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Publisher's description: \par The aim of this book is to provide the reader with a basic understanding of Fourier series, Fourier transforms and Laplace transforms. The book is an expanded and polished version of the authors' notes for a one-semester course, for students of mathematics, electrical engineering, physics and computer science. Prerequisites for readers of this book are basic courses in calculus and linear algebra. Otherwise the material is self-contained with numerous exercises and various examples of applications.\par Contents: Preface; 0. Notation and terminology; 1. Background: inner product spaces; 2. Fourier series; 3. The Fourier transform; 4. The Laplace transform; Appendix A: The residue theorem and related results; Appendix B: Leibniz's rule and Fubini's theorem. |
Functions
You can't go through algebra without learning about functions. This tutorial shows you a great approach to thinking about functions! Learn the definition of a function and see the different ways functions can be represented. Take a look!
Further Exploration
Reflections
When you look in the mirror, you see a reflection of yourself. Reflections in math involve flipping something over a line called the line of reflection. This tutorial shows you how to reflect a function over a chosen |
The calculate activity provides a generic calculator. The interface provides the simplest functions directly and should therefore be easy to use for the youngest children. However, it does support more complicated math and variables.
1) After pressing the Power button, the main boot screen will begin to load
2) After XO is completely booted, bring the mouse pointer down to the task bar at the bottom
of the screen.
3) Arrow over until Calculate is highlighted
4) Select Calculate
5) Allow to Activity page to load
Calculate Basic Functions:
When Calculate is fully loaded this is the first screen you see is the Activity Page.
The options consist of…
1) Edit
2) Algebra
3) Trigonometry
4) Boolean
5) Constants
6) Format
Basic calculation: Each of the buttons on the calculator are interactive and the calculator works the same as a normal calculator.
Click Edit
Simple editing options located on top of page.
1) Copy: Highlight item then click Copy to Copy the information.
2) Paste: After the information has been copied, select this to paste it to where you would like
3) Cut: Cut removes the selected information from the screen and allows you to place it elsewhere.
These Copy, Paste, and Cut functions can be used to take a previously used function and paste it
back into the calculator.
Algebra:
Algebra with 5 Choices, Screen from VM Ware Player
Algebraic functions are displayed across the top bar
1) Square:Multiplies the result by itself
Ex: Solution = 2 (Hit 'square' button) = 4
2) Sqrt: Short for Square Root, takes square root of a value.
3) Exp: Allows you to raise a value to an exponent that is different then 2.
4) ln: Takes the Natural Log of a variable.
5) Fac: Factorial function allows the user to take the factorial of the answer displayed.
Trigonometry:
Trigonometry with Trig options, Screen from VM Ware Player
-Common Trigonometric functions listed with Hyperbolic and Inverse Trig functions
1) Sin: Enter a value and select sin to show the sin of the value.
2) Cos: Enter a value and select cos to show the cos of the value.
3) Tan: Enter a value and select tan to show the tan of the value.
4) asin: Arcsin- Click asin to take the Arc Sin of the value displayed
5) acos: Arccos- Click acos to take the Arc Cosine of the value displayed
6) atan: Arctan- Click atan to take the Arc Tangent of the value displayed
Hyperbolic Functions
1) sinh
2) cosh
3) tanh |
Academic Courses
Course Descriptions
Course Description
This is the first of a two-course sequence designed for students who plan to enter elementary school teaching. The course examines elementary school math topics and mathematics curriculum from an advanced standpoint with an emphasis on conceptual understanding and problem solving. The course covers problem solving, number theory, sets, algebraic concepts and functions, numeration, the real numbers and their properties and operations. |
Eigenvalues and Eigenvectors
In this lesson our instructor talks about eigenvalues and eigenvectors. First, he discusses some definitions and examples on the topic. Then he talks about two helpful theorems and does a review of the lesson.
This content requires Javascript to be available and enabled in your browser.
Eigenvalues and Eigenvectors |
Tutorials: CXC CSEC math topic - Algebra
This is a full algebra course.
Please don't forget to do the problems at the end of each lesson.
Also please let us know if you like the link and find it useful to you. You can do this by leaving a comment on the page with the link.
This 'Algebasics' site is more about demonstration that interaction, but it is very good for those of you who need a lot of help with the basics of algebra. You will need to click along the green bar at the bottom of the page for the demonstration to progress.
Rate these sites and let us know if we should keep it! Write a comment by clicking on the "add a comment' link at the end of this page.
The Math Warehouse has a very clear and simple explanation of matrices that you might want to take a look at if you are unclear about matrix notation, as well as how to add and subtract matrices. |
The Admissions Magazine
Popular Classes
History of Mathematics
In Math 112 we trace the evolution of mathematics from its earliest roots to the invention of the calculus in the 17th century. We examine the major mathematical ideas of each era by focusing on the character and achievements of the different civilizations... |
Mathcentre provide this resource which covers the slope intercept form, an aspect of geometry that involves the gradient and vertical intercept of a graph, which can be established from the terms of a linear equation.
Comprehensive notes, with clear descriptions are provided, together with relevant diagrams and examples. Students…
Mathcentre provide these resources which cover aspects of arithmetic, often used in the field of engineering. They include fractions and their associated arithmetic, calculations involving surds, using standard form, as well as understanding and drawing the graph of a function.
Comprehensive notes, with clear descriptions, for…
Mathcentre provide this numeracy refresher resource, which was developed and trialled by staff of the University of Birmingham Careers Centre and subsequently used widely throughout the HE Sector. There are sections which review decimals, fractions, averages, percentages and ratios, making it a useful resource for Key Stage Three… |
Providence, RI Statistics
...Despite its seminal importance in the modern world, calculus introduces only one truly new concept: the limit. The other two major tools of calculus - differentiation and integration - are simply application of the limit to different kinds of problems. Mastering calculus requires a strong foundation of algebra and trigonometry, followed by an in-depth understanding of limits |
PDEs - Mathematical Modeling and Numerical Simulation
Many phenomena occurring in real life applications (i.e. physics, finance, biology…) are modeled by means of ordinary (ODE) and partial (PDE) differential equations. These mathematical models are usually sets of equations and relations, which describe the essential behavior of a natural or artificial system, in order to forecast and control its evolution [1].
Objectives
The aim of the course is twofold. Firstly, we will give the students an overview on the construction of differential mathematical models for some basic physical applications; these examples of models will turn out to be particular cases of the more generic class of so called conservation laws. Then, focusing on the arising PDEs, their theoretical mathematical background will be discussed. As a matter of fact, the understanding of PDEs is closely connected to understand their physical meaning and the qualitative and quantitative behaviour of their solutions. This, whenever dealing with a certain PDE, we will directly introduce a numerical solution method, which will allow for studying the behaviour of the PDE under consideration numerically. In this way, theoretical and practical aspects of deriving and solving PDEs will be carefully intertwined. For example, we will deal with the weak formulation of the PDEs, which form the mathematical framework of state of the art simulation methods – such as the finite element method – employed for numerical solution. Theoretical findings will thus be accompanied by doing numerical experiments and by learning about modern solution algorithms. Particular attention will be paid to the applied aspects and implementation activities: to this purpose, whenever possible, the mathematical subjects will be presented in a more practical and intuitive manner (rather than a purely formal one).
Contents
Fourier law of heat conduction
Introduction to Fluid Dynamics
Introduction to Finite Difference method
Hilbert spaces
Weak formulation of elliptic problems
Introduction to Finite Element method
Weak formulation of evolution problems
Heat Equation
Numerical Simulation of the heat equation
Advection and reaction dominated problems
Teaching mode
The course will be based on lectures and exercise sessions, in which students are asked to participate actively. The students will also implement the discussed methods and will exploit their behaviour in numerical experiments. Moreover, on the basis of numerical experiments, a quantitative understanding of the treated PDEs will be achieved.
Other important and required activities are private study and readings. |
Spring,
2011 Teaching : MATH 236 CALCULUS 2
How can it be that mathematics, being after all a product of human
thought independent of experience, is so admirably adapted to the
objects of reality? --Albert Einstein Syllabus |
We start this unit by learning to visualize functions of several variables using graphs and level curves. Following this we will study partial derivatives. These will be used in the tangent approximation formula, which is one of the keys to multivariable calculus. It ties together the geometric and algebraic sides of the subject and is the higher dimensional analog of the equation for the tangent line found in single variable calculus. We will use it in part B to develop the chain rule.
We will apply our understanding of partial derivatives to solving unconstrained optimization problems. (In part C we will solve constrained optimization problems |
Abstract
This paper presents an approach for teaching and learning dc-dc converter design using MathCAD. MathCAD provides advantages that greatly improve teaching and learning process especially when long and complicated design equations are involved such as those found in dc-dc converters. A design example using Excel is presented and then compared with the same example using MathCAD. Experience learned from using MathCAD in power electronic courses at Cal Poly will be discussed in this paper. |
Kemblesville Physicsn...
...I have taken numerous college courses dealing with discrete mathematics. My Ph.D. thesis involves solving a set of simultaneous partial difference equations with boundary values. I used discrete math concepts to solve several projects I worked on in industry |
Survey of Mathematics with Applications, A (9th Edition)
9780321759665
ISBN:
0321759664
Edition: 9 Pub Date: 2012 Publisher: Addison Wesley
Summary: This textbook serves as a broad introduction to students who are looking for an overview of mathematics. It is designed in such a way that students will actually find the text accessible and be able to easily understand and most importantly enjoy the subject matter. Students will learn what purpose math has in our lives and how it affects how we live and how we relate to it. It is not heavy on pure math; its purpose ...is as an overview of mathematics that will enlighten students without an intense background in math. If you want to obtain this and other cheap math textbooks we have many available to buy or rent in great condition online.
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New and Published Books
21-30 of 76 results in Discrete Mathematics and Its Applications
Accessible to undergraduate students, Introduction to Combinatorics presents approaches for solving counting and structural questions. It looks at how many ways a selection or arrangement can be chosen with a specific set of properties and determines if a selection or arrangement of objects exists...
An Introduction to Combinatorics, Second Edition
Emphasizes a Problem Solving ApproachA first course in combinatorics
Completely revised, How to Count: An Introduction to Combinatorics, Second Edition shows how to solve numerous classic and other interesting combinatorial problems. The authors take an easily accessible approach that introduces...
From the exciting history of its development in ancient times to the present day, Introduction to Cryptography with Mathematical Foundations and Computer Implementations provides a focused tour of the central concepts of cryptography. Rather than present an encyclopedic treatment of topics in...,...
Methods Used to Solve Discrete Math ProblemsInteresting examples highlight the interdisciplinary nature of this area
Pearls of Discrete Mathematics presents methods for solving counting problems and other types of problems that involve discrete structures. Through intriguing examples, problems,...
Exploring one of the most dynamic areas of mathematics, Advanced Number Theory with Applications covers a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory. Written by a recognized leader in algebra and number theory, the book includes a page...
Retaining all the key features of the previous editions, Introduction to Mathematical Logic, Fifth Edition explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. The...
