Linear Law
üExpressinga relationship in the linear form Y = mX + c
üPlottingan appropriate straight line and to find the values of m and c | 677.169 | 1 |
Professional Commentary: Students construct charts to examine number patterns and use these patterns to generate a graph. The story of Tortisha and Harry is presented to the class: Harry is so sure that he can run faster than Tortisha, that he will give her a 2 mile head start in a race....
Professional Commentary: Students use matrices and technology to solve the Meadows or Malls problem, a linear programming problem with six variables. Students who have not done linear programming problems before are advised to begin with The Busing Problem before attempting Meadows or Malls....
Professional Commentary: This activity focuses on having students create and solve systems of linear equations in real-world settings. By solving a system of two equations in two unknowns, students find the equilibrium point for supply and demand....
Professional Commentary: Students solve two linear programming problems. The first one, Researching Research Papers, involves three variables; the second, The Busing Problem, involves four variables Students will find tutorials, Java applets, drills, computer programs, quizzes, and LiveMath notebooks and animations on a variety of precalculus topics. More than 100 subsections of the site address polynomial, rational, exponential, trigonometric, and logarithmic functions, as well as piecewise definitions, parametric equations, and polar coordinates.... | 677.169 | 1 |
An English-Vietnamese math dictionary for Vietnamese high school and college students is presented. The dictionary was developed for students within the Vietnamese-speaking refugee community in Australia, many of whom are advanced in mathematics but are held back by their unfamiliarity with English terminology. The first column in the dictionary gives the English term; the second column its Vietnamese equivalent; and the third column describes and explains each term in Vietnamese. The first column is arranged in alphabetical order rather than under a general heading (i.e., inscribed angle and obtuse angle are alphabetically listed rather than under the general heading 'angle'). Where Vietnamese words of similar meaning correspond to the same English word, the Vietnamese words are separated by commas, and when an English word has more than one meaning in Vietnamese, these meanings are numbered. Cross references are also included, and a table of mathematical symbols is appended. (SW) | 677.169 | 1 |
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About AMC
The MAA American Mathematics Competitions (MAA AMC)
The MAA American Mathematics Competitions (MAA AMC) is dedicated to the goal of strengthening the mathematical capabilities of our nation's youth. We believe that one way to meet this goal is to identify, recognize, and reward excellence in mathematics through a series of national contests called the:
For over 60 years many excellent exams have been prepared by individuals throughout our mathematical community in the hope that all secondary students will have an opportunity to participate in these problem solving and enriching mathematics experiences. The MAA AMC contests are designed to engage students and teachers in effective mathematical problem-solving that are consistent with curricular goals, and prepare students for future mathematical success.
In addition to the 5 contests listed above, we also have an invitation-only summer program, at which we choose the final six contestants for an international competition:
For a calendar of current contest dates, please visit and bookmark our calendar.
Historical Beginning
On Thursday, May 11, 1950 the first Mathematical Contest, sponsored by the New York Metropolitan Section of the Mathematics Association of America (MAA) took place. It was given in approximately 238 schools to around 6,000 students in the New York area only. The following exerpt is taken from the Report of the Committee addressed to that year's participating teachers:
The first mathematics contest sponsored by the New York Metropolitan Section of the MAA is now history. It was a lot of work getting the contest organized and finally holding it. Like all new projects, we worried about it. Would the High Schools participate? Would they like the test? Is it worth while? Will any good be produced by it? Will it be a success?
Today
Over 60 years and three generations later we can answer all of the Committee's questions with a resounding Yes! Yes! Yes! The overall success of this program can be viewed by simply looking at our growth in numbers. Each year over 350,000 students in roughly 6000 schools participated in the MAA AMC Contests. Of these, 10,000 students qualify each year to participate in the AIME scheduled for late March/early April. From this group approximately 500 students will be invited to take the prestigous USAMO in early May.
MAA is proud to be able to provide the opportunity for students, together with their teachers, to engage in high-quality mathematical problem-solving. The American Mathematics Competition sets the standard for preparing today's students for succeeding in mathematics in postsecondary education and carreers. We're truly preparing today's students to solve tomorrow's challenges. | 677.169 | 1 |
Check the
INFO
posted on the webpage of the Instructor in Charge about the final exam.
Read the relevant sections of Stewart's textbook: note that the
webpage with my scanned lecture notes
also indicates the pages in the
textbook corresponding to each topic.
Also, the examples in the book are different than the ones
that we covered in class, so you might want to take a look at both the
book and the lecture notes for a diverse source of examples.
The best way for you to prepare for the final exam is to do one or
more rehearsals: print a past final exam and solve it!
Maybe the hint will give you the initial push that you need to
complete the answer to the question without looking at the full
solution!
You will make the most value out of the past exams if you solve the
questions yourself, or at least try to do so before you look at the
solutions. This is the best way to come in terms with your strengths and
weaknesses, also it is very instructive to make a mistake during
rehearsal and recognizing it, and then not making the same mistake again on the
real final exam.
Some advice on which questions from the past exams you should IGNORE
(because the course material keeps on changing over the years) can be found on
this webpage with the Sample Final Exams , created by the Instructor in Charge.
Remember that at least 2/3 of the questions on the final exam will
be similar to
homework problems,
including WEBWORK and
SUGGESTED HOMEWORK problems.
Log in to the Piazza page of our MATH 101 class
here to discuss
your questions regarding the final exam. | 677.169 | 1 |
Algebra and Trigonometry - 3rd edition
Summary: This best selling author team explains concepts simply and clearly, without glossing over difficult points. Problem solving and mathematical modeling are introduced early and reinforced throughout, providing students with a solid foundation in the principles of mathematical thinking. Comprehensive and evenly paced, the book provides complete coverage of the function concept, and integrates a significant amount of graphing calculator material to help students develop insight into math...show moreematical ideas. The authors' attention to detail and clarity, the same as found in James Stewart's market-leading Calculus text, is what makes this text the market leader149151174.31 | 677.169 | 1 |
Algebra 1
Algebra 1 can seem like a big step from the concrete world into abstracts. This can bamboozle many students - but it's not that hard... There are really simple and quick ways to make this a seamless and EASY process. 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
Algebra 2 kicks in with much more powerful analysis tools to describe and evaluate real-life situations in hundreds of scientific disciplines. It is a must for those following the sciences - but can intimidate if the core concepts aren't fully mastered. Getting a solid grounding in core concepts is the key to turning Algebra 2 from a scary snake into an inoffensive (but very useful) worm.
