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Mathematics Report 2002
The mathematics department is one of the largest in the school with all learners taking mathematics as a subject from Grade 8 to Grade 12. The grade 8,9 and 10 have eight 55-minute periods in a two-week cycle and Grades 11 and 12 have nine 55-minute periods. Additional mathematics is offered as... |
Nuffield Advanced Mathematics
This Nuffield Foundation Project was a collaboration which drew on the expertise of the Supported Self Study Unit in Northumberland, the Mechanics in Action project in Manchester, teachers in several Local Authorities as well as the insights of team members at the King's College London an... |
What is the difference between matrix theory and linear algebra? - MathOverflow most recent 30 from is the difference between matrix theory and linear algebra?kolistivra2010-01-13T17:17:41Z2010-04-04T18:10:56Z
<p>Hi,</p>
<p>Currently, I'm taking matrix theory, and our textbook is Strang's Linear Algebra. Besides matri... |
Complex Numbers from A to ...Z2994
FREE
About the Book
It is impossible to imagine modern mathematics without complex numbers. Complex Numbers from A to . . . Z introduces the reader to this fascinating subject that, from the time of L. Euler, has become one of the most utilized ideas in mathematics.
The exposition... |
This book introduces students with diverse backgrounds to various types of mathematical analysis that are commonly needed in scientific computing. The subject of numerical analysis is treated from a mathematical point of view, offering a complete analysis of methods for scientific computing with appropriate motivations... |
QAX - The Complete Mathematics Solution
What is QAX?
QAX Mathematics can be used for your school's entire mathematics program. It covers the secondary curriculum for each Australian state, negating the need for other teaching resources. Each topic within the curriculum has a supply of questions and an introduction in... |
Prerequisites: MATH20132 Calculus of Several Variables; MATH20222 Introduction to Geometry (optional); MATH31051 Introduction to Topology (optional)
Future topics requiring this course unit: differentiable manifolds are used in almost all areas of mathematics and its applications, including physics and engineering.
De... |
...Algebraic math is a major stepping stone to multiple sciences and must be mastered to facilitate future academic progress in the sciences. As algebra skills consolidate, we move toward calculus (differential and integration calculus) which employs extremely powerful math skills. Pre-calculus is the bed rock of algeb... |
This book is an excellent introduction to the Fourier analysis. It is the first volume of the four planned volumes based on a series of four one-semester courses taught at Princeton University whose purpose was to present, in an integrated manner, the core areas of analysis. As the authors write: ``The objective was to... |
Algebraic Videogame Programming
Bootstrap is a FREE curriculum for students ages 12-16, which teaches them to program their own videogames using purely algebraic and geometric concepts.
Our mission is to use students' excitement and confidence around gaming to directly apply algebra to create something cool.
We work... |
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more.
Course Hero has millions of course specific materials providing students with the best way to expand
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Definite Integral Word ProblemsExample 1 An empty bucket is placed under a tap and... |
Journal of Online Mathematics and its Applications
Lite Applets
Introduction
The following image is "live" -- click on it to see what happens. Then think about how you might use this tool in material for mathematics instruction.
This "image" has two parts: a static image (the map), for which you can substitute any ... |
Description
Mathematical proofs, functions, formulas—oh, and word problems too: welcome to Algebra, the branch of math that provides tools to solve for the unknown. This video course will take you through the kinds of topics and problems covered in Algebra I and II courses. It's a great introduction for those who have... |
AcademicsNumber Theory
Course Outline: Number theory is primarily
concerned with the properties of and relationships between
whole numbers. Topics we will study:
1. Prime numbers
2. Modular arithmetic
3. Sums of squares
4. Pythagorean triples
5. Fermat's Last Theorem
6. Magic squares
7. Continued fractions
8. ... |
Miles Reid's Undergraduate Algebraic Geometry is an excellent topical (meaning it does not intend to cover any substantial part of the whole subject) introduction. In particular, it's the only undergraduate textbook that isn't commutative algebra with a few pictures thrown in. |
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more.