A One-Stop Source of Known Results, a Bibliography of Papers on the Subject, and Novel Research Directions
Focusing on a very active area of research in the last decade, Combinatorics of Compositions and Words provides an introduction to the methods used in the combinatorics of pattern avoidance...
Codes, Ciphers and Discrete Algorithms, Second Edition
Using mathematical tools from number theory and finite fields, Applied Algebra: Codes, Ciphers, and Discrete Algorithms, Second Edition presents practical methods for solving problems in data security and data integrity. It is designed for an applied algebra course for students who have had prior...
Design Theory, Second Edition presents some of the most important techniques used for constructing combinatorial designs. It augments the descriptions of the constructions with many figures to help students understand and enjoy this branch of mathematics.
This edition now offers a thorough... |
GEOMETRIC ALGEBRA: AN ALGEBRAIC SYSTEM FOR COMPUTER GAMES AND ANIMATION
Published on July 1, 2011 by admin
Evangelist Vince, "Geometric Algebra: An Algebraic System for Computer Games and Animation"
S r-r | Pages: 198 | 2009 | ISBN 1848823789 | PDF | 1,6 MB
Geometric algebra is ease aerated as an fog division of algebra and most books hit been cursive by effective mathematicians in a rattling nonfigurative style. This restricts the readership of much books especially by programmers employed in machine graphics, who only poverty counselling on formula design.
Geometric algebra provides a unified algebraic grouping for finding a panoramic difference of nonrepresentational problems. Evangelist Vince reveals the example of this algebraic support and communicates to the reverend newborn and extraordinary mathematical concepts using colouration illustrations, tabulations, and easy-to-follow algebraic proofs.
The aggregation includes some worked examples to exhibit how the algebra entireness in training and is primary datum for anyone participating in artful 3D nonrepresentational algorithms. |
College Prep: Math
College Prep: Math is designed to help students build the knowledge and skills they need for college-level math courses. With successful completion of College Prep: Math, students can meet entrance requirements, successfully complete college placement tests, and transition to college-level math without remediation. The course includes an academic year of content, and the following six units of content are covered: Basic Operations and Applications: Number Concepts and Properties; Expressions, Equations, and Inequalities; Functions; Graphs and Measurement; Probability, Statistics, and Data Analysis.
Interactive components throughout the course serve to engage students and enhance learning. |
Put the fun into functional skills with specially written engaging real-life situations that use mathematics. Students will become confident in applying maths to a range of problems that prepare them for work and life. Ready-to-use tasks can be accessed via your VLE to cover Level 1 and Level 2 functional skills.
About this resource
• Set functional skills homework with easy access to the digital edition available for your VLE • Develop problem solving skills with 40 totally new and inspiring topics, some familiar and some unfamiliar, grouped into three sections: beginner, improver, advanced • Build, apply and secure the functional and process skills that are integral to the 2010 GCSE Maths Specifications • Challenge students at all levels with open questions that can be approached in different ways • Encourage discussion and collaboration between students to encourage team work and responsibility • Make mathematics relevant and useful, with scenarios such as Coastguard Search and Rescue, and Investigating Design and Cost in Tea Bag Production • Promote self-assessment with 'How did you find these tasks?' questions at the end of each topic • Answers and guidance are given in the separate Teacher's Pack ISBN 978-0-00-741007-1 |
Discrete Mathematics
COURSE DESCRIPTION
Welcome to Discrete Mathematics, a subject that is off the beaten track that most of us followed in school but that has vital applications in computer science, cryptography, engineering, and problem solving of all types. Most of the mathematics taught after elementary school is aimed at
preparing students for one subject—calculus, which is the mathematics of how things grow and change continuously, like waves in the water or clouds in the sky. Discrete mathematics, on the other hand, deals with quantities that can be broken into neat little pieces, like pixels on a computer screen, the letters or numbers in a password, or directions on how to drive from one place to another.
While continuous mathematics resembles an old-fashioned analog clock, whose second hand sweeps continuously across a dial, discrete mathematics is like a digital watch, whose numbers proceed one second at a time. As a result, discrete mathematics achieves fascinating mathematical results using relatively simple means, such as counting.
Explore this modern realm of digital math in Discrete Mathematics, 24 mind-expanding lectures by veteran Teaching Company Professor Arthur T. Benjamin, an award-winning educator and mathemagician who has designed a course that is mathematically rigorous and yet entertaining and accessible to anyone with a basic knowledge of high school algebra.
Problems, Proofs, and Applications
Discrete mathematics covers a wide range of subjects, and Professor Benjamin delves into three of its most important fields, presenting a generous selection of problems, proofs, and applications in the following areas:
Combinatorics: How many ways are there to rearrange the letters of Mississippi? What is the probability of being dealt a full house in poker? Central to these and many other problems in combinatorics (the mathematics of counting) is Pascal's triangle, whose numbers contain some amazingly beautiful patterns.
Number theory: The study of the whole numbers (0, 1, 2, 3, ...) leads to some intriguing puzzles: Can every number be factored into prime numbers in exactly one way? Why do the digits of a multiple of 9 always sum to a multiple of 9? Moreover, how do such questions produce a host of useful applications, such as strategies for keeping a password secret?
Graph theory: Dealing with more diverse graphs than those that plot data on x and y axes, graph theory focuses on the relationship between objects in the most abstract sense. By simply connecting dots with lines, graph theorists create networks that model everything from how computers store and communicate information to transportation grids to even potential marriage partners.
Learn to Think Mathematically
Professor Benjamin describes discrete mathematics as "relevant and elegant"—qualities that are evident in the practical power and intellectual beauty of the material that you study in this course. No matter what your mathematical background, Discrete Mathematics will enlighten and entertain you, offering an ideal point of entry for thinking mathematically.
In discrete math, proofs are easier and more intuitive than in continuous math, meaning that you can get a real sense of what mathematicians are doing when they prove something, and why proofs are an immensely satisfying and even aesthetic experience.
The applications featured in this course are no less absorbing and include cases such as these:
Internet security: Financial transactions can take place securely over the Internet, thanks to public key cryptography—a seemingly miraculous technique that relies on the relative ease of generating 1000-digit prime numbers and the near impossibility of factoring a number composed of them. Professor Benjamin walks you through the details and offers a proof for why it works.
Information retrieval: A type of graph called a tree is ideal for organizing a retrieval structure for lists, such as words in a dictionary. As the number of items increases, the tree technique becomes vastly more efficient than a simple sequential search of the list. Trees also provide a model for understanding how cell phone networks function.
ISBN error detection: The International Standard Book Number on the back of every book encodes a wealth of information, but the last digit is very special—a "check digit" designed to guard against errors in transcription. Learn how modular arithmetic, also known as clock arithmetic, lies at the heart of this clever system.
Deepen Your Understanding of Mathematics
Professor Benjamin believes that, too often, mathematics is taught as nothing more than a collection of facts or techniques to be mastered without any real understanding. But instead of relying on formulas and the rote manipulation of symbols to solve problems, he explains the logic behind every step of his reasoning, taking you to a deeper level of understanding that he calls "the real joy and mastery of mathematics."
Dr. Benjamin is unusually well qualified to guide you to this more insightful level, having been honored repeatedly by the Mathematical Association of America for his outstanding teaching. And for those who wish to take their studies even further, he has included additional problems, with solutions, in the guidebook that accompanies the course.
With these rich and rewarding lectures, Professor Benjamin equips you with logical thinking skills that will serve you well in your daily life—as well as in any future math courses you may take.
LECTURES
24Lectures
In this introductory lecture, Professor Benjamin introduces you to the entertaining and accessible field of discrete mathematics. Survey the main topics you'll cover in the upcoming lectures—including combinatorics, number theory, and graph theory—and discover why this subject is off the beaten track of the continuous mathematics you studied in high school.
Combinatorics is the mathematics of counting, which is a more subtle exercise than it may seem, since the question "how many?" has at least four interpretations. Investigate factorials as well as the binomial coefficient, n choose k, which shows the number of ways that k things can be chosen from n objects.
As an overview of combinatorial concepts, explore 12 different interpretations of counting by asking how many ways x pieces of candy can be distributed among b bags. The answers depend on such factors as whether the candies and bags are distinguishable, and how many candies are allowed in each bag.
Devised to calculate the payout in games of chance, Pascal's triangle is filled with beautiful mathematical patterns, all based on the binomial coefficient, n choose k. Professor Benjamin demonstrates some of the triangle's amazing properties.
How many ways can you choose three scoops of ice cream from 31 flavors, assuming that flavors are allowed to be repeated? Using the method of "stars and bars," you find 5,456 possibilities if the order of flavors does not matter. The technique also works for counting endgame positions in backgammon.
Learn how the principle of inclusion-exclusion allows you to solve problems such as these: What is the probability that a five-card poker hand has at least one card in each suit? If homework papers are randomly distributed among students for grading, what are the chances that no student gets his or her own homework back?
Proofs by induction are a fundamental tool in any discrete mathematician's toolkit. This lecture guides you through several inductive proofs and then introduces geometric proof, also known as proof without words, and combinatorial proof. You see how all three techniques can prove properties of Pascal's triangle and Fibonacci numbers.
Investigate some interesting properties of Fibonacci numbers, which are defined using the concept of linear recurrence. In the 13th century, the Italian mathematician Leonardo of Pisa, called Fibonacci, used this sequence to solve a problem of idealized reproduction in rabbits.
Starting the section of the course on number theory, explore some key properties of numbers, beginning with what you know intuitively and working toward surprising properties such as Bezout's theorem. You also prove several important theorems relating to divisibility and prime factorization.
Study the building blocks of integers and how numbers can be created additively or multiplicatively. For example, every integer can be expressed as the sum of distinct powers of 2 in a unique way. Similarly, every integer is the product of a unique set of prime numbers.
Explore fascinating examples of two ideas: the pigeonhole principle, which can be used to prove that a mathematical situation is inevitable, such as that there must be a power of 3 that ends in the digits 001; and the parity principle, which is useful for proving that certain outcomes are impossible.
Introducing the important tool of modular arithmetic, Professor Benjamin uses the example of a clock to show how practically everyone is already adept with mod 12 arithmetic. Among the technique's many applications are the ISBN codes found on books, which use mod 11 for error detection.
Exploring more applications of modular arithmetic, examine the Chinese remainder theorem, used in ancient China as a fast way to count large numbers of troops. Also learn about password protection, the mathematics behind the "perfect shuffle," and the "seed planting" technique for raising big numbers to big powers.
Use modular arithmetic to investigate more properties of prime numbers, leading to a practical way to test if an integer is prime. At the same time, meet two important figures in the history of number theory: Pierre de Fermat and Leonhard Euler.
The idea behind public key cryptography sounds impossible: The key for encoding a secret message is publicized for all to know, yet only the recipient can reverse the procedure. Learn how this approach, widely used over the Internet, relies on Euler's theorem in number theory.
This lecture introduces the last major section of the course, graph theory, covering the basic definitions, notations, and theorems. The first theorem of graph theory is yet another contribution by Euler, and you see how it applies to the popular puzzle of drawing a given shape without lifting the pencil or retracing any edge.