Calculus
Calculus is where math really brings years of preparation into fine focus and offers powerful ways of resolving extremely complex problems - easily and quickly. Many students are unecessarily scared of calculus. Don...
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General Computer
I was really lucky to find a fabulous computer teacher in the 90's. He taught me how to knock down and rebuild a computer and all the fancy stuff that software could do. I was then on PC's and stuck there for years. Most Remember that the secret is NOT...
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Geometry
Geometry can seem daunting because you "have to" memorize so many theorems. But, in reality, if you break each theorem down into common sense (often with a quick sketch) then a hazy notion or idea can turn into a clear understanding instantly.
Microsoft Word
Physics
Physics is a fascinating subject and universally useful. But, it can seem daunting at first. The secret is to keep your cool and get clear explanations of the concepts. Once this is down and mastered you'll see that you can do it too!
Prealgebra
Most students struggle with Algebra because they haven't gotten their minds around the notion of strange variables like "x".
This barrier can be broken down in minutes with a common sense explanation.
Algebraic math is a major stepping stone to multiple sciences and must be mastered to facilitate future academic progress in the sciences.
Precalculus
Trigonometry
Trigonometry is basically the mathematical measurement of shapes and the angles that form them. Terms like tangents, sines, and cosines - are concepts that must be mastered in order to move forward. As Read More
Portuguese
Portuguese shares common roots from the Latin. English anything else. Once the "mechanics" of the structure are mastered it's a simple matter to build vocabulary and add on words and phrases. The speed of learning can...
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Statistics
Statistics deals with gathering, organizing, analyzing, and interpreting events and measurement of data that have been recorded.
It shows how meaningful conclusions can be drawn quickly from large amounts of data that might appear confusing.
Statistics makes sense of large amounts of data with meaningful conclusions.
TOEFL
Teaching of English as a Foreign Language is a particular skill when it is applied to adults. A mother tongue is a powerful part of our psyche and can be used to facilitate, or hinder, assimilating a new language. Children, by nature, do not have this potential barrier. A fast and successful learning curve can be obtained for adult students when constructive comparisons are made with the essential structure of the mother tongue and target language. When essential structures,...
Read More
Probability
Probability is the calculation of the likelihood of something happening, or not. If it is certain, then it gets a 1, meaning 100% certain. If it is impossible, then it gets a zero.
This branch of math has applications in a myriad of life and work situations, like insurance, financial decisions, business strategies, and even gambling - they all use probability calculations to make them viable.
Phonics
Phonics is the art of translating vowel sequences into long or short sounds. Long sounds can be equated to the sounds of the alphabetic vowels, a, e, i, o, u. The short sounds, are like, cat, get, bit, cot, and cut. Most I have used phonics...
Read More
ESL/ESOL
I lived in Brazil for 30 years and had a school teaching English to executives in multinational companies.
We developed an easy system to show how English works.
English is very different from Spanish and Portuguese. Understanding the differences helps you to see HOW to speak English.
We know how hard English can be for people from other countries.
queremos ayudarle a aprender rápido y fácil
hasta luego,
ate logo
Differential Equations
I have experience tutoring differential and integralcalculus with another tutoring service for 3+ years. This encompasses the study of differential equations. The students have all been 11th and 12th grade in various schools around Gwinnett county in Georgia.
Some functions can be more complex and require powerful ways to find their differentials, (which can also be called "prime" of a function). Examples are: The Chain Rule which resolves prime of f(g(x)) into f'(g(x))...
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Public Speaking
Many say they would rather die than speak in public - but it is easy with practice and knowledge. I first learned with Toastmasters Club. We would meet once a week and each of us would make a brief presentation on our week and the week to come. Practice makes perfect! There are many helpful techniques, like voice projection, for example which allow for good clear diction without forcing the vocal chords - scanning the audience as if in a conversation - doing mouth relaxation before to soften facial...
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Career Development
As a graduate engineer, entered multinationals via steel manufacture (England) and then auto parts (US Steel, Brazil). From there moved into hospital products (Johnson & Johnson Brazil) and on into self employment. Taught Career Development in Technical Colleges (resume building, interview techniques, behavior, anger management, office technology, etc). Great experience in change management and its impact on careers.
Experience as a technical person in manufacture, engineering management,...
Read More
Macintosh
I learned Microsoft Windows in the mid 1980's with a great teacher, but, it didn't take long to discover that Windows really is a massive bandage covered in band-aids! Just look at the volumes of updates they put out constantly to "fix" issues.
Two years ago, I finally made it to my MacBook and they say, "Once on a Mac - Never Go Back!
It takes a little while to adjust to Mac's interface. That's where I can help you.
Education
Has made a good connection with my child. —
This tutor goes out of his way to meet the student on their level. Finding out what their needs are and how he can reach them best. His use of technology with the on-line sessions appeals well to my technology savy teenager, but even these sessions are conducted in such a way as to give the student the personal touch they need. Having the ability to fit in lessons when both parties are available ...
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Week-Long Math Courses
1 - Meaningful Algebra using Technology
Visual Algebra is a free research-based software platform which supports students from the early years of algebra learning to build solid foundations for their algebraic thinking and their manipulative skills. Built using TI-Nspire, but freely accessible online as well as on handheld and computer, this is a rich and powerful learning environment that offers students scaffolded support in using a range of computer-based tools and representations. Explore the ways in which this tool can change your algebra classroom at any level - and bring along your iPad or Android tablet!
2 - History of Mathematics: Algebra, Analytic Geometry and Calculus
Leader: Jeff Ibbotson, Phillips Exeter Academy, Exeter, NH
We will explore the invention of complex numbers, the soap opera behind the solution to the general cubic polynomial equation, the invention of analytic geometry and early aspects of the calculus. Fermat, Descartes, Cardano, Kepler and many other famous mathematicians will "join" us for chats on their life and times. If you are teaching precalculus or calculus and want to know some of the history behind the mathematics (and see some real lesser known "nuggets" of mathematics), this course is for you!