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Stewart Calculus ET 5e 0534393217;14. Partial Derivatives; 14.3 Partial Derivative... |
Binomial Theorem
In the last lecture of Algebra 2, Dr. Eaton ends with Binomial Theorem. She first begins with Pascal's Triangle and how it represents the expansion of a binomial. Next, she moves into the properties as well as a refreshment course on factorials before the binomial theorem and how to find a specific te... |
GCS - Algebra I Curriculum Guide
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gaston county schools algebra i curriculum guide course description ·the purpose of the algebra i course is to formalize and extend the mathematics that students learned in the middle grades this course deepens and extends understand... |
Maths from Scratch for Biologists
Numerical ability is an essential skill for everyone studying the biological sciences but many students are frightened by the 'perceived' difficulty of mathematics, and are nervous about applying mathematical skills in their chosen field of study. Having taught introductory maths and ... |
Course Description:This course is built on the basic concepts and principles in Algebra I. Students will work extensively with nonlinear functions while continuing to develop their power to think and work systematically. The content outline for Algebra II and Algebra II Honors is the same, but the Algebra II Honors cla... |
Monday, June 25, 2012
Real math! Romance! Karate! That's what the back of this unusual math book promises to its readers. Odd as it may seem to teach math with a comic book, The Manga Guide to Linear Algebra does a pretty good job of teaching the basics through comics and some light storytelling.
The book starts off ... |
Description
Goldstein's BriefCalculus and Its Applications, Twelfth Edition is a comprehensive print and online program for students majoring in business, economics, life science, or social sciences. Without sacrificing mathematical integrity, the book clearly presents the concepts with a large quantity of exceptional... |
For the faculty members whose main focus is teaching
undergraduate students, PCMI offers the opportunity to renew excitement about mathematics,
talk with peers about new teaching approaches, address some challenging research
questions, and interact with the broader mathematical community.
Each year the theme of the UF... |
Combinatorics is an area of mathematics that is frequently looked on as one that is reserved for a small minority of mathematicians: die-hard individualists who shun the limelight and take on problems that most would find boring. In addition, it has been viewed as a part of mathematics that has not followed the trend t... |
will break concepts down to a basic level, allowing the student to master the basics, and then return to the more complex problem that the student is trying to understand, but now the student has a better understanding of the fundamentals, and can now master more advanced concepts. I can expla... |
1449649165
9781449649166 They Will Encounter In Future Calculus Courses. In Far Too Many Texts, Process Is Stressed Over Insight And Understanding, And Students Move On To Calculus Ill Equipped To Think Conceptually About Its Essential Ideas. This Text Provides Sound Development Of The Important Mathematical Underpinn... |
Please note: Because we have had such a wonderful response to this workshop, we have run out of space. We're sorry for any inconvenience, but this has forced us to close registration. Thank you for your support and interest in Math Education. For over two decades, the teaching and learning of algebra has been a focus o... |
Mathematics Department
Teachers: Mr David Hobson, Mrs Heather Kingston, Mr Anthony Hibbard
Overview Mathematics is a reasoning and creative activity employing abstraction and generalisation to identify, describe and apply patterns and relationships. It is a significant part of the cultural heritage of many diverse so... |
Product Description
This powerful NCTM Standards-based program combines a variety of instructional strategies with test preparation to help students get back on track. It is designed for after-school, tutoring, summer school, and other extended learning programs, and includes components that review, instruct, provide,... |
NUMERICAL METHODS, 4E, International Edition emphasizes the intelligent application of approximation techniques to the type of problems that commonly occur in engineering and the physical sciences. Students learn why the numerical methods work, what kinds of errors to expect, and when an application might lead to diffi... |
Trigonometry Smarts!
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Are you having trouble with trigonometry? Do you wish someone could explain this challenging subject in a clear, simple way? From triangles and radians to sine and cosine, this book takes a step-by-step approach to teaching tr... |
This introduction to complex variable methods begins by carefully defining complex numbers and analytic functions, and proceeds to give accounts of complex integration, Taylor series, singularities, residues and mappings. Both algebraic and geometric tools are employed to provide the greatest understanding, with many d... |
Objective: On completion of the lesson the student will be able to calculate the gradient of a line given any two points on the line and also be capable of checking whether 3 or more points lie on the same line and what an unknown point will make to parallel lines.