Use matrices to answer the question, How many ways are there to "walk" from one vertex to another in a given graph? This exercise leads to a discussion of random walks on graphs and the technique used by many search engines to rank web pages.
Apply graph theory to social networks, investigating such issues as the handshake theorem, Ramsey's theorem, and the stable marriage theorem, which proves that in any equal collection of eligible men and women, at least one pairing exists for each person so that no extramarital affairs will take place.
Discover some interesting properties of tournaments that arise in sports and other competitions. Represented as a graph, a tournament must contain a Hamiltonian path that visits each vertex once; and at least one "king chicken" competitor who has either beaten every opponent or beaten someone who beat that opponent.
When you call someone on a cell phone, you can think of yourself as a leaf on a giant "tree"—a connected graph with no cycles. Trees have a very simple yet powerful structure that make them useful for organizing all sorts of information.
Professor Benjamin introduces the concept of a planar graph, which is a graph that can be drawn on a sheet of paper in such a way that none of its edges cross. Then, encounter the two simplest nonplanar graphs, at least one of which must be contained within any nonplanar graph.
According to the four-color theorem, any map can be colored in such a way that no adjacent regions are assigned the same color and, at most, four colors suffice. Learn how this problem went unsolved for centuries and has only been proved recently with computer assistance.
Examine more problems in graph theory, including the shortest path problem, the traveling salesman problem, and the Hamiltonian cycle problem. Some problems can be solved efficiently, while others are so hard that no simple solution has yet been found.
In his final lecture, Professor Benjamin reviews areas where combinatorics, number theory, and graph theory overlap. Then he looks ahead at topics that build on the course's solid foundation in discrete mathematics. He closes with a flourish of mathematical magic, including the "four-ace surprise."
Dr. Arthur T. Benjamin is Professor of Mathematics at Harvey Mudd College, where he has taught since 1989. He earned a B.S. from Carnegie Mellon University in 1983 and a Ph.D. in Mathematical Sciences from Johns Hopkins University in 1989.
Professor Benjamin's teaching has been honored repeatedly by the Mathematical Association of America (MAA). In 2000, he received the MAA Deborah and Franklin Tepper Haimo National Award for Distinguished College or University Teaching of Mathematics. The MAA also named Professor Benjamin the 2006–2008 George Pólya Lecturer.
His research interests include combinatorics, game theory, and number theory, with a special fondness for Fibonacci numbers. He is also a professional magician, whose techniques are explained in his book Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks. He is coauthor of Proofs That Really Count: The Art of Combinatorial Proof, which received the Beckenbach Book Prize from the MAA. Professor Benjamin also served for five years as coeditor of Math Horizons magazine.
Professor Benjamin has appeared on dozens of television and radio programs and has been featured in publications, including Scientific American, People, and The New York Times. In 2005, Reader's Digest called him "America's Best Math Whiz."
VIDEO OR AUDIO?
This course features thousands of visual elements that make discrete mathematics clear, including detailed animations, graphics, and on-screen text of formulas and equations. |
Mathematics courses are demanding and it is very important
for your success that you be correctly placed. Since there is a strong
correllation between students' grades in a class and
Mathematics Placement
levels, you are VERY strongly advised to follow the guidelines
below. (Note: although a D is a passing grade, a C in the
prerequisite course is required for the next course in a calculus
sequence or for most other courses requiring mathematics as a prerequisite.)
BASIC MATHEMATICS COMPETENCE.
This is attained by fulfilling ONE of the
following conditions:
75 or more on the Regents Sequential III exam; 525 or more in Math SAT II;
560 or more in Math SAT I; 56 or more in the Math part of PSAT; 23 or
more in ACT Math test; Math Placement Level 3, or C or better in
MAP 103 or an equivalent course.
SATISFACTION OF DEC CATEGORY `C'.
DEC category C is satisfied by a grade of C or better in any
mathematics course of at least 3 credits
and with a prerequisite of at least Basic Mathematics
Competence. In particular, all courses below
except MAP 101, MAP 103, MAT 130 and MAT 160 satisfy
DEC category C.
MAP 103: Proficiency Algebra.
Essential preparation for students who need an introduction to
or review of high school algebra, in preparation for other
mathematics.
Completion of this
course satisfies the Basic Mathematics Competence requirement.
Does not count towards graduation but counts toward semester
credit load. Students obtaining C or better
can continue into any class in mathematics or statistics
that requires Placement Level 3.
PLACEMENT LEVEL 2+ AND SATISFACTION OF SKILL 1,
BASIC MATH COMPETENCE
AMS 101-C: Applied Precalculus (3 credits)
An applied course on precalculus topics that is intended
as a terminal mathematics course for most students. Can also serve
as a preparation for MAT 122. Students with an A or A- can
continue into MAT 125 by taking MAT 130 (1 credit) at the same
time as MAT 125.
AMS 102-C: Elements of Statistics (3 credits)
An introduction to statistics
for a general audience, covering common ways to describe
data and test statistical hypotheses about data. Multiple sections:
lectures with either 55 students taught by TAs or 120 students
taught by faculty.
MAT 118-C: Mathematical Thinking (3 credits)
Suitable for those whose programs do not require calculus.
Topics include: logic and reasoning, numbers, graphs,
functions and modeling, combinatorics and probability.
Through experience in problem solving, students develop appreciation for
the intellectual scope of mathematics.
Students who place at level 2+ and plan to take calculus shouuld
re-take the mathematics placement exam after thorough studying and review.
Those whose final grade is 2+ should take MAP 103 Proficiency Algebra
for best preparation for future calculus courses.
Students who place at level 3 and need only a one-semester
overview should take MAT 122 Overview of Calculus with Applications.
Students who place at level 3 and plan to take additional calculus
courses should take MAT 123 Introduction to Calculus.
These sequences all cover approximately the same syllabus, but differ
in the speed with which material is presented, the amount of emphasis laid on
applications and
in the teaching methods used. Since MAT 125, 126, 127 takes 3 semesters,
it is the best choice
for students who need extra time to assimilate the material.
The classes MAT 125, 126, 127, 131 and 132 all use the same
textbook (Stewart: Calculus, Concepts and Contexts).
This emphasizes conceptual understanding and graphical methods
and at the same time develops algebraic and computational skills.
AMS 151 - 152 uses
the more applications-oriented text
(Hughes Hallett: Calculus, 2nd edition).
MAT 141 - 142 uses
(Thomas and Finney: Calculus, 9th edition) which more thoroughly
explores foundational ideas.
Important Note: All students in MAT 125, MAT 131, MAT 141 and AMS
151 will take a common exam
on Tuesday evening, September 14, at 8:30 pm.
A detailed syllabus and sample questions are available
here.
This exam is intended to ensure that students are correctly placed,
and students may be advised to change their registration
on the basis of their score. The exam counts as 10% of
the final grade in these courses; it will be regraded on an
appropriate scale if the student changes to a different
math course.
PLACEMENT LEVEL 3:
MAT 122-C: Overview of Calculus with Applications
(3 credits) A
brief overview of differential and integral calculus, including exponential
and logarithmic functions and the fundamental theorem,
intended for students who
only want to take one semester of calculus.
Satisfies the mathematics requirements for the Psychology and Economics
majors.
Students who later decide to take more calculus
must take the one credit MAT 130 at the same time as MAT 125 or 131.
Textbook: Hughes-Hallett, Applied Calculus.
MAT 123-C: Introduction to Calculus (3 credits)
Comprehensive
preparation for the regular calculus sequence including an introduction to
differential calculus. Trigonometric, exponential and logarithmic functions,
asymptotics and limits. Students may go on to MAT 125, 131, 141 or AMS 151.
Textbook: a custom version of Stewart: Precalculus and Calculus.
PLACEMENT LEVEL 4:
MAT 125-C: Calculus A
(3 credits) Differential calculus emphasizing
conceptual understanding,
computations and applications. Multiple secitons:
lectures of 140 students twice a week with
recitations of 35 students twice a week. Followed by
MAT 126 and MAT 127. Engineering and pre-engineering students
at level 4 may elect to take MAT 131; however MAT 131 will move
at a significantly faster pace.
MAT 130: Functions (1 credit)
Intended to bridge the gap between
MAT 122 and the regular calculus sequence by a detailed discussion of
the properties of functions, especially trigonometric, exponential
and logarithmic functions. Spring only.
PLACEMENT LEVEL 5:
Note: Students may choose among the following
courses. Both AMS 151 and MAT 141 are small classes intended for especially
well motivated students.
MAT 131-C: Calculus I
(4 credits) Differential and integral calculus
emphasizing conceptual understanding, computations and applications.
Multiple sections: lectures
of 70 students twice a week with
recitations of 35 students twice a week.
AMS 151-C: Applied Calculus I (3 credits)
A calculus course that uses
extensive applications to motivate the study of single-variable
calculus. Two classes of 40 students that use collaborative learning with
little lecturing. Intended primarily for CEAS majors.
Fall only.
MAT
141-C: Honors Calculus I (4 credits)
An enriched version of MAT
131 with greater emphasis on the underlying theory of calculus.
One section: lecture of 70 students twice a week with
recitations of 35 students twice a week.
PLACEMENT LEVEL 6:
Note:
Students who place at Level 6 or beyond and who are also taking
Physics in their first year should take
MAT 126 or another second semester calculus class.
MAT 126-C: Calculus B
(3 credits)
A continuation of MAT 125 covering integral calculus
and the fundamental theorem of calculus.
Multiple secitons:
lectures of 140 students twice a week with
recitations of 35 students twice a week.
PLACEMENT LEVEL 7:
MAT 132-C: Calculus II
(4 credits)
A continuation of MAT 131 covering applications of integration,
infinite series and differential equations.
In Fall 99, one section: lecture of 180 students twice a week with
recitations of 35 students twice a week. In Spring. lectures of 70.
AMS 161-C: Applied Calculus II(3 credits)
A continuation of AMS 151.
Sections of 40 students that use collaborative learning with little lecturing.
Spring only
MAT 142-C: Honors Calculus II
(4 credits)
An enriched version of MAT
132 with greater emphasis on the underlying theory of
calculus. One section: lecture of 30 students twice a week,
recitation twice a week.
PLACEMENT LEVEL 8:
Students may choose from among MAT 127, 132, 142 and AMS 161.
Students interested in the physical sciences are encouraged to take
MAT 142.
MAT 127-C: Calculus C
(3 credits) Infinite series and differential equations.
Completes the 125, 126, 127 sequence. Will incorporate some use of Web-based
homework on computers, as well as some use of computer-aided problem solving
(using Maple).
Of special interest to all students:
A one credit course, MAT 160: Mathematical Problems and
Games, is also offered each semester. It has S/U grading and helps
students at all levels sharpen their problem solving skills and
their ability to formulate and express mathematical ideas, through
challenging puzzles and problems.
(Does not satisfy DEC category C.)
Note to students planning to take physics courses:
Those who place at level 4 should take PHY 125. Those who place at
level 5 should take PHY 131.