3 - Just A Bunch of Good Geometry Labs
Leader: Dan Butler, Mounds View High School, Arden Hills, MN
By the time students get to precalculus, a great deal of their geometry know-how has gone the way of the slide rule. Let's bring some excitement back into geometry through great problems and great explorations, and rediscover how geometry really lies at the heart of mathematics.
4 - Just Five Good Precalculus Labs
Leader: Dan Butler, Mounds View High School, Arden Hills, MN
Let's spice up our precalculus curriculum with some amazing labs. We will use Excel, the Geometer's Sketchpad, Geogebra, the TI-84, hands-on materials and anything else we decide to use to explore some of the concepts of precalculus through great problems and interesting constructions. We will also take some time to discuss what needs to be in a precalculus course in light of the current state mathematics education.
5 - The High School Classroom in the 21st Century
While graphing calculators are not new to mathematics education, the ability to network them makes them even more valuable. In this course, participants will work with the TI-Nspire CX calculator (on loan) and TI Navigator to examine a series of problems from algebra, geometry, advanced algebra, and trigonometry. Participants will work with Vernier probes - temperature, motion, and microphone - to collect and analyze data. The TI Navigator wirelessly networks each student's calculator to a teacher computer allowing teachers to track progress, view student work, and provide instant feedback.
6 - GeoGebra for Beginners
Learn how to use GeoGebra 4.2, a free and open source dynamic mathematics software program. GeoGebra is very easy to use, with a point and click interface. You and your students can quickly create interactive applets that illustrate concepts in all of the major high school mathematics curriculum areas - geometry, algebra, and calculus. This course will be geared towards users with no prior experience with GeoGebra, but participants who would like a refresher in the basics are also welcome. You will spend most of your time in this course building applets for use with your classes.
7 - GeoGebra - How to Use it in Precalculus and Calculus
This course will focus on GeoGebra 4.2 in precalculus/calculus but will quickly cover some geometric constructions early in the week. GeoGebra is a free program that can perform geometric constructions, graph functions, create sliders, find derivatives and integrals and change everything dynamically. GeoGebra 4.2 has CAS (new) and enhanced statistics. Learn how to create html files that will be available to anyone with a browser. Participants can bring a laptop or use a provided classroom computer. Most of the class time will be spent creating GeoGebra applets which will be shared with all.
8 - Greatest Hits of Higher Mathematics
Leader: Diana Davis, Brown University, Providence, RI
This course will explore the most fascinating parts of the undergraduate math major or math graduate school curriculum: real analysis, algebra, topology, and number theory, each for one class period. The goal of the course is to dig into interesting problems, and think deeply about the nature of shapes and numbers. Only high school mathematics is required!
9 - Math Research
Leader: Diana Davis, Brown University, Providence, RI
In this course, we will do math research: We will work on solving a problem that no one knows the answer to, or stated differently, on understanding a system that no one else understands yet. It will be a geometric problem about a beam of light bouncing around in various tilings of the plane (contact me for specifics). Tools we may use include pencil and paper, computer programs, and group collaboration. We will write our results into a paper. No background is necessary, except for an inquiring and analytical mind!
10 - Moving Forward with Problem-Based Learning
Leader: Carmel Schettino, Deerfield Academy, Deerfield, MA
This is a great course for teachers who are interested in first-time learning how to integrate problem-based learning into their curriculum. Participants will discuss pedagogy, theory and student instruction using sample PBL problems from the classroom. Teachers will simulate the student process of discussion and use of prior knowledge through geometry, algebra, and trigonometry problems. Learn how to focus your class on student ideas, discourse, and reflection through problem solving while supporting student engagement and empowerment. Come get inspired to implement PBL in your classroom!
11 - Learning Mathematics through Problem Solving - Active Involvement for All Students
Traditional mathematics lessons tend to be teacher-centered and targeted towards the average student. This course will provide strategies for actively engaging students of all abilities through the use of problems that allow multiple access points. The course will also have a focus on the use of differentiated instruction. Participants will explore a selection of rich problems that can be used in conjunction with a variety of curricula.
12 - Astronomy and Precalculus - A Match Made in the Heavens
Where and when do you look for the moon? Can we model the motion of that "star?" Will that asteroid hit? How was the Earth's position in space determined over 2,500 years ago? Want to go to Mars? There's prep to every trip! This class will explore these and other ideas. Why? Because they get students' attention! I've tried everything from temperature, to tides, to Ferris Wheels, and overall, the response was lackluster. Then I started using astronomical ideas and things changed. No more inputting arrays of data and forcing out context, rather, we observe and model!
13 - Physics For Mathematics Teachers
Participants will gain a conceptual understanding of the physics used in the secondary-school mathematics curriculum. We'll study concepts and problem solving, without laboratories. If you had physics a long time ago and remember little to nothing or have never had a physics class, this is for you! Stress level for this class is rated as ZERO! Topics include: measurement and uncertainty, dimensional analysis, kinematics (motion) in one and two dimensions, dynamics (forces) and circular motion will be covered in depth. Work, energy, and momentum will be covered, if time permits.
14 - The Geometry of Origami
Leader: Philip Mallinson, Phillips Exeter Academy, Exeter, NH
This workshop is about using paper folding to illustrate mathematical ideas and using mathematical ideas to explain origami phenomena. We will explore limits, how to construct regular polygons both approximately and exactly, when paper can be folded flat and how to divide a segment into an arbitrary number of equal parts. We will see that the axioms of origami are richer than Euclid's and they will enable us to trisect angles and solve cubic equations. We will explore folding polygons into polyhedra and the inverse problem of unfolding polyhedra to polygons.
15 - Challenging the Mathematically Challenged (and others)
Many of the students we teach find it difficult to grasp mathematical concepts at the level of abstraction expected. They see no relevance in what they are asked to do and are unwilling to learn mathematical processes in an isolated and unrelated context. Despite this, these students can solve problems. Participants will work with existing activities as well as create their own activities using standard software packages and Internet access. Previous participants have found it useful to work in groups and have created activities for the full range of student abilities and grade levels.