Objective: On completion of the lesson the student wi... |
Letts and Lonsdale's Success Revision Guides offer accessible content to help students manage their revision and prepare for exams efficiently. The content is broken into manageable sections and advice is offered to help build students' confidence. Exam tips and techniques are provided to support students throughout th... |
Description
By connecting applications, modeling, and visualization, Gary Rockswold motivates students to learn mathematics in the context of their experiences. In order to both learn and retain the material, students must see a connection between the concepts and their real-lives. In this new edition, connections are... |
On-line Quizzes
Each week, students must complete a single timed online quiz at before 4 pm on Friday of the week after the lecture and lab for that topic. Be sure to plan time for completing each week's quiz. Quizzes are (generally) available from 4 pm on Thursday after Team Lab for that week's topic to 4 pm on Frida... |
Students
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Understanding the value of math
Whatever you plan to do in your life, at school, at home or in your future career, you need mathematical skills to succeed in our society.
Mathematical concepts are present in everything you do. Knowing and understanding these concepts will serve you well ... |
Web Codes
Funded and approved by the National Science Foundation, Connected Mathematics is a complete middle school curriculum that helps students develop an in-depth understanding of key mathematical ideas and make connections between them and to other disciplines. The program, rated exemplary by the U.S. Department ... |
This textbook is devoted to Combinatorics and Graph Theory, which are cornerstones of Discrete Mathematics. Every section begins with simple model problems. Following their detailed analysis, the reader is led through the derivation of definitions, concepts and methods for solving typical problems.
Best Internet Links... |
Book Description: Teaching Secondary Mathematics, Third Edition is practical, student-friendly, and solidly grounded in up-to-date research and theory. This popular text for secondary mathematics methods courses provides useful models of how concepts typically found in a secondary mathematics curriculum can be delivere... |
Elementary Algebra With Bca Tutorial, and Infotrac
9780534400415
ISBN:
0534400418
Publisher: Thomson Learning
Summary: Jerome Kaufmann and Karen Schwitters discuss algebra with clear and concise exposition, numerous examples, and plentiful problem sets. They reinforce the following common thread - learn a skill, u... |
From the Ishango Bone of central Africa and the Inca quipu of South America to the dawn of modern mathematics, The Crest of the Peacock makes it clear that human beings everywhere have been capable of advanced and innovative mathematical thinking. George Gheverghese Joseph takes us on a breathtaking multicultural tour ... |
MATH 111 - College Algebra
A course in Algebra for college students with a strong emphasis on problem-solving and applications. Topics include: introduction to functions and their graphs; linear and quadratic functions; solution of a variety of types of equations and inequalities using algebraic, numeric and graphical... |
TI-84 Plus graphing calculator offers three times the memory, more than twice the speed and a higher contrast screen than the TI-83 Plus model. It's keystroke-for-keystroke compatible, too. Count on TI calculators at exam time. |
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more.
Course Hero has millions of course specific materials providing students with the best way to expand
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MATH XL Homework Notes for Students: MathXL is only accessible through the Interne... |
In this section
Intermediate 1 Mathematics
The Intermediate 1 Course is designed to build upon and extend candidates' previous mathematical learning, to introduce them to the areas of algebra and elementary statistics.
Depending on the optional unit chosen, learners will either be introduced to trigonometry and furt... |
Supplements
ALGEBRA: FORM AND FUNCTION features a host of resources to assist you and your students in becoming fluent speakers of algebra!
The Instructor′s Manual contains information on planning and creating lessons and organizing in-class activities. There are focus points as well as suggested exercises, problems ... |
M2= Math Mediator
Algebra 2 High School Lesson Plans
Click on this link: Lesson Plan Example
for an example of one of the lesson plans available. Notice that each lesson
plan offers:
Designed for 55 minutes of class time
Includes topics to meet math standards
Exercises are included with answers
Activities are use... |
About the Cover
The Big Bend Region is the westernmost region of Texas. Known for its
wide open skies, it is home to the International El Paso Balloon
Festival. The distance that a balloon travels is determined by its rate, or
speed, and the time it is in the air. Mathematically, these three
variables are related by t... |
This course begins with a discussion of the geometry of two-
and three-dimensional space, vectors, basic linear algebra, and
quadric surfaces (surfaces defined by a 2nd-degree polynomial
e.g. spheres, ellipsoids, hyperboloids, etc.). Then we will
extend the scope of calculus so that it covers vector-valued
functions an... |
This book contains a modern introduction to the use of finite difference and finite element methods for the computer solution of ordinary and partial differential equations. After a review of direct methods for the solution of linear systems, with emphasis on the special features of the linear systems that arise when d... |
Exploring mathematics builds on the concepts and techniques in Using mathematics (MST121) and uses the same software. It looks at questions underlying some of those techniques, such as why particular patterns occur in mathematical solutions and how you can be confident that a result is true. It introduces the role of r... |
Mathematics
"A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas".