June 3, 1999 |
HCD 85: Diagnostic Learning in Mathematics
This course is designed for students with disabilities who have difficulty learning mathematics through traditional modes of instruction. The emphasis is on assisting students with learning disabilities to prepare for college-level mathematics. It offers individualized, self-paced instruction based upon students/' current skills and educational goals. This course may be taken four times for credit.... more »
Credits:2
Overall Rating:0 Stars
N/A
Thanks, enjoy the course! Come back and let us know how you like it by writing a review. |
Learn More!
For each chapter, this section provides a step-by-step worked-out example of
a computational problem from the book. Be sure that you understand each step before
moving on, and don't be afraid to take your time with each problem. |
test if a given sequence is an Arithmetic Progression or not and be capable of finding a formula for the nth term, find any term in the A.P. and to solve problems involving these concepts.
Objective: On completion of the lesson the student will be able to make an arithmetic progression between two given terms. This could involve finding one, two, or even larger number of arithmetic means.
Objective: On completion of the lesson the student will be able to test if a given sequence is a Geometric Progression or not and be capable of finding a formula for the nth term, find any term in the G.P. and to solve problems involving these concepts.
Objective: On completion of the G.P. lesson the student will understand the compound interest formula and how to use it and adjust the values of r and n, if required, for different compounding periods.
Objective: On completion of the lesson the student will be able to identify the hypotenuse, adjacent and opposite sides for a given angle in a right angle triangle. The student will be able to label the side lengths in relation to a given angle e.g. the side c is op
Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles in questions that are more difficult than previously completed. Students will also learn to use other geometric properties as well as set out log
Objective: On completion of the lesson the student will be able to identify which geometric properties are needed to complete a question and be able to use formal reasoning to write out this information.
Objective: On completion of the lesson the student will be able to find the surface areas of cones by finding the area or the base 'p r . 'and the area of the curved surface ' p r l'. The student will also be able to find the slant height 'l' given the perpendicul
Objective: On completion of the lesson the student will be able to: use formulae to find the volume of prisms, calculate the volume of a variety of prisms, and explain the relationship between units of length and units of volume.
Objective: On completion of the lesson the student will be able to: calculate the volume of cylinders, spheres and hemispheres using the appropriate formulae, and use the relationship between litres and other measures of volume.
Objective: On completion of the lesson the student will be able to: dissect composite solids into simpler shapes so that the volume can be calculated, calculate the volume of a variety of composite solids, and use formulae appropriately.
Objective: On completion of the lesson the student will be able to use the Sine rule to find the length of a particular side when the student is given the sizes of 2 of the angles and one of the sides.
Objective: On completion of the lesson the student will understand how to find the first derivative of various functions, and use it in various situations to identify increasing, decreasing and stationary functions.
Objective: On completion of the Calculus lesson the student will be able to find a second derivative, and use it to find the domain over which a curve is concave up or concave down, as well as any points of inflexion.
Objective: On completion of the Calculus lesson the student will be able to use the first and second derivatives to find turning points of a curve, identify maxima and minima, and concavity, then use this information to sketch a curve.
Objective: On completion of this lesson the student will be able to define basic logarithmic functions and describe the relationship between logarithms and exponents including graph logarithmic functions. The student will understand the relationship between logarit
Objective: On completion of the lesson the student will be able to state whether matrix by matrix multiplication is possible, predict the order of the answer matrix, and then perform matrix by matrix multiplication.
Objective: On completion of the lesson the student will be able to place ordered pairs into a matrix, then perform translation by addition using a transformation matrix, then extract ordered pairs from an answer matrix.
Objective: On completion of the lesson the student will be able to convert ordered pairs to elements of a matrix, multiply matrices together, where possible, and interpret the answer matrix on a number plane |
MCS119 Calculus with Pre-calculus Review 1b (Spring 2012)
General
Day to Day
Course Description
Prerequisite
MCS 118
Text
Calculus I with Precalculus, 2nd Edition, by Larson, Hostetler and Edwards
Calculators
You should have a graphing calculator available for use in class and on exams.
If you are buying a new one, we encourage the use of Texas Instruments calculators,
in particular the TI83/84 Plus, TI83/84 Plus Silver Edition, or the TI89 (though
the use of some of its features may be restricted, so that I will want you to use
another calculator on quizzes and tests). If you have the standard version
of any of these calculators there is no need to purchase a new calculator.
If you have another brand of calculator please see me before purchasing a new one
as you may be able to continue using it.
Classes
Classes will be used for discussions, problem solving, lectures, and other fun
activities. You should prepare for classes by doing the reading beforehand,
thinking about the problems in the text, doing the prep problems, and formulating
questions of your own. You should also participate as much as possible in class.
Class meetings are not intended to be a complete encapsulation of the course
material. You will be responsible for learning some of the material on your own.
Two comments:
Attendance, both physical and mental, is required. We reserve the right to lower your
grade if you habitually miss class or fail to participate in class.
Texting is not permitted in class. If you receive an urgent phone call, please just leave the
class quietly and deal with the call.
Absences from class
Should you need to miss a class for any reason, you are still responsible for
the material covered in that class. This means that you will need to make sure
that you understand the reading for that day, that you should ask another student
for the notes from that day, and make sure that you understand what was covered.
If there is an assignment due that day, you should be
sure to have someone hand it in. You do not need to explain why you missed a class
unless there is a compelling reason to do so.
Homework
You will need to read a section or two of the
book and do problems for each day that we have class. The homework page
lists the assignments and their due dates. You should only hand in
the required homework. Our graders will grade some of the required ones.
Homework problems are designed to help you learn the material we cover
in class and in the reading. You should read the material and attempt
the problems before coming to class. You should finish the problems
after class. Approximately twice a week, you will hand in your
solutions to the required homework that is due. These should be neatly
written on standard sized paper, and with all of the pages stapled
together. The sections and problem numbers should be clearly
labeled. My grader will only grade a few sample problems.
On the day that study problems are due, you will be asked to place your work in the red homework folder. After
class, I place the folder outside my office door for the grader. Any homework that is not in this folder when
the grader gets it is considered late. Late homework will be accepted as long as I get it before my grader hands
back the graded assignments. (Alternatively, you can put it in the blue folder for late homework.) In that case,
the homework will be graded but you will lose 30% of the points on that assignment.
Prep problems
Prep problems are generally very simple problems to encourage you to read the text before coming to class.
Sometimes they are review and other times simple questions about the reading in the given section. There are
generally two prep problems for each section. Prep problems are always done using Moodle and you will need to
play close attention to the Moodle page and the course schedule to keep up with these assignments. Prep problems
should be completed before coming to class as we have set up Moodle to "close" the quiz during class and thus
you will not be able to complete them after class. Here are a few pointers on approaching these problems:
Read the text then complete the prep problems.
You can do them multiple times, so if you get one wrong you can try again. Each time you submit a wrong answer 0.1 points is subtracted from your score.
We drop the lowest 3 scores. There are no "make-ups".
Because these are only worth 5% of your course grade, you should probably limit the amount of time you spend on them to no more than 10 minutes
Quizzes and Exams
We will have four in-class quizzes during
the semester, as well as two evening exams and a final exam. These quizzes and exams will make
up the majority of your semester grade. In particular, be sure not to
underestimate the importance of quizzes. If you do poorly on quizzes,
you will do poorly in the course.
Course grade
I will provide you with a grade on each assignment and quiz, in addition
to the mid-term and final grades, so that you may keep track of your
performance. As a guideline, the components will contribute in the following
proportion to the final grade:
Prep problems
5%
Homework
15%
Quizzes
20% (5% each)
Evening exams
40% (20% each)
Final Exam
20%
Note: As noted above, we reserve the right to lower your course grade if you habitually miss class or don't participate.
Academic Integrity
You are expected to to adhere to the highest standards of academic honesty, to uphold the Gustavus Honor Code and
to abide by the Academic Honesty Policy. A copy of the honor code can be found in the
Academic Bulletin and a copy of the academic
honesty policy can be found in the Academic
Polices section of the Gustavus Guide.
On homework, you should make a real effort to solve each problem by
yourself, although you can and should discuss problems and their
solutions with your classmates after you've made this effort. You
should give credit to any people or texts that helped you find
solutions. On tests, you are expected to work completely by
yourself
You will be expected to sign the honor pledge on every quiz and
exam.
A first violation of the honor code will result in a grade of 0 on
the assignment in question. Any further violations will result in a
grade of F for the course. In all cases, I notify the office of the
Provost.
Disability Services
Gustavus Adolphus College is committed to ensuring the full participation of all students in its programs. If you
have a documented disability (or you think you may have a disability of any nature) and, as a result, need reasonable
academic accommodation to participate in class, take tests or benefit from the College's services, then you should
speak with the Disability Services Coordinator, for a confidential discussion of your needs and appropriate plans.
Course requirements cannot be waived, but reasonable accommodations may be provided based on disability documentation
and course outcomes. Accommodations cannot be made retroactively; therefore, to maximize your academic success at Gustavus,
please contact Disability Services as early as possible. Disability Services
is located in the Advising and Counseling Center.
Help for Students Whose First Language is not English
Support for English Language Learners (ELL) and Multilingual students is available via the College's ELL Support staff
person, Andrew Grace (7395). He can meet individually with students to consult about academic
tasks and to help students seek other means of support. The ELL Support person can also consult with faculty members
who have ELL and multilingual students enrolled in their classes. The College's ELL staff person can provide students
with a letter to a professor that explains and supports academic accommodations (e.g. additional time on tests,
additional revisions for papers). Professors make decisions based on those recommendations at their own discretion.
In addition, ELL and multilingual students can seek help from peer tutors in the Writing Center. |
MAA Review
[Reviewed by Tom Schulte, on 01/12/2011]
This slim collection of varied visual "proofs" (a term, it can be argued, loosely applied here) is entertaining and enlightening. I personally find such representations engaging and stimulating aids to that "aha!" moment when symbolic argument seems not to clarify. Since such pictures can be found sprinkled in the pages of many mathematics periodicals and even in the occasional textbook, others obviously feel the same way. A collection of a gross of them in a single volume is really a delight to peruse.
The proofs are arranged by topic into six main chapters: Geometry & Algebra, Trigonometry, Calculus & Analytic Geometry, Inequalities, Integer Sums, Sequences & Series, and a final chapter of Miscellaneous. Geometry & Algebra leads off with the classic subject for this approach: the Pythagorean Theorem. This includes one of my favorites, the one by President James Garfield. Having several to compare can be particularly illustrative (literally) of how proof-like reasoning can be done in an image. I would wager that any student that can apply the Pythagorean to find a missing side of a right triangle can also, with little or no help, figure out how most of these Pythagorean proofs "work". Of course, this particular theorem lends itself very well to such an approach, which makes it very apt initial material
The Inequalities chapter presents various approaches to the five basic means and slightly more arcane inequalities, such as the Cauchy-Schwarz Inequality and those of Napier, Bernoulli, and Aristarchus. Up to this point an ambitious high school student or college student in first semester calculus would make fine progress.