16 - Mathematical Activities that Build from Year to Year
This workshop allows participants to start with a series of simple, concrete activities and use them as building blocks to extend to more sophisticated concepts as students' knowledge and skills progress from middle school to high school. The activities are great for use on the TI-84, but even better on the TI-Nspire and CAS TI-Nspire. In addition to these activities, participants will have an opportunity to use the latest Navigator software and assess its potential gains for use in the classroom.
17 - Integrating Mathematics and English! Seriously!
This workshop allows participants to integrate English and mathematics in a problem solving and decision making environment by examining the English material through a mathematical lens. Despite being accessible by middle school students, the level of mathematics involved is far from trivial and includes combinatorial mathematics, exponentials, sequences, geometry and trigonometry to name just a few. Participants will be encouraged to explore these samples with a view to creating new examples for their own classroom use.
18 - Using the iPad to Enrich and Revolutionize the Teaching and Learning of Mathematics
We will examine the numerous ways in which iPad applications can be used by students to deepen their understanding of mathematics; make their own discoveries; use digital content such as photos, videos, newspaper articles and e-books to explore their own mathematical questions about our world; create, share and discuss solutions to mathematics problems; and experience mathematics in a dynamic environment that fosters innovation and creativity. Participants must bring their own iPad 2 or 3.
19 - Geometry 2013
Leader: Jonathan Choate, Groton School, Groton, MA
Using numerous technologies, the traditional geometry course can be greatly enriched. Participants will learn how to use two- and three-dimensional geometric construction packages, the Internet and spreadsheets to teach topics in new ways. Manipulatives, such as Jovos, and Zometools, will be used to supplement the teaching of non-traditional topics. Participants will see a variety of problems that can be used to motivate important geometric concepts, as well as a collection of elegant proofs.
Using technology and physical models, all high school students can explore and understand topics covered in a calculus course without actually knowing any calculus. This focus can lead to students having a more meaningful experience in their algebra, geometry and pre-calculus courses. We will work through activities related to topics such as the fundamental notion of change, max-min problems, related rate problems, and arc length. This course will be of interest to teachers looking for activities and projects that are engaging and designed to deepen students' understanding of mathematics.
21 - Introduction to Complex Systems I
Leader: Maria Hernandez, The North Carolina School of Science and Mathematics, Durham, NC
In the past 20 years, the study of complex systems has revived such mathematical topics as fractals and chaos and linked these topics to various sciences. We will use matrices, trigonometry, and multiple reduction copy machines to create fractals and learn about iterating both real-valued and complex-valued functions, eventually leading to the Mandelbrot set. These fascinating topics can be used to enhance a precalculus or calculus course or can serve as a basis for a stand-alone course in complex systems along with the topics studied in Introduction to Complex Systems II.
22 - Using Mathematics To Analyze Issues of Social Justice
Leader: Ken Collins, Charlotte Latin School, Charlotte, NC
This course focuses on how we can integrate social, political, and economic justice issues (fair voting, prison rates, pollution, affordable housing, military recruitment patterns) into our mathematics classes. We will discuss how to explore mathematical topics from a social justice perspective while making sure that the work is mathematically rigorous. Help our students recognize the power of mathematics as an analytical tool to understand and change their world, to deepen their understanding of social and economic issues, and to develop their own power to help build a democratic society.
23 - Great Simulations for Teaching Statistical Concepts
Leader: Julie Graves, North Carolina School of Science and Mathematics, Durham, NC Co-Leader: Floyd Bullard The North Carolina School of Science and Mathematics, Durham, NC
The best way to teach many statistical concepts is to have students see principles in action. In this hands-on course, participants will engage in classroom simulations that explore hypothesis testing, confidence intervals, power, the t-distribution family, and other difficult topics. Most of the simulations will use manipulatives, and some the TI-84. All topics are part of the AP Statistics curriculum.
24 - Technology Labs to Enliven Statistics
Leader: Kyle Barriger, Castilleja School, Palo Alto, CA
All students need a fundamental statistical education. This workshop will look at five technology labs that we use with our students to teach them how to work with real data using statistical analysis software (JMP from SAS). These labs are an integral part of the data analysis unit that all students take as part of their algebra 2 course. We will also look at the structure of this data analysis unit and the data used along with the technology skills that the students are taught.
25 - A Student-centered, Problem-based Approach to Algebra I
Leader: Karen Geary, Phillips Exeter Academy, Exeter, NH
Participants will use the Exeter Math 1 materials to explore ways we can toss out the standard textbook, to use problem-solving and a discussion format to build content with students, rather than for them. Using accessible and contextual problems, we can empower students to discover, develop, and apply general principles and transferrable techniques. The problems will span typical algebra I topics, to including some typical and atypical "word" problems. We will also discuss the way in which various forms of technology can supplement learning in this dynamic classroom format.
26 - Teach and Apply Algebra Concepts with Full Color and High Resolution in the New TI-84 C
Leader: Stuart Moskowitz, Humboldt State University, Arcata, CA
The TI-83/84's have been making math meaningful for our students since 1996 because they are well made and easy to use. 2013 brings the TI-84 C with a full color and high resolution screen along with innovative new functionality. Now we can import our own photographs right into the graph screen, then use concepts from algebra to analyze our own world more easily than ever! By week's end, we all will have new ways to teach (as well as a better understanding of) the algebra we already teach. TI-84 C loaners will be available.
Leader: Tom Reardon, Austintown Fitch High School and Youngstown State University, Youngstown, OH
Learn to incorporate and obtain all of my favorite TI-84 activities including mathematical modeling, e-Study Cards and The Great Applied Problem, but now on the new TI-84 C color graphing calculator. Learn creative teaching ideas for SMART Boards (including Fluid Math & TI-SmartView) - use color as a powerful teaching and learning tool. Obtain hundreds of colorful classroom-ready interactive documents that can be used with the new FREE Document Player (use Nspire without owning it!) For algebra 1 through AP Calculus. Investigate some of my favorite iPad APPs for high school math.