G.H Hardy, 'A Mathematician's Apology'
Mathematics is the means of looking at the patterns that make up our world and the intricate and beautiful ways... |
An investigation into the extent and nature of the understanding first year college of education students have of aspects of arithematic and elementary number theory
Oliphant, Vincent George
(1996)
An investigation into the extent and nature of the understanding first year college of education students have of aspects... |
TExES Mathematics-Physics 8-12 143
From understanding the real number system and attributes of functions to identifying and analyzing forces of motion and magnetic materials' properties, this comprehensive study guide provides the core content found on the TEXES Mathematics-Physics 8-12 certification exam. It covers t... |
...Evaluate an expression written with function notation. (VIII)
17. Find the log of a number and rewrite log expressions using the log properties. (VIII)
Geometry includes an in-depth analysis of plane, solid, and coordinate geometry as they relate to both abstract mathematical concepts as we... |
Links
- This article was written by one of the Stepping Stone Algebra Tutors. If you know of anyone who might be interested in reading tuition, please do get in
contact.
Algebra, once only studied by advanced mathematicians and scientists, is now taught to every seventh and eighth grade child across the United States... |
Introduction to the PascGalois JE Applets
So what is PascGalois JE? The PascGalois project was started in the late 1990's
as a new and innovative way to visualize concepts in an introductory abstract algebra course,
primarily group theory. Although this is still its main function the project has branched out into
area... |
Mathematics for the Liberal Arts Student
Fred Richman, Carol L. Walker,
Robert J. Wisner, James W. Brewer
This text is for a one or two semester terminal course in
mathematics. Such a course allows for leisurely exploration in place of
drill---it is a course in mathematics appreciation. For this audience one
must con... |
Module 3G2 - Mathematical Physiology
This course focuses on the quantitative modelling of biological systems. A wide variety of topics are touched upon, from biochemistry and cellular function to neural activity and respiration. In all cases, the emphasis is on finding the simplest mathematical model that describes th... |
Graphing Calculator MatchingManiaGraphing Calculator MatchingMania consists of 12 functions. Students work together using a graphing calculator to find the zeroes, minimums and/or maximums and the points of intesection of two functions. This is a great calculator review activity or learning activity to begin the school... |
Aquasco ACT knows how to tap into each kid?s learning style. ItMy philosophy for studying is that it is insufficient to merely memorize formulas; it is necessary to understand the formula's derivation as well as its potential applications. This leads to a much greater understanding of the subject material.A solid algeb... |
The calculus of differential forms has significant advantages over traditional methods as a tool for teaching electromagnetic (EM) field theory. First, films clarify the relationship between field intensity and flux density, by providing distinct mathematical and graphical representations for the two types of fields. S... |
Practical Approach to Merchandising Mathematics, RevisedMerchandising math is a multifaceted topic that involves many levels of the retail process, including assortment planning; vendor analysis; markup and pricing; and terms of sale. A Practical Approach to Merchandising Mathematics, Revised 1st Edition, brings each o... |
...The course of study is designed to extend the development of numbers to include the study of the complex numbers as a mathematical system, to expand the concept of functions to include quadratic, exponential and logarithmic
functions, to analyze the concepts, and to develop additional problem-sol... |
CRAFTY leads national initiatives to renew mathematics course work and instruction offered for students in their first two years of college. In making decisions about timely renewal efforts concerning lower level courses and programs, CRAFTY considers CUPM recommendations including the CUPM Curriculum Guide and informa... |
Exponential and Logarithmic Functions
4.1 Exponential Functions and Their Applications
4.2 Logarithmic Functions and Their Applications
4.3 Rules of Logarithms
The Trigonometric Functions
5.1 Angles and Their Measurements
5.2 The Sine and Cosine Functions
5.3 The Graphs of the Sine and Cosine Functions
5.4 The Other T... |
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in Our World
"Mathematics in Our World" is designed for mathematics survey courses for non-science majors. The text covers a variety of topics designed to foster ...Show synopsis"Mathematics in Our World" is designed for mathematics survey courses for non-science majors. The text covers a variety of topics designed to... |
The
matrix
algebra
index
begins
with
applications
and
properties
of
matrices,
works
through
systems
of
linear
equations,
explains
determinants
(including
Cramer's
Rule),
and
finishes
with
lessons
on
eigenvalues
and
eigenvectors.