This leads me to my only complaint here. This book is part of the MAA's Classroom Resource Materials and as a teacher I find it an excellent resource to enliven the odd lecture. However, I also like to think of the independent mathematics enthusiast with this book in hand and in that situation I feel an opportunity was missed to add a few words of explanation here and there. For example, one could point out the geometric connection to topics such as inner product spaces and norms, or include a sentence or two on combinatorial notation, or describe the simple choreography that results in a cycloid.
Of course, very few pages here could really benefit from such added verbiage and a diligent reader will still enjoy the book even if a few of the proofs require further investigation. The collection does have a good explanation for the confection-inspired optical illusion of The Problem of Calissons. Along with non-attacking queens and characteristic polynomials, this is in the final miscellany section. Whether one is seeking to ornament undergraduate lectures or simply to exercise one's mathematically-inclined mind, this book is a worthwhile purchase.
Tom Schulte surprises the occasional drowsy undergrad with visual proofs at Oakland Community College in Michigan.
BLL* — The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries. |
The LIFEPAC Math (Algebra I) complete set contains all 10 student workbooks for a full year of study plus the comprehensive Teacher's Guide.
Topics covered include:
Variables and Numbers
Solving Equations
Problem Analysis and Solution
Polynomials
Algebraic Factors
Algebraic Fractions
Radical Expressions
Graphing
Systems
Quadratic Equations and Review Lifepac Math, Grade 9 (Algebra I), Complete Set
Review 1 for Lifepac Math, Grade 9 (Algebra I), Complete Set
Overall Rating:
5out of5
Lifepac 9 Math
Date:June 11, 2012
AnnaExcellent as a primary math book, and the teacher's guide has all the ideas you would need for anything "extra", based on the student's needs. Combining the Grade 9 with the Grade 10 Lifepac Math is also an excellent idea, depending on your classes motivation and progress.
Share this review:
0points
0of0voted this as helpful.
Review 2 for Lifepac Math, Grade 9 (Algebra I), Complete Set
Overall Rating:
5out of5
Date:June 17, 2010
Karen Breland
This is my first time to use the Lifepac curriculum and I must say I am very pleased with it. The lessons are very easy to understand. I have ordered this for a refresher for my daughter over the summer. I will most likely be using this curriculum for all of her subjects in the fall.
Share this review:
+1point
1of1voted this as helpful.
Review 3 for Lifepac Math, Grade 9 (Algebra I), Complete Set
Overall Rating:
4out of5
Date:November 17, 2008
James Clark
It is a great curriculum but it would be better served by having more self testing areas more often.
Share this review:
+1point
1of1voted this as helpful.
Review 4 for Lifepac Math, Grade 9 (Algebra I), Complete Set
Overall Rating:
5out of5
Date:September 27, 2007
Laura Savin
Very detail material. Make sure your student comprehends the pre-algebra first before doing this. In the beginning it's easy, as you go further it gets harder but has good examples to go by and explanations.
Share this review:
+1point
1of1voted this as helpful.
Review 5 for Lifepac Math, Grade 9 (Algebra I), Complete Set
Overall Rating:
4out of5
Date:September 14, 2007
Mimi Robinson
After having tried ABeka and Saxon I felt this gave more opportunity for comprehension than the others. It also is set up to work at a at your own pace style. Love It! |
Mathematical Excursions - 3rd edition
Summary: MATHEMATICAL EXCURSIONS, Third Edition, teaches students that mathematics is a system of knowing and understanding our surroundings. For example, sending information across the Internet is better understood when one understands prime numbers; the perils of radioactive waste take on new meaning when one understands exponential functions; and the efficiency of the flow of traffic through an intersection is more interesting after seeing the system of traffic lights represented in a math...show moreematical form. Students will learn those facets of mathematics that strengthen their quantitative understanding and expand the way they know, perceive, and comprehend their world. We hope you enjoy the journey. ...show less
1111578494 |
This course covers mathematical principles and tools used the development of algorithms and the analysis of their feasibility and performance. Topics are generally in the domain of discrete mathematics: propositional and predicate logic, mathematical proofs including induction, counting and basic probability theory, logarithmic and exponential functions, elementary graph theory, and complexity analysis. Prerequisites: none. Spring.
Other academic years There is information about this course number in other academic years: |
Our International GCSE in Mathematics (specification A) aims to give students a foundation in mathematical skills and develop their knowledge and understanding of how to use and apply mathematical techniques and concepts to solve problems. It is suitable for delivery in schools and colleges and is a two-tiered qualification, graded A* to G. Assessment is via two examinations. Read more
Results for this qualification will be only be recorded in school performance tables up until 2013. |
A is for Algebra-and that's the grade you'll pull when you use Bob Miller's simple guide to the math course every college-bound kid must take. With eight books and more than 30 years of hard-core classroom experience, Bob Miller is the frustrated student's best friend. He breaks down the complexities of every problem into easy-to-understand pieces... more...
Bob Miller's fail-safe methodology helps students grasp basic math and pre-algebra. 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... more...
Everything you need to know to ace the math sections of the NEW SAT!. He's back! And this time Bob Miller is helping you tackle the math sections of the new and scarier SAT! Backed by his bestselling ''Clueless'' approach and appeal, Bob Miller's second edition of SAT Math for the Clueless once again features his renowned tips, techniques, and insider... more...
With Bob Miller at your side, you never have to be clueless about math again!. Algebra and calculus are tough on high school students like you. Professor Bob Miller, with more than 30 years' teaching experience, is a master at making the complex simple, and his now-classic series of Clueless study aids has helped tens of thousands understand the... more...
A memoir of growing up in mob-run Sin City from a casino heir-turned-governor who?s seen two sides of every coin When Bob Miller arrived in Las Vegas as a boy, it was a small, dusty city, a far cry from the glamorous, exciting place it is today. Driving the family car was his father Ross Miller, a tough guy?though a good family man?who had operated... more...
This second edition is an extensive modernization of the bestselling introduction to the subject of adaptive array sensor systems. With the number of applications of adaptive array sensor systems growing each year, this look at the principles and fundamental techniques that are critical to these systems is more important than ever before. Introduction... more...
Effectively managing people, facilities, and partnerships can make or break an institution. In this book, we look at managing those paid or unpaid staff who contribute daily to the museum, provide tools for operations, address maintenance and safety issues, and discuss collaboration with outside organizations. more...
Small museums need affordable ways to provide care for their collections and the tools to lobby for additional funds for their long-term health. In this book, we offer practical tips for collections care, including preservation strategies for historic properties, strategies for managing collections, developing policies, and planning for the future... more... |
Calculus Derivatives and Integrals MatchingManiaCalculus Derivatives and Integrals MatchingMania consists of 2 activities - Natural Log & Exponentials and Trig Functions. Students are given at least 10 functions and work with a partner to find the inegral as well as the first and second derivative of the original function. They match the problem to its answers and complete a worksheet to return to the teacher. This activity is a great review activity for the AP test.
This activity is also available in the Advanced Math MatchingMania Book. This book includes 10 other similar activities.
PDF (Acrobat) Document File
Be sure that you have an application to open this file type before downloading and/or purchasing.
60.18 |
Math
1050, Summer 2012
Instructor: Dr. Seth Armstrong, ELC 402, email: [email protected]. Please communicate by email if
possible; I check voice mail about once per decade. If you have an emergency
(not just that you aren't coming to class one day, but maybe something I really
need to know), you may text or call at 590-4516. There will often be things
posted on my web page – including this syllabus and previous exams – at
Meeting times and Office hours: Consultation in my
office will be daily from 1:30-2:30 p.m. If it is not possible for you to make my
office hour, please talk to or email me to schedule another time.
Prerequisite: Intermediate Algebra (Math
1010) with at least a C or a math ACT of 23, either within the last two years.
You may also use the Accuplacer to test into Math 1050.
Objectives: To explore the concept
of functions: linear, polynomial, rational, inverse, logarithmic and
exponential, with an emphasis on graphing and applications; to study polynomials
and the fundamental theorem of algebra; to solve systems of equations using
matrices; to learn conic sections. A graphing calculator will be used in the
course.
Policies and
Procedures:
1.Attendance is required.
I will be unwilling to go through material that you miss without excuse. I
will drop your lowest 100-pt test score (see #3) if it helps your grade if you
have no unexcused absences.
2.If you are
not in a position to complete each homework (HW) assignment before the next
meeting time you should probably drop the course. We move very fast –
especially in Summer II – and it will be essential to have HW almost completed
before the next day's lecture. You should do your HW as independently as
possible: That is, do all you can first on a problem before seeking
outside help. This is because struggling through a problem for a while on your
own is the best way to learn difficult material. College Algebra is not an easy
course for most students, so keeping up and being constantly engaged will be
very important. Homework will be turned in about every other day on those days
marked with an asterisk (*); it is due in class or by 2:30 outside my office
and is up through the material covered the previous day. It should be neat with
the problems done in order and should show complete work to receive credit. Though
it will be looked at and assigned some credit, our course TA can grade very few
problems. Therefore, it will be up to you to check with the back of the book to
make sure you get the correct answers and seek help if you can't get them. I
will not give any time extension on the HW except for prolonged excuses. Late
HW will not be accepted. The Math Tutoring Lab is open for business in summer
and you should plan to live there, at least for a few hours per day….
3.Only three
of your four exam scores will count toward your grade unless you have too many
absences (see #1). Should you fall ill or have to be gone for some legitimate
excuse during testing days, email me to schedule a makeup test and let me know
when you are available the next day or two to make it up. If you wait more than
one day to contact me, then the score on the test you miss will simply
be a zero regardless of excuse (i.e., so if you have been absent less than the
allotted days, that will be your dropped one). You must be prepared to provide
documentation for missing a test. The exams will be administered in the Testing
Center on the bottom floor of the ELC. Do not plan on "dropping" any tests so
if you get a lower score on a later exam you don't have to
count that score toward your grade.
4.Academic Integrity: Scholastic dishonesty
will not be tolerated and will be prosecuted to the fullest extent. You are
expected to have read and understood the current issue of the student handbook
(published by Student Services) regarding student responsibilities and rights
for information about procedures and about what constitutes acceptable
on-campus behavior. HW
plagiarism (copying from a solutions manual or someone else's HW) will result in a
zero on any assignment; if it is repeated, you will get a zero on the entire HW
score (of 50 points). Passing any test information to another student
that hasn't yet taken it is prohibited and dishonest and will also be fully
prosecuted.
5.The
sharing of copyrighted material through peer-to-peer (P2P) file sharing, except
as provided under U.S. copyright law, is prohibited by law. Detailed
information can be found at http://
6.Students with medical,
psychological, learning or other disabilities desiring academic adjustments,
accommodations or auxiliary aids will need to contact the Southern Utah
University Coordinator of Services for Students with Disabilities (SSD), in
Room 206F of the Sharwan Smith Center or phone (435)865-8022. SSD determines
eligibility for and authorizes the provision of services.
7.In
case of emergency, the University's Emergency Notification System (ENS) will be
activated. Students are encouraged to maintain updated contact information
using the link on the homepage of the mySUU portal. In
addition, students are encouraged to familiarize themselves with the Emergency
Response Protocols posted in each classroom. Detailed information about the
University's emergency management plan can be found at
emergency-procedures.html.