28 - A Problem-Based Approach to Trigonometry
Leader: Kevin Bartkovich, Phillips Exeter Academy, Exeter, NH
This course will be taught using sequences of problems that allow students to build their understanding of many important results in trigonometry at a level appropriate for precalculus classes. Technology, especially the TI-89, will be integrated seamlessly into the course. Topics to be covered include graphs of trig functions, solving triangles, periodicity, addition of sine curves, vector components, rotation matrices, and extended problems using trig models. The dynamics of a problem-based, student-centered Harkness classroom will be modeled and discussed throughout the course.
29 - Mathematics of Sustainability
Leader: Kevin Bartkovich, Phillips Exeter Academy, Exeter, NH
This course covers investigations related to sustainability, societal inequities, and environmental conservation. What difference will it make in carbon emissions if MPG ratings for new cars are raised by 50%? How long will the world supply of oil last? How can we quantify income inequity? These are some of the questions we will investigate by introducing the situation and then seeing where the relevant mathematics takes us. Most of the math we will use is found at the algebra 2 level and higher. The investigations are data driven; thus, facility with spreadsheet software is a prerequisite.
30 - Exploring Functions with Mapping Diagrams
Leader: Martin Flashman, Humboldt State University, Arcata, CA
Mapping diagrams provide a very illuminating tool to visualize functions that complement the more commonly used graph. This course will give a thorough treatment of the use of mapping diagrams for the study of functions. The coverage will connect to the mathematics curriculum from beginning and intermediate algebra through to trigonometry and college algebra with some references to calculus. The course will provide examples that illustrate the power of mapping diagrams as well as sample problems and exercises to support teachers and students who are just starting to use mapping diagrams.
In the spirit of the Common Core Standards, we will use simulations and hands-on activities to focus on: 1) inference 2) probability - conditional, binomial, geometric 3) two-way tables, tree diagrams and 4) data analysis. All applications will be applicable to algebra, geometry and precalculus. A contextual approach to mathematics will be developed. Fathom will be used for demonstrations and participants are welcome to take with them the prepared demos for use in their own classroom.
32 - Dynamic Geometry with Geogebra and Sketchpad
Leader: David Bannard, Collegiate School, Richmond, VA
Whether you use Geogebra (free) or the Geometer's Sketchpad, make geometry dynamic. This course will teach you how to use whichever program you prefer. The course will focus on ways to design labs and demonstrations using both programs to make your geometry class more dynamic. We will also discuss and demonstrate the Exeter Geometry course, which is free to download. This material makes effective use of coordinate geometry problems to teach geometry.
33 - The iPad as a Dynamic Math Learning and Teaching Tool
Leader: Nils Ahbel, Deerfield Academy, Deerfield, MA
It is now possible for your iPad to be a dynamic math writing surface that, based on your own handwriting, will create graphs and tables, simplify expressions, and solve equations. Participants will learn FluidMath.net, an easy-to-use web application that interprets your math notation handwritten with your finger or a stylus. Topics from algebra to precalculus will involve both student discovery activities and teacher demonstrations, including activities that take advantage of Fluidmath's robust computer algebra system. Participants must bring their own iPad 2 or 3 with iOS5 or later.
34 - Mathematics in the 21st Century Classroom
How do we create a dynamic classroom where students are engaged and motivated to learn even if we can't change the curriculum? This course will allow you to try a variety of activities for algebra I to precalculus, using new and old technologies that foster curiosity and a love of learning. Get started on Twitter where you will develop a fantastic personal learning network and discover the source of many new ideas and activities. Learn about free on-line tools, apps and some very "old school" ideas that work for both students and teachers. Come learn, share and have fun doing math!
35 - Made Possible by Wolfram Alpha
Leader: Harry O'Malley, University at Buffalo, Buffalo, NY
How are paper sizes related to one another? How are colors related to each other in 3-dimensional space? How close are you to a flying commercial airliner right now? Wolfram Alpha, a high quality software tool available to anyone with a web browser, can make problems like these accessible to high school students at all levels. In this course, we will engage in the fun of solving problems like these, learn tested techniques for incorporating Wolfram Alpha into our instruction, and mine Wolfram Alpha as a class, looking for more fruits to turn into great math experiences for our students.
36 - Hands-On Calculus
Leader: Maria Hernandez, The North Carolina School of Science and Mathematics, Durham, NC
Participants will explore hands-on calculus problems and ways to incorporate modeling into the calculus curriculum for AP courses. We'll explore some problems that lend themselves to building physical models and others that include applications involving pollution in The Great Lakes, peak oil production and the effectiveness of blubber as an insulator for seals. These activities will give you a way to actively engage your students as they strive to build a deeper understanding of the calculus topics. Work will be done using a computer and either the TI-83/84 or TI-89.
37 - Geogebra in Calculus and Algebra
Leader: David Bannard, Collegiate School, Richmond, VA
Geogebra is a free, powerful, and easy-to-use program that can greatly enhance your classes. Learning to effectively use the program is easy for both teachers and students. The focus of this class is for participants to learn how to make effective demonstrations in 5 to 15 minutes that dynamically illustrate concepts, as well as create labs that enhance students' understanding. I have found that I now use Geogebra almost daily in class and students use it at home to better understand the mathematics they are studying.
Leader: Tom Reardon, Austintown Fitch High School and Youngstown State University, Youngstown, OH
Investigate some of my favorite iPad APPs for teaching and for presentations. Learn to use TI-Nspire CX (color) on a handheld, on desktop, and with the new FREE Document Player (use Nspire without owning it!) Obtain hundreds of colorful classroom-ready interactive documents and learn to create your own. Learn creative teaching ideas utilizing CAS (Computer Algebra Systems). We will look at how to use FluidMath on SMART Boards. See the power of TI-Nspire Navigator, a student response system and classroom management solution. For algebra 1 through AP Calculus.