Each
section
includes
an
introduction
to
the
topic
and
example
problems
as
well
as
notes,
t... |
HOME-EDUCATION-MATHEMATICS
AcaStat A low-cost alternative for producing basic summary statistics at home, school or work. Create and analyze crosstabulations, descriptive statistics, and basic significance tests. Create data files with AcaStat or import from spreadsheets, data tables, or statistical software. Includes... |
Algebra And Trigonometry - 7th edition
Summary: For undergraduate courses in Algebra and Trigonometry with optional Graphing Calculator usage.
The Seventh Edition of this dependable text retains its best features -- accuracy, precision, depth, strong student support, and abundant exercises -- while substantially upda... |
Vedic Mathematics for Schools offers a fresh and easy approach to learning mathematics. The system was reconstructed from ancient Vedic sources by the late Bharati Krishna Tirthaji earlier this century and is based on a small collection of sutras. Book 1 of the series is intended for primary schools in which many of th... |
HOMEWORK QUICK START
This book is straightforward and easy-to-read review of arithmetic skills. It includes topics that are intended to help prepare students to successfully learn algebra, including: * Working with fractions * Understanding the decimal system * Calculating percentages * Solving linear equalities * Gra... |
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Abstract
We show that students rearranging the terms of a mathematical equation in order to separate variables prior to integration use gestures and speech to manipulate the mathematical terms on the page. They treat the terms of the equation as physical objects in a landsc... |
All of the courses in the junior high, high school, and college mathematics curriculum require a thorough grounding in the fundamentals, principles, and techniques of basic math and pre-algebra, yet many students have difficulty grasping the necessary concepts. Utilizing the author's acclaimed and patented fail-safe me... |
Algebra 1
71110-20
Course#
Course Name
71110-71120
Algebra 1 Sem A & Sem B
General Course Description:
In this course offered via the Web, students learn about algebraic concepts such as integers, linear equations, linear inequalities, and factoring. As students work through each interactive lesson, they will ha... |
Thursday, February 28, 2013
Now then, helping one determine what the icse mathematics project and weight of the icse mathematics project and now on the icse mathematics project and used defined rules to calculate the icse mathematics project is giving you. In the icse mathematics project, the icse mathematics project ... |
A free Algebra 1course just came out this week, this one from Curriki, a provider of free, K-12 open educational resources. This is a full course, broken into modules, so you can use it in its entirety, or just the parts you want. The course includes lesson plans, with links to related Khan Academy videos, worksheets a... |
Properties: Evaluate The learner will be able to
evaluate mathematical and algebraic expressions using the following properties: associative, commutative, identity, substitution, inverse and zero properties.
Data Collection: Organize The learner will be able to
collect, organize ,and display data with appropriate nota... |
STP Mathematics for Jamaica Grade 8
by
Sue Chandler - Ewart Smith
STP Mathematics for Jamaica is an, up-to-date, Mathematics course created by the STP Mathematics author team and Jamaican experts in Mathematics education and tailored to the needs of Lower Secondary students of Jamaica.
Top page |
ICS eLearning
The age of information and technology has rapidly expanded the field of mathematics. In order to develop confident, effective students of mathematics, the mathematics teachers at ICS Addis endorse four primary beliefs.