8.Grading The total
will be 500 or 600 points, including 50 total from HW, 300 or 400 from the
one-hour tests (see Item 3) and then 150 from the final exam. The grading scale
will be the following. Please note that I will not raise a grade because of
need. It is up to you to get the grade you want. |
For two years I have focused my classroom approaches on developing student habits of mind with problem solving processes. Through my classroom inquiry into these approaches I have learned that students can learn to solve problems in ways that help them develop "habits of mind" with problem solving processes if:
Students get lots of problem solving practice, with an emphasis on long term learning of habits of mind
Students are introduced to the idea of multiple representations early, and this approach is reinforced through the curriculum materials in meaningful ways and in all aspects of the course
Students have many opportunities to share their problem solving "publicly" through board work
On this Web site, you will see how the components of a Problem Solving Process were integrated into class activities, homework, and pedagogy (interventions), as well as the assessment of student work through homework, class presentations of their solutions, and final exams.
Through different measures I have learned about how this approach improves student learning and increases student self-confidence, which I believe is one of the most important long term goals of the course.
I have been a member of the Math Developmental Ed Committee at Los Medanos College almost since its founding. I have also been a member of several teaching communities that have focused on Intermediate Algebra, Elementary Algebra and PreAlgebra. I was also involved in a review of teaching of Calculus and Pre-Calculus at Los Medanos, as well as participating in several workshops for the teaching of Calculus. I have an abiding interest in the search for effective computer-aided instruction (CAI) that may be infused into my teaching strategies.
The course that was the focus of my project is Intermediate Algebra. This class is the pre-requisite course for any transferable Math course to a 4-year college. A link below will open the Course Outline of Record (COOR) for Intermediate Algebra at Los Medanos College. |
epub shortcomings, mathematics
epub shortcomings, mathematics |
25
Total Time: 3h 37m
Use: Watch Online & Download
Access Period: Unlimited
Created At: 12/02/2008
Last Updated At: 07/20/2010
Taught by Professor Edward Burger, these lessons were really helped me work with Complex Rational Expressions. I was really lost when dealing with these buggers but I watched the video 5 times before I really began to understand these expressions. Everything was explained clearly in the video. I will be looking for a part 2 to this topic.
I was struggling to grasp this concept when reviewing for an exam, as the examples in my text were not sufficient enough. This video was able to articulate the concept in a very clear manner and I can finally exhale and feel confident going into my exam. Thanks!
I love how animated his style is; it makes his teaching style even more engaging. Even when you thought it couldn't get more interesting, his bright orange tie makes it that much more fun to watch his lessons.
But to rate his lesson based on knowledge and ability to teach, I would give it a 10. It's so much easier to learn from a video tutorial than it is for me to read a textbook or sit through a lecture. I can start and stop whenever I want and take breaks without interrupting a class, etc. It's so much easier for me to learn at my own pace! Having these videos on integral algebra online makes me very happy.
Very happy indeed.
Below are the descriptions for each of the lessons included in the
series:
Int Algebra: Solving a Mixture Problem
In this lesson, you will learn how to approach word problems that involve equalities and ratios or fractions percentages, ratios, recipes, mixes, etc an Average
In this lesson, you will learn how to approach word problems that involve averages or means averages or means (many of which include grades or scores Factor Sums and Differences of Cubes
In this lesson, you will learn how to factor the difference of two cubes and how to factor the sum of two cubes. Neither of these are simple factorizations, so Professor Burger will show you what the factorization is and then explain where it comes from. Additionally, he'll show you some ways to remember what these factorizations are. (x^3 - y^3) = (x - y)(x^2+xy+y^2) and (x^3+y^3) = (x+y)(x^2-xy+y^2) Long Division with Polynomials
You know how to use long division to divide two numbers; you can also use long division when dividing polynomials. In this lesson, Professor Burger will review with you how to long divide and then show you how to use long division with polynomials (to evaluate things like (x^4+3x^2-5x-10)/(X^2+3x-5) ). When long dividing, you often end up with a remainder, and this will be the case when using long division on polynomials, as well. This lesson will show you how to find both the quotient and the remainder when dividing two polynomials using long division Synthetic Division with Polynomials
You know how to use long division to divide two numbers; you can also use long division when dividing polynomials. In this lesson, Professor Burger will show you how to eliminate several of the steps in long division by u sing synthetic division. Synthetic division only works when you are dividing by (x + ?) or (x - ?) where ? is a number. In synthetic division, you start by using the coefficients of the polynomial in the numberator with switched signs. In the end, you will end up with the same answer for both the quotient and remainder as you would using long division, but it will be a less harrowing path to get there Multiply-Divide Rational Expressions
In math, a rational expression or rational function is any function which can be written as the ratio of two polynomials. These are inevitably expressed as fractions. In this lesson, you will learn how to multiply and divide rational functions. Rational expressions can be multiplied or divided just like fractions. In walking you through examples of this type of multiplication and division, Professor Burger will highlight things to watch out for and shortcuts that can help you along the way. He will also show you why dividing is the same thing as multiplying by the reciprocal Add-Subtract Rational Expressions
In math, a rational expression or rational function is any function which can be written as the ratio of two polynomials. These are inevitably expressed as fractions. In this lesson, you will learn how to add and subtract rational functions. As with any fractions, to do this, you'll need to find a common denominator. In walking you through examples of this type of addition and subtraction, Professor Burger will highlight things to watch out for and shortcuts that can help you along the way Rewriting Complex Fractions
In math, a rational expression or rational function is any function which can be written as the ratio of two polynomials. These are inevitably expressed as fractions. Dealing with complex rational expressions is the same basic thing as dealing with other rational functions. In a complex rational expression, you generally end up with a variable within a fraction that's with another fraction that also includes another variable. The approaches to addition, subtraction, multiplication and division that are used with simple rational expressions all work the same here. You will need to invert and multiply in order to divide and you will need to find common denominators and least common multiples, etc. In this lesson, you will see a series of examples to see how these complex rational expressions are handled (things like (1/(1/x))/(1/(1/x)^2)). Containing Radicals
When working with equations, you often end up with a radical of some sort (like a square root) on one side of the equation. These type of equations are called radical equations because they contain a square root. To evaluate this type of equation, you'll want to get rid of the radical. This lesson will show you how to approach and solve this type of equation by getting rid of the radical (by isolating the radical alone on one side of the equals sign and then squaring both sides of the equation). When evaluating this type of equation, you will always want to check your solutions in the original equation to make sure that you don't end up with an extraneous root as a solution. Even if the equation solves to give you an extraneous root, it is not a valid solution. An extraneous root is something that is a root to the quadratic but not to the original equation with Two Radicals
In this lesson, Professor Burger will show you how to solve equations that contain two radicals (roots). When you have an equation with two square roots, you'll want to have them on opposite sides of the equal sign. Then, you'll square both sides of the equation. If there is still a radical remaining, you'll have to isolate it on one side of the equation and then square both sides once again. There will be several examples included in this lesson that will show you how to approach this type of problem and then how to check your work Functions and the Vertical Line Test
A function is basically a machine that takes an input value (x) and processes it to produce an output value (y). With a function, if an x value is known, you can find the y value. When graphed, a curve is a function if it passes the vertical line test. In this lesson, Professor Burger will show you how the vertical line test means and how to recognize when a curve does not pass the vertical line test. The vertical line test looks to verify that, for every value of x, only one y value is produced. If something doesn't pass the vertical line test, it is called a relation and not a function Function Notation and Values
In this lesson, Professor Burger will show you how to correctly denote functions and values. By definition, a function has only one value of y for each value of x. A function can always be expressed using the term f(x) instead of y. This lesson will walk through when to use this notation and how to use it correctly to indicate what you want it to be. Additionally, Professor Burger will show you how to verbally say the new notation in addition to how to write it. Last, he'll walk you through a few examples involving functions and their notation and evaluation Domain and Range
While a function always satisfies the vertical line test (for any value of x there is only one value of y), there are functions in which the domain of the function does not include all values of x. In this lesson, we look at the domain of a function (all of the values of x for which we can evaluate the function and find a value of y) and the range of a function (all the values of y that may be generated by evaluating the function for some value of x). In addition to learning about evaluating a function to find the domain and range, Professor Burger will graphically show you how to identify the domain and range Satisfying the Domain of a Function
In this lesson, you will learn how to find all of the allowable x values for a particular function (the function's domain). An allowable x value is one in which you can evaluate the function. There are certain types of numbers which are not allowable, like square roots of negative numbers, numbers with 0 in the denominator, etc. If you evaluate a function and end up with one of these types of numbers, then the x value is deemed to be outside of the domain for the function. Professor Burger will also show you how to correctly denote the domain of a function once you determine what it is Composite Functions
In this lesson, you will learn about a method that you can use to combine functions. The composition of two functions is the way to combine two functions. In this lesson, you will learn how to combine functions (for example, to find f(g(x)) ). There are specific ways to denote these types of composite functions, and you will also learn how to correctly write composite functions (f(g(x)) or (f o g)(x) ). To compose a function (find the composition of functions), you'll have to take the answer of one function and plug it into the other function (to find something like, 'g composed of f of 3'. Professor Burger will also highlight why g(f(3)) is not always equal to f(g(3)). Substitution
In this lesson, Professor Burger will show you how to solve systems of equations using a technique known as substitution. In this approach, you will solve one equation for one of the variables (eg y) and then plug the value (what y is equal to) into into the other equation (anywhere a y appears). This substitution will allow you to solve for x and then in turn solve for y. In order to fully explain how this works, Professor Burger will walk you through several different types of examples Elimination
While you can often solve systems of equations using substitution, you may also find that elimination is a simple approach for some systems of equations. When evaluating a system of linear equations with two linear variables using elimination, you will look for ways to combine the equations (or multiples of the equations) such that the sum of the equations will eliminate one of the variables. Once you eliminate one variable, it should be easy to deduce the value of the other equation. Once you have this, you should be able to plug it in to one of the original equations to solve for the eliminated value by Completing the Square This lesson will teach you how to find solutions by completing the square. In this technique, you'll start by isolating all constants on one side of the equation and all variable terms on the other side. Then, you'll add or subtract something to both sides to complete the square. In this case, you'll end up with x^2+6+9 = 9-1. This equation will be easier to evaluate given that you can simplify it to (x+3)^2 = 8. When you finally get to a solution value for x using this approach, you may need to rationalize a denominator (take radicals out of it), and Professor Burger will review this in the lesson, too Completing the Square: An Example In this lesson, you will learn more advanced techniques to use when solving an equation by completing the square. This lesson will cover what to do when the initial x^2 term contains a coefficient, how to solve problems that involve fractions, how to handle denominators with fractions, etc. This technique is the basis for the quadratic formula, which can always been used to solve quadratic equations Find Vertex by Completing the Square