39 - Winplot from Algebra I to Calculus
Leader: Floyd Bullard, The North Carolina School of Science and Mathematics, Durham, NC Co-Leader: Julie Graves North Carolina School of Science and Mathematics, Durham, NC
Winplot, a free, downloadable program created by Rick Parris at Phillips Exeter Academy, is a graphing tool that is as powerful as it is easy to use. In this course we'll do ten different "labs" covering problems both abstract and applied, from algebra I to calculus. In these labs students learn how a flashlight beam is focused, how credit cards work, and more. Some time will also be dedicated to showing how you can create new animated problems out of old, static ones.
40 - The Rubik's Cube - Theory and Practice
Leader: Ian Winokur, Greenfield Community College, Greenfield, MA
In this course you will learn how to solve the Rubik's Cube, and much more! You will develop an understanding of the theory, mechanics and history of the cube. You will calculate the number of distinct scrambles by using some beautiful combinatorics and group theory. We will use the cube to discuss factorials, inverses, modular arithmetic and commutators. No experience necessary but experienced cubers will be given tips on how to solve more fluidly and efficiently. Sign up for this course and learn how to restore your cube to a state of chromatic bliss!
41 - Introduction to Sensible Calculus - A Thematic Approach
Leader: Martin Flashman, Humboldt State University, Arcata, CA
Using the outlines presented in most calculus texts to make sense of the material presented in a calculus course can be a challenge. This course will provide participants with three themes for organizing calculus that connect all the major concepts, skills, and applications of calculus: modeling, approximations, and differential equations. Examples and exercises will allow participants to see how these themes connect all important topics covered in a one year course in calculus: differentiation, integration, infinite series, and applications.
42 - The Beginner's Guide to Flipping a Classroom
Leader: Darren Ripley, The Davidson Academy of Nevada, Reno, NV
Instructors will be be given specific skills to learn how to use what is fast becoming the wave of the future for education, flipping the classroom. By the end of the course instructors will have installed and be proficient with Camtasia screen capture software, used a Bamboo Tablet and Logitech microphone to create a lesson done completely on their computers, and uploaded the finished, edited version onto a YouTube account which they have created. The course will emphasize trouble-shooting the many problems that sometimes make classroom flipping daunting and impractical.
43 - Scaffolding and Developing a PBL course
Leader: Carmel Schettino, Deerfield Academy, Deerfield, MA
This course is for teachers who have an already established PBL curriculum (such as CMP, IMP or PEA materials) who want to do more with the problems and learn to adjust their pedagogy, techniques or add in more scaffolding tools. Teachers will look at how a problem can be broken down into layers and connections to prior knowledge in order to serve their particular audience. Other PBL tools like classroom discourse, metacognitive writing and student listening will be discussed. Experienced PBL teachers should bring a laptop and a part of their curriculum they would like to develop.
44 - Introduction to Complex Systems II
Leader: Dan Teague, NC School of Science and Mathematics, Durham, NC
The fractal and chaotic processes we found so exciting in 80's have grown up into the modern subject of complex systems. Using techniques of complex systems, calculus students can model biological, physical, economic, and social processes in ways that were unimaginable even 20 years ago. This workshop will focus on agent-based models and cellular automata, using Netlogo to develop new approaches to understanding such varied topics as the spread of infectious diseases in a network, how TI gained control of the educational calculator market, and the process of social segregation.
We already solve puzzles for fun; now let's solve puzzles as a way to get kids (and teachers) to learn & love math! From Tangrams, Pentominoes, and disappearing rabbits, to trick locks, and magically appearing money, mechanical puzzles have been around for 1000s of years. We'll use slope, Fibonacci and Heron's Formula to explain how bunnies and money can appear and disappear. We'll use (and build) mechanical puzzles to study concepts in geometry, topology, and graph theory. By week's end, participants all will be puzzle collectors!
A continuation of Puzzles 101, but 101's not a prerequisite. Instead of mechanical puzzles, we'll explore Monty Hall and Traveling Salesman problems, look for squares in squares, solve Kakuro, and just play with numbers (wouldn't you love students to want to play with numbers just for fun?!) We'll study number theory, logic, graph theory, probability and more. But puzzles aren't just for fun; Richard Restak writes in The Playful Brain that they stimulate brain growth, with specific puzzles targeting specific parts of the brain. Start now: What's the smallest natural number with all 6 vowels?
Using the TI-84, CBR and spreadsheets, we will explore problems that can be solved with precalculus and algebra. The math includes exponential functions, trig, recursion, parametric equations, and linear and non-linear curve fitting. We will use math to explore the path of a playground swing, population of cane toads in Australia (favorite problem of summer 2012 class), predator-prey scenarios, CO2 in the atmosphere, satiation rates of mantids, and free throw percentages. Most problems lend themselves to multiple solution paths, thus allowing students to experience authentic problem solving.
With all of the options, what technology works best and how do you use these tools most effectively? Through a series of problems, activities, and applications, participants will explore options like Smartnotebook, iPad apps, e-books, Geogebra, Smartview, Wolfram demonstrations, videos, and other website apps to see what you might use in your classroom. A day each will be spent using animations, simulations, and visualizations. Strategies, methods, and techniques will be discussed. No prior experience is expected, just a willingness to try new things.
49 - Creating Powerful Learning Tools with TI-Nspire
Having trouble finding technology-rich support for your students? There is so much out there, and yet how often do you find something that is just right for your class? In the end, you are the best person to provide learning materials for your students! In this course, using the new TI-Nspire Lua scripting language, you will learn how easily you can create interactive learning documents. Even if you are a beginner with programming or TI-Nspire, this course will provide you with the skills and resources to develop great activities, for anything from prealgebra through geometry to calculus.
50 - Searching for Harmony and other Perfect Problems
What constitutes a "perfect problem?" For me, it is one that spans the high school years, accessible for the young and less able in a genuine way, but challenging for seniors-something for everyone! It CONNECTS the various branches of mathematics, and INTEGRATES mathematics with other disciplines. It must, of course, ENGAGE and cognitively EXTEND our students but, ideally, be relatively simple in expression. Finally, it should give opportunities for creative expression. Not surprisingly, my favorite perfect problems are best explored using good technology. Come and share some of my favorites.