Students are capable of learning mathematics and gaining confidence in their understa... |
Do you own an iPhone? Do you also have toddlers or kids who are about to enter school? Put the iPhone and the kids together with some of the apps listed below to keep the kids busy as they prepare themselves
A=B This book is about identities in general, and hypergeometric identities in particular, with emphasis on com... |
Software to Accompany Chapters 3–11
To enhance the accuracy of calculations for the exercises that appear at the end of each chapter and make them easier to use, we have developed web-based software to accompany material in Chapters 3–11. The software covers the following topics: |
Wolfram Offers Next Innovation in Education Technology with Wolfram
Education Portal
January 18, 2012—Wolfram today announced the launch of the Wolfram
Education Portal, providing teachers and students alike with a new way
to integrate technology into learning.
The Wolfram Education Portal, available at education.wolfr... |
Search Mathematical Communication:
Mathematical Communication
Welcome to MathDL Mathematical Communication
Topic Teaching Tip(s):
Courses in which students communicate about mathematics | Including writing in math classes | Including oral communication in math classes | General principles of mathematical communicati... |
Using the Standards - Algebra, Grade 4
Book Description Communi... More Communication, Connections, and Representation. The vocabulary cards reinforce math terms and the correlation chart and icons on each page help to easily identify which content and process standards are being utilized. Includes a pretest, post tes... |
If you can be explicit about free algebra worksheet, I could provide help to solve the math problem. If you don't want to pay for a math tutor, the next best option would be a accurate computer program which can help you to solve the problems. Algebrator is the best I have come upon which will elucidate every step to a... |
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Lecture Description
A basic tutorial on the gradient field of a function. We show how to compute the gradient; its geometric significance; and how it is used when computing the directional derivative. The gradient is a basic property of ve... |
Essential Mathematics
9780060406028
ISBN:
006040602X
Edition: 2 Pub Date: 1994 Publisher: Addison-Wesley
Summary: Designed for a basic mathematics course, this text offers a detailed look at the core concepts and then some! It includes a chapter on statistics, two chapters on basic algebra, stresses developing num... |
This is the first course in a sequence of courses designed to provide students with a rigorous program of study in mathematics. It includes complex numbers; quadratic, piecewise, and exponential functions; right triangles, and right triangular trigonometry; properties of circles; and statistical inference. (Prerequisit... |
This book provides students with the modern skills and concepts needed to be able to use the computer expressively in scientific work. The author takes an integrated approach by covering programming, important methods and techniques of scientific computation (graphics, the organization of data, data acquisition, numeri... |
Differential Calculus
Differential Calculus is one of the most important topics in the preparation of IIT JEE, AIEEE, DCE, EAMCET and other engineering entrance examinations. This is the easier part of Calculus and there is no doubt it is scoring too. It is also important to learn Differential Calculus to proficiency ... |
The Mathematics curriculum follows the guiding principles of the Massachusetts Mathematics
Curriculum Framework:
1) mathematical ideas must be explored,
2) all students must have access to high quality mathematics programs,
3) mathematics learning is a lifelong process,
4) mathematics instruction must connect with othe... |
Posted: Tue Apr 22, 2003 6:23 pm ; Post subject: abstract algebra hungerford homework solutions
There's no way I'm going to learn this without some help. Everyone else in my class is confused about the abstract algebra hungerford homework solutions Many algebra tutorials teach you how to solve math equations that barel... |
Mathematics
Academic Staff
The teaching provision at Jesus College is generous in relation to the number of Mathematics students. The college has tutors in all the main branches of Mathematics, who are committed to mathematical research as well as to teaching, and who together cover a wide range of subjects.
Fellows... |
Concept Maps
By drawing concept maps, students strengthen their understanding of how a new concept is related
to others they already know.
Background and Purpose
Concept maps are drawings or diagrams showing
connections between major concepts in a course or section of a course.
I have used concept maps in precalculu... |
"Teach Yourself Basic Mathematics "gets you up and running with all the math you need to confidently meet the numerical challenges of everyday living. Here you will learn how to rapidly perform basic arithmetic procedures; change between different systems of measurement; master fractions, decimals, and percentages; int... |
Curriculum and Requirements
Related Links
For well over two thousand years, mathematics has been a part of the human search for understanding. Mathematical discoveries have come both from the attempt to describe the natural world and from the desire to arrive at a form of inescapable truth through careful reasoning t... |
Partial differential equations (PDEs) occur widely in all branches of engineering science, and this course provides an introduction to the various classes of PDE and the physical nature of their solution. The second part of the course demonstrates how variational calculus can be used to derive both ordinary and partial... |
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