In this lesson, you will learn how to find the vertex of a parabola given the formula for the parabola. To do this, you will complete the square. By completing the square of the parabola equation, you will be able to get the equation into a standard form that can be more easily evaluated. A parabola is a conic section in which the locus of points constructing it are equidistant from the focus and the directrix. Once we've identified the vertex of a parabola, we can get a good sense for how the parabola is positioned on the Cartesian coordinate plane the Quadratic Formula
The quadratic formula is used to solve for x in quadratic equations, which come in the form ax^2+bx+c=0. This formula is most commonly used when the expression can't be easily factored for evaluation. Oftentimes, this is because the two solutions to the equation are not real numbers. In this lesson, Professor Burger will walk you through when to use the formula, what the alternatives to the formula are and how to apply the formula. He will also explain how and why the formula can give imaginary numbers as solutions and what that means Predict Solution Type by Discriminant
When working with quadratic equations and the quadratic formula, there is a way to determine what type of solutions you will find and how many there will be (2 real solutions or 2 complex solutions or 1 solution) by looking at the coefficients of the quadratic formula. In this lesson, you will learn how to do this by calculating and evaluating the discriminant (d) of the quadratic formula (equal to b^2-4ac, which is a component of the quadratic formula The Pythagorean Theorem
The Pythagorean Theorem describes the relationship between the sides of a right triangle. It asserts that if the hypotenuse is length c and the other two legs are a and b, then a^2+b^2=c^2. This formula has a number of applications, and you will go through many of them in this lesson. Professor Burger will show you how to find one leg of a right triangle if you know the other two or if you know the length of one side and have two polynomials to express the lengths of the other two sides (e.g. if you know the three sides are c=x+2 and a=x and b=x+2 Quadratic Inequalities
In this lesson, Professor Burger will teach you how to solve quadratic (non-linear) inequalities. In a quadratic inequality, there are things like x^2 included. To evaluate these inequalities, we once again start by factoring. Next, you'll find the values for x, for which the quadratic inequality is positive such that you will be able to make a sign chart and then determine the sign (positive or negative) for ech interval delineated on the sign chart. Once you have identified the intervals that satisfy the equation, Professor Burger will show how to properly denote the answer using correct notation Writing an Equation for a Parabola
A parabola is a conic section in which the locus of points constructing it are equidistant from the focus and the directrix. To find the formula of this equation when given the vertex (h,k) and the distance from the focus (p), this lesson will show you how to find the equations for the parabola described by these criteria. There will be two formulas depending on whether p is positive or p is negative (which should indicate whether the parabola opens up or down). |
Learn . Create . Succeed: Algebra
This site is dedicated to assisting Science, Technology, Engineering and Mathematics (STEM) instructors in incorporating SolidWorks into their course curriculum.en-USFri, 13 Mar 2009 17:04:03 -0400 with My Yahoo!Subscribe with NewsGatorSubscribe with My AOLSubscribe with BloglinesSubscribe with NetvibesSubscribe with GoogleSubscribe with PageflakesMath2Go Accelerated Curriculum
Accelerated Curriculum applies science and mathematics concepts to designing a race car. With 10th scale RC Cars, students maximize performance and drive farther, faster, and all while exploring concepts in physics. The Upside Down Wings exercise takes a student...]]>AlgebraCalculusPhysicsSTEM CourseMatthew WestWed, 23 May 2007 11:37:53 -0400 with SolidWorks
exercise will assist students in visualizing and discovering how to find the formula to figure the sum of the interior angles of an n-gon. For both algebra and geometry students for an exercise in discovery learning. Contributed by Paul...
]]>AlgebraGeometryMarie PlanchardThu, 16 Nov 2006 16:13:57 -0500 and Extuded Cuts
lesson examines the extrusion of a cube then removes the material from each side using different geometrical shapes. Applications in basic math, algebra and drafting. Contributed by Gary Mills. Lesson Plan: solidworksextrusion_hatc2.doc Sample Parts: Cube1.SLDPRT ; Cube2.SLDPRT This lesson examines the extrusion of a cube then removes the material from each side using different geometrical shapes. Applications in basic math, algebra and drafting. Contributed by Gary Mills.
]]>AlgebraMechanical EngineeringMarie PlanchardWed, 19 Jul 2006 13:55:40 -0400 Plan: Parabola from Algebra to Calculus
lesson develops two examples with a parabola. The first example explores graphing a parabola from an equation, finding the area bounded by the x axis, center of mass, and volume of a solid in revolution about a line parallel... This lesson develops two examples with a parabola. The first example explores graphing a parabola from an equation, finding the area bounded by the x axis, center of mass, and volume of a solid in revolution about a line parallel to the x-axis. Understanding a parabola in algebra can lead to success in Calculus and Calculus based science classes such as physics, engineering mechanics and dynamics. The second examples bounds the parabola by both the x and y axis, explores the centroid and volume in revolution. |
This book is a collection of 375 completely solved exercises on differentiable manifolds, Lie groups, fibre bundles, and Riemannian manifolds. The exercises go from elementary computations to rather sophisticated tools. It is the first book consisting of completely solved problems on differentiable manifolds, and therefore will be a complement to the books on theory. A 42-page formulary is included which will be useful as an aide-memoire, especially for teachers and researchers on these topics. The book includes 50 figures. Audience: The book will be useful to advanced undergraduate and graduate students of mathematics, theoretical physics, and some branches of engineering.
DJVUThis book follows the successful Mathematical Activities by the same author and has been written to provide teachers with further ideas to enrich their teaching of mathematics. It contains 127 investigations, puzzles, games and practical activities together with a commentary which provides solutions and additional ideas. These activities are suitable for use with children from age nine upwards to stimulate their interest and encourage mathematical thinking. ...
A complete preparation course for IELTS offers topic development to encourage students to think critically. A Language for Writing syllabus covers grammar and vocabulary. Help Yourself pages with activities to support self-study are provided.
This text gathers together 81 classroom proven strategies designed to build or reinforce the langiage skills of intermediate to advanced students.
This is an overall great "idea" book for the ESL classroom.It is basically a book of activities for each different aspect of language teaching. It devotes entire units to more difficult-to-teach topics such as developing listening skills. Most of the activities are extremely interactional and would enhance student's communicative abilities, either directly or indirectly. This book is a great resource for finding just the right activity for your lesson plan. All activities are also easily adaptable for level and for subject area.
This popular First Certificate course has been updated to prepare students for the new examination syllabus introduced from December 2008. A clear organisation and fresh approach have already made it a popular route to success at FCE in many countries: thirty short units provide thorough training in exam skills, solid language development, and lively class discussion. The course is written by experienced authors who have an in-depth knowledge of the FCE exam, and understand the needs of both students and teachers alike. |
Skowhegan Area High School Mathematics Department
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Objective
of Curriculum
The curriculum for "Contemporary Mathematics in
Context" builds upon the theme of mathematics as sense-making. Investigations
of real-life contexts leads to discovery of important mathematics that make sense
to students and, in turn, enable them to make sense out of new situations and
problems. Each year the four strands of mathematics are studied: algebra and functions,
geometry and trigonometry, statistics and probability, and discrete mathematics.
Problems are integrated across curriculum areas: math, science, social studies,
English, and business. Topics are multicultural as well. All areas of conventional
high school math are covered in this curriculum.
Learning is done collaboratively in small teams with
assistance from teachers. Students are assessed in a number of ways, including
daily work, homework, projects, and tests and quizzes. While the TI-83 graphing
calculator is used extensively, students learn to solve problems numerically,
graphically, and symbolically.
Objective
of this Project
As a final project, Seniors from the Class
of 2003, who have taken Math I,II,III,IV have reviewed each unit that is listed
at the left and have created web pages that summarize the relevant topics. These
web pages may be used by students, teachers, and parents who are interested in
review, preview, and learning.
MEA and Sat Results
Maine Learning Results
The Integrated Math curriculum demonstrates the Guiding
Principles identified by the Department of Education
Each Maine
student must leave school as:
I.
A clear and effective communicator
II. A
self-directed and life-long learner
III. A
creative and practical problem solver
IV. A
responsible and involved citizen
V. A
collaborative and quality worker
VI. An
integrative and informed thinker
Furthermore, the Integrated Math curriculum requires
proficiency in all topics described in the Maine Learning Results (specifics are
identified with each unit): |
The Mathematics Curriculum: Algebra in the teaching of algebra and mathematical aspects of algebra in the school setting are discussed. Topics covered include functions and mappings, solving equations, matrices and simultaneous equations, relations and inequalities, and algebraic structure. The book is a guide to the historical context of algebra teaching at the time and reviews some of the textbooks available. Many of the resources will be out of date but the principles are still relevant today |
Because individual students have different needs, interests and abilities, there are three different courses in mathematics: Mathematical Studies SL, Mathematics SL and Mathematics HL.
These courses are designed for different types of students: those who wish to study mathematics in depth, either as a subject in its own right or to pursue their interests in areas related to mathematics; those who wish to gain a degree of understanding and competence better to understand their approach to other subjects; and those who may not as yet be aware how mathematics may be relevant to their studies and in their daily lives. |
Conquer Calculus and Truly Understand the Subject!
Calculus is the foundation of modern Mathematics and Physics.
It allows us to calculate everything from the trajectory of a basketball to the path of a rocket. Although it is incredibly useful, Calculus can be an intimidating subject when first introduced to the student.
The DVDs in this section are designed to immediately overcome that intimidation and teach the topics of Calculus with step-by-step example problems.
Every DVD on ScienceAndMath.com comes with a Money Back Guarantee! Our DVDs are guaranteed to raise grades immediately. If you are not fully satisfied, simply send the DVD back for a full refund.
The Calculus 1 & 2 Tutor -- 8 Hour Course This 8 hour 2-DVD series is a complete course in Calculus that teaches the topics by working example problems. All of the core topics in Calculus are covered such as the limit, derivatives, integrals, and many techniques of integration. It is an excellent resource to increase your understanding of complex Calculus topics and also serves as a reference for hundreds of fully worked problems. more info > > > |
Course Syllabus for Intermediate Algebra
Catalog Description:
Topics include factoring techniques, radicals, algebraic fractions , complex
numbers, graphing linear equations and inequalities , quadratic equations, systems of equations, an
introduction to functions, and
graphing quadratic functions. Emphasis is placed on the algebraic techniques
needed in order to
successfully complete Math 1314 College Algebra. A departmental final
examination must be passed
with a score of 60% or higher in order to pass the course.
Course Intent & Audience:
This course is intended for students who require state mandated remediation. It
is the final course in the
developmental mathematics sequence, and its purpose is to prepare students for
College Algebra.
Policy on Late As signments and Make –Up Exams: All
homework assignments will be due on the day
of each exam. Also, there will be NO makeup exams. If you miss an exam, the
final exam will count
twice. It will count once for the missed exam and again for the final exam
itself. If you know in
advance that you will be absent on an exam day, please let me know as soon as
possible.
Course Schedule
Chapter 3 Graphs, Linear Equations, and Functions 3.1 The Rectangular Coordinate System
3.2 The Slope of a Line
3.3 Linear Equations in Two Variables
3.4 Linear Inequalities in Two Variables (Omit compound inequalities.)
3.5 Introduction to Functions
The content of the following sections include material
that is embedded in other sections of the
course or that was covered in the previous math course or that will be studied
in the next course MATH
1314. Based on this, the instructor may discuss the sections listed below if
time permits: |
Algebra : Introductory and Intermediate all the support of the renowned Aufmann approach, this popular combination text helps your students prepare to master college algebra and to apply algebra in the real world."New!" Bulleted annotations have been added to the solution steps of "Examples" and to the "You Try It" solutions in the appendix, further enhancing the Aufmann Interactive Method."New!" Examples have been clearly labeled "How To," allowing students to more easily refer back to solution steps when completing corresponding exercises."Updated!" The "Chapter Summary" has b... MOREeen reformatted to include an example column, offering students the additional support of an algebraic representation of concepts, rules and definitions."Updated!" In response to instructor feedback, the number of "Chapter Review Exercises" and "Cumulative Review" Exercises has increased."Updated!" More operation application problems integrated into the "Applying the Concepts" exercises encourage students to judge which operation (adding, subtracting, multiplying, dividing) is needed to solve a word problem."New!" "Integrating Technology" (formerly Calculator Notes) margin notes provide suggestions for using a calculator in certain situations. For added support and quick reference, a scientific calculator screen is displayed on the inside back cover of the text."New!" "Objective-based Worksheets" accompany every section in the book for extra classroom practice or homework. These worksheets are found on the ClassPrep CD and Online Teaching Center."Aufmann Interactive Method (AIM)" encourages students to try the math as it is presented. Every section objective contains one or more sets of matched-pair examples. The first example is completelyworked out; the second example, called 'You Try It, ' is for the student to work. Complete worked-out solutions to these examples in an appendix enable students to check their solutions and obtain immediate reinforcement of the concept.Integrated, easy-to-navigate learning system organized by objectives guides students with a consistent, predictable framework. Each chapter opens with a list of learning objectives, which are woven throughout the text and integrated with the print and multimedia ancillaries.The "AIM for Success Student Preface" guides students in making the most of the text's features. "Study Tip" margin notes throughout the text refer students back to the Student Preface for advice."Prep Tests" at the beginning of each chapter help students prepare for the upcoming material by testing them on prerequisite material learned in preceding chapters. The answers to these questions can be found in the Answer Appendix, along with a reference to the objective from which the question was taken. The "Go Figure" problem that follows the Prep Test is a challenge problem for interested students.Extensive use of applications that use real source data shows students the value of mathematics as a real-life tool."Focus on Problem Solving" section at the end of each chapter introduces students to various problem-solving strategies. Students are encouraged to write their own strategies and draw diagrams in order to find solutions.Unique Verbal/Mathematical connection simultaneously introduces a verbal phrase with a mathematical operation, followed by exercises that require students to make a connection between a phrase and a mathematical process."Projects and Group Activities" at the end ofeach chapter offer ideas for cooperative learning.Unique "Instructor's Annotated Edition" features a format rich with new instructor support materials, which are provided at point-of-use in the margins surrounding reduced student pages.
Note: Each chapter begins with a Prep Test and concludes with Focus on Problem Solving, Projects and Group Activities, a Chapter Summary, a Chapter Review, and a Chapter Test. Chapters 2–12 include a Cumulative Review |
Get everything you need for a successful and pain-free year of learning math! This kit includes Saxon's 3rd Edition Algebra 1 textbook and tests/worksheets book & answer key. as well as the DIVE Algebra 1 CD-ROM. A balanced, integrated mathematics program that has proven itself a leader in the math teaching field, Algebra 1 covers signed numbers, exponents, and roots; absolute value; equations and inequalities; scientific notations; unit conversions; polynomials; graphs; factoring; quadratic equations; direct and inverse variations; exponential growth; statistics; and probability.
The DIVE software teaches each Saxon lesson concept step-by-step on a digital whiteboard, averaging about 10-15 minutes in length; because each lesson is stored separately, you can easily move about from lesson-to-lesson as well as maneuver within the lesson you're watching. DIVE teaches the same concepts as Saxon, but does not use the problems given in the text; it cannot be used as a solutions guide. |
Get the most out of Sketchpad® with these add-on curriculum modules. Builds upon the strengths of dynamic mathematical representations to enrich the study of first-year algebra. Topics include ratios and exponents; algebraic expressions; so7 2-55 Get the most out of Sketchpad® with this add-on curriculum module. This collection of Sketchpad® activities is an excellent introduction to Sketchpad® for both students and teachers. Topics include operations and a..
Prices listed are U.S. Domestic prices only and apply to orders shipped within the United States. Orders from outside the
United States may be charged additional distributor, customs, and shipping charges. |
Differential Equations
9780495012658
ISBN:
0495012653
Edition: 3 Pub Date: 2005 Publisher: Thomson Learning
Summary: Incorporating a modeling approach throughout, this exciting text emphasizes concepts and shows that the study of differential equations is a beautiful application of the ideas and techniques of calculus to everyday life. By taking advantage of readily available technology, the authors eliminate most of the specialized techniques for deriving formulas for solutions found in traditional texts and replace them with topi...cs that focus on the formulation of differential equations and the interpretations of their solutions. Students will generally attack a given equation from three different points of view to obtain an understanding of the solutions: qualitative, numeric, and analytic. Since many of the most important differential equations are nonlinear, students learn that numerical and qualitative techniques are more effective than analytic techniques in this setting. Overall, students discover how to identify and work effectively with the mathematics in everyday life, and they learn how to express the fundamental principles that govern many phenomena in the language of differential equations.[read more]
Book may have signs of cover wear. Inside pages may have highlighting, writing, and/or underlining. Includes CD-ROM. Ships same day or next business day. Free USPS Tracking N [more]
Book may have signs of cover wear. Inside pages may have highlighting, writing, and/or underlining. Includes CD-ROM. Ships same day or next business day. Free USPS Tracking Number. Excellent Customer Service. Ships from TN[less] |
Description of Edurite CBSE Class 7 Maths (1CD Pack)
Mathematics requires a thorough understanding of concepts. It is important to understand the subject right from middle school to score well in the board exams. Edurite's CDs have been developed by teachers who are experts in the subject and have several years of experience teaching students. Our CDs are completely mapped to the class 7th CBSE Mathematics curriculum and offer detailed topic wise coverage for each chapter with both a voice over as well as textual explanation and relevant diagrams and tabulations, You also get an extensive section on practice questions organized chapter wise along with the answer key, Revise what you have learned by going through the chapter synopsis or just get some tips on scoring more in exams. It includes chapters such as Equations, Lines & Angles, Rational Numbers |
In this year long course, students develop algebraic fluency by learning the skills needed to solve equations and perform manipulations with numbers, variables, equations, and inequalities. They also learn concepts...
Algebra I A: This course covers such key concepts as variables, function patterns, and graphs. Students learn operations with rational numbers and properties of rational numbers. Students
solve linear equations and...
The purpose of this Algebra I course is to allow the student to gain mastery in working with and evaluating mathematical expressions, equations, graphs, and other topics in a year long course. Topics included are real...
Class.com Algebra 1 is a traditional two semester middle or high school algebra course that equates to approximately 80 hours of instructional time per semester. Numerous interactive and multimedia components within each...
Publisher: Class.com (Cambium Learning)
Also published by Class.com (Cambium Learning)
Algebra I is a full-year, high school credit course that is intended for the student who has successfully mastered the core algebraic concepts covered in the prerequisite course, Pre-Algebra. Within the Algebra I course,...
Algebra I begins with a review of algebraic properties, integers, exponents, and roots. Students will then build on that knowledge as they study rational numbers, solving equations, proportions, and absolute values,... |
I may start working my way through Brown myself when I finish RUSSIAN MATH by Nurk & Telgmaa.
Algebra Through Problem Solving by Hillman & Alexanderson - This book has been placed on the Web by the Science Education Team at Los Alamos National Laboratory to help students better prepare for careers in mathematics and science. The topics are essential for success in college level mathematics but tend to be taught inadequately, if at all, due to discontinuities between high school and college courses. The treatment here also provides experience with pattern recognition and other problem solving techniques. (authors also have a book on complex numbers and trigonometry posted online)
state of CA frameworks for algebra - best in the country:
Mary Dolciani
"Mary Dolciani [full citation t/k] is good, but there are others as good also. Foerster has been recommended, so should be checked out. The problem with Dolciani is she tends to be a bit TOO formal at times. But still she gives a good rigorous treatment of algebra with lots of problems."
In Don't teach in a montone, part 1, Carolyn writes that, "Early texts in a math field, written when the topic is new and hot, generally have a lot of life; they start out talking about what motivates the creation of an idea -- they do examples -- they talk about what's known and what isn't. When the theory is better understood, the presentations get terser and cleaner, less emotional, and in a very real sense less useful. This is the higher life form to which mathematics texts seem to evolve, and I think it's a mistake."
Bernie, who is Carolyn's husband, write NUMBERS AND SYMMETRY as an early text, with the life and emotion of authors discovered a new field of mathematics.
algebra online
Action Math (fantastic website teaching individual problems - aimed to middle school students I think & not limited to algebra)
Hot Math looks excellent: "We show step-by-step explanations for the actual homework problems in your math textbook." pre-algebra through calculus and college algebra; subscription website also inclues what look to be free online workbooks in each subjected created by Hotmath
Catherine speaking: I assume the Virginia tests are useful, partly because I liked the looks of the 5th grade test, and partly because Cheri Pierson Yecke was, as Virginia's Secretary of Education, involved in creating Virginia's state standards. On the other hand, the Fordham Report on The State of State Math Standards gives Virginia's math standards a grade of C. Still, it was Ralph Raimi, I believe, who told me in an email that one shouldn't obsess over finding the perfect test; he said just to pull questions from the Singapore curriculum and use those if you want to know how your child is doing in math. I'm sure he's right. The important thing is to 'test the tests.' Give your child a not-overly-involved assessment at home just to make sure that your state tests aren't way off-track. Trust, but verify!
Daily Grammar wonderful, thorough set of lessons on every aspect of grammar, including sentence variety; includes quizzes; not sure how many worksheet-type assignments there are - writeup: Mr. Bill Johanson is the author of the lessons. He has taught high school and junior high school English classes for thirty years, doing a great job of preparing his students for college.
summer reading lists
Dobbs Ferry, the town next door to me (Catherine) has an International Baccalaureate program, and most of the school reading lists I've looked at are are terrific. They include recommendations from the kids, which is great. You can also compared reading lists for the IB & AP courses to reading lists for the non-IB, non-AP courses. Grade 6 list Grade 7 list
You can access all of the lists from both of these pages.
The Paideia School's extensive lists for junior high and high school readers are probably excellent. Fiction, nonfiction, and poetry. Type "reading list" in the search field.
For ktm readers' lists of books their children liked see Comments threads here and here.
fraction manipulatives to print by Doug Sundseth (pdf files)
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geogaphy
geometry
Geometry by Edwin E. Moise and Flloyd L. Downs
A mathematically rigorous