51 - Mathematical Research in High School
Leader: Dan Teague, NC School of Science and Mathematics, Durham, NC
Thousands of students completing calculus before their senior year have the mathematical creativity and intellectual curiosity to engage in a mathematical research project. In NCSSM's research course, students work for a term on research problems modified from summer REU programs. In this workshop, participants will work in teams to investigate research problems suitable for post-calculus students. We will discuss strategies for instituting and supporting student research. The instructor will work with interested teachers throughout the year via a webpage dedicated to high school research.
52 - The Exeter Mathematics Program
Leader: Jeff Ibbotson, Phillips Exeter Academy, Exeter, NH
The mathematics program at Exeter is structured around problem sets of integrated materials. The materials feature problems of varying levels of difficulty and are designed to prompt students to discover and construct mathematical meaning for themselves. At the same time, there is a premium placed on seminar-style discussion as a guiding element of teaching. This course will introduce teachers to both of these by allowing them to participate as students while working through selected problems from the Math 2, Math 3, and Math 4 materials.
53 - An Alternative to Precalculus
Leader: Nils Ahbel, Deerfield Academy, Deerfield, MA
What do you do with students who struggle in algebra 2? This course outlines a free full-year alternative to traditional precalculus which includes linear, quadratic, exponential, log, and trig functions, but in the context of rich applications that can engage all students. Curve fitting functions to data will be emphasized. The course also includes probability and statistics with an entire chapter devoted to the normal distribution. By week's end you will be able to teach the course as is or choose parts to supplement an existing course.
54 - Calculus Modeling Problems that Make Students Think
Leader: Philip Rash, North Carolina School of Science and Mathematics, Durham, NC
In this course we will explore several engaging calculus-based modeling problems that students will remember for years. Unlike exercises that can be solved in only a few minutes, common to most textbooks, these problems require significantly more time and demand that students think more deeply about mathematics. The problem topics will include, among others, designing a subway, skydiving, and spread of an infectious disease. TI-83/84 calculators and computer software (MS-Excel) will be used with most problems. | 677.169 | 1 |
This text provides a creative, inquiry-based experience with geometry that is appropriate for prospective elementary and middle school teachers. The coherent series of text activities supports each student's growth toward being a confident, independent learner empowered with the help of peers to make sense of the geometric world. This curriculum is explicitly developed to provide future elementary and middle school teachers with
experience recalling and appropriately using standard geometry ideas,
experience learning and making sense of new geometry,
experience discussing geometry with peers,
experience asking questions about geometry,
experience listening and understanding as others talk about geometry,
experience gaining meaning from reading geometry,
experience expressing geometry ideas through writing,
experience thinking about geometry, and
experience doing geometry.
These activities constitute an "inquiry based" curriculum. In this style of learning and teaching, whole class discussions and group work replace listening to lectures as the dominant class activity.
CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book. | 677.169 | 1 |
Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for). | 677.169 | 1 |
Students Currently in 7 th to a continuum of appropriate coursework for identified gifted learners Both Pre AP and AP English Courses are accelerated classes that exceed State at the end of 11th and/or 12th grade earn college units.
know the Pythagorean theorem and solve problems in which they compute the length of an Rewrite the scientific notation numbers below in standard decimal notation. 1. 4.385 x. Grade 7. This data represents 12 scores on a math test:
Mathematical Practices (MP) Grade 7 Mathematics – Unpacking the Delaware Common Core State from State Departments of Education for Utah, Arizona, North Carolina, and Ohio to make muffins to take to a neighbor that had just moved in down the street. will form a straight line through the origin (0 books cost 0
Encribd is NOT affiliated with the author of any documents mentioned in this site. All sponsored products, company names, brand names, trademarks and logos found on this document are the property of its respective owners. | 677.169 | 1 |
The chankya shikshan sanstha has been conducted the survey about mathematical drawbacks. And it is found that, now a days number of students as well as people who are working in
private or government sectors are very poor in mathematical concepts like :-
Confusion in sign given to algebraic sum.
for example : i) - 5 + 15 = ii) -5 - 15 = iii) 5 - 15 = iv) 5 + 15 =
Confusion in sign given in product or division of same and opposite sign number.
Every person has a wish to be clear and clever in mathematics concepts. He or she wanted to become an expert in mathematics. But according to school syllabus pattern, the continuity mathematics syllabus should not be retained properly because the student in the 5th class, when he goes in the 6th std. he/she forgets the important basic concepts. And it is not better, when he/she will admit in 6th std. It will creat problems.
And so, we have arranged three level exam. The student in the 8th std, if he is clever he can complete 8th std syllabus easily but he wanted to learn 9th and 10th std syllabus for such a student the exam is good.
In this three level mathematic exam, the syllabus of middle school/highschool isalso included.
As one will complete three level course, his basic mathematic concepts will be clear and easily he/she will become an expert in mathematics. | 677.169 | 1 |
Advanced Engineering MathematicsThrough previous editions, Peter O'Neil has made rigorous engineering mathematics topics accessible to thousands of students by emphasizing visuals, numerous examples, and interesting mathematical models. Now, ADVANCED ENGINEERING MATHEMATICS features revised examples and problems as well as newly added content that has been fine-tuned throughout to improve the clear flow of ideas. The computer plays a more prominent role than ever in generating computer graphics used to display concepts and problem sets. In this new edition, computational assistance in the form of a self contained Maple Primer has been included to encourage students to make use of such computational tools. The content has been reorganized into six parts and covers a wide spectrum of topics including Ordinary Differential Equations, Vectors and Linear Algebra, Systems of Differential Equations and Qualitative Methods, Vector Analysis, Fourier Analysis, Orthogonal Expansions, and Wavelets, and much more. | 677.169 | 1 |
Peer Review
Ratings
Overall Rating:
This site is a collection of geometric derivations and demonstrations of problems from many areas of mathematics including Buffon?s needle problem, an exploration of the catenary, deriving the volume of a torus, a description of the centers of triangles, a look at the Reuleaux Triangle, and an investigation of properties of electrical force fields, to name a few. The author supports his derivations visually using carefully prepared images, Java applets and downloadable Geometer?s sketchpad (GSP) sketches. In cases where derivations are not given (for example the tangent circle applets), the applets are self-explanatory and are suitable for student exploration.
Learning Goals:
Presentation of the derivation of various facts from geometry, physics, calculus, and algebra.
Target Student Population:
Varies widely.
Prerequisite Knowledge or Skills:
Some topics only require elementary geometry. Others (hanging ropes) require even some differential equations to fully appreciate the derivation.
Evaluation and Observation
Content Quality
Rating:
Strengths:
Explanations are very well written and are carefully presented in a friendly non-technical manner, avoiding the use of jargon and all-too-deep mathematics when more intuitive methods are available. References and historical background are provided when possible and the illustrations are very helpful. Many lessons include some questions that are excellent for students doing group exploration, while others are suitable for undergraduate research problems. If the reader has Geometer's Sketchpad the nearly 30 downloadable sketches make the site worth it by themselves. These sketches allow visitors to interactively explore some fairly complicated, but very interesting mathematics, as well as being able to see some very useful and intricate GSP constructions.
Concerns:
None.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
This site is an excellent supplement for any textbook covering similar materials and many of the applets could be used for demonstration purposes during a lecture. Readers that use this site will, most likely, find themselves drawn to the other parts. The sense of enthusiasm the author conveys is most certainly contagious.
Some lessons, such as the Chinese Handcuffs lesson, are simply an interesting GSP sketch or java applet together with a list of questions for further exploration. Some of these questions may be (or lead to) problems that are appropriate for undergraduate research.
Other lessons such as the Tangent Circles lesson have interesting questions that many students would never think to ask, such as:
-Why do some configurations have fewer solutions than others?
-Why do some configurations have no solutions?
With its excellent visual presentation of some very interesting and (dare we say) fun problems from several fields of mathematics,
this has site uses that are too numerous to list in one review
Concerns:
None.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
Aside from the need for GSP the pages read like a well-written text. The applets and GSP sketches were either explained well or self-explanatory. But like any textbook most students will need some guidance through most of these lessons. It seems that all of the Java applets were created using GSP and Java Sketchpad, hence there is continuity to the look and operation of each interactive component. Furthermore, using the Show All Hidden command in GSP, students and teachers alike can discover some of the surprising capabilities of GSP.
Concerns:
None | 677.169 | 1 |
Culver City Algebra 1 builds on the topics explored in Algebra 1. These topics include: real and imaginary numbers, inequalities, exponents, polynomials, equations, graphs, linear equations, functions and more. For me, the skills gained in Algebra 2 were the very foundation of my study in Civil Engineering.
...They are confronted with new ideas often expressed in an abstract manner. These can be difficult to keep track of and to understand the differences of each and of each religion. I have helped students with this as well as making Religion a subject less intimidating to study but one that they will feel encouraged to move forward in.All that has to be done to solve a problem is as follows: write down all the formulas from the summery of each chapter on a piece of paper. Make sure you understand what all the variables and constants represent and understand the units. From then on it will just be plugging in numbers into equations. | 677.169 | 1 |
Infinite Series and Infinite Sequences.- Operations with Power Series.- Linear Transformations of Series. A Theorem of Cesàro.- The Structure of Real Sequences and Series.- Miscellaneous Problems.- Integration.- The Integral as the Limit of a Sum of Rectangles.- Inequalities.- Some Properties of Real Functions.- Various Types of Equidistribution.- Functions of Large Numbers.- Functions of One Complex Variable. General Part.- Complex Numbers and Number Sequences.- Mappings and Vector Fields.- Some Geometrical Aspects of Complex Variables.- Cauchy's Theorem. The Argument Principle.- Sequences of Analytic Functions.- The Maximum Principle. | 677.169 | 1 |
The focus of this website is to help in the transition from a paper oriented environment to one using OER materials with an...
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The focus of this website is to help in the transition from a paper oriented environment to one using OER materials with an emphasis in elementary and secondary school mathematics. The website's material is divided into five major topics: 1. Why OER materials? 2. The learner's environment - a world in change. 3. Mathematics past and present. 4. Exploring OER materials and 5. International mathematics education developments. An emphasis has been placed on linking to other OER materials to cover and expand on each topic. online book that contains exercises regarding current assets. There are 8 problem sets that contain...
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This is a free, online book that contains exercises regarding current assets. There are 8 problem sets that contain worksheets and solutions. One must sign up for their newsletter to download the free book.
This guide introduces the student to the fundamental principles of project scheduling and control. On completion of the...
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This guide introduces the student to the fundamental principles of project scheduling and control. On completion of the session the student will be able to: •Gather information from all the relevant stakeholders and sequence project activities; •Determine the activity time durations using all relevant information available; •Calculate the project duration using established planning techniques; •Analyse the project resource schedules; •Use an appropriate medium to communicate the schedule to all project participants •Monitor the project progress, updated schedules and present the information to the client.A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically such a...
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A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically such a student will have taken calculus, but this is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form.PDF versions are available to download for printing or on-screen viewing, an online version is available, and physical copies may be purchased from the print-on-demand service at Lulu.com. GNU Free Documentation License | 677.169 | 1 |
Next: Addition and Subtraction Phrases as Expressions
Previous: Data Display Choices
Chapter 12: Equations and Functions
Chapter Outline
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Description
Presents information about equations, functions, and probability, including writing expressions and equations, solving equations using addition and subtraction, solving equations using multiplication and division, an introduction to functions and graphing functions, an introduction to probability, finding outcomes, and understanding the probability of independent events | 677.169 | 1 |
I have the first and third books and the first one is an introductory book but there is still an assumption that you're educated in undergraduate linear algebra and calculus. If you've never taken math at that level or are very rusty you'll have a hard time following. You have to be completely honest about how good your math skills are as most people believe they can just learn it when they need to but the truth is if you couldn't learn it while in school you probably can't learn it on your own. | 677.169 | 1 |
Algebra I Workbook For Dummies
Book Description: From signed numbers to story problems — calculate equations with ease100s of problems!Hundreds of practice exercises and helpful explanationsExplanations mirror teaching methods and classroom protocolsFocused, modular content presented in step-by-step lessonsPractice on hundreds of Algebra I problemsReview key concepts and formulasGet complete answer explanations for all problems | 677.169 | 1 |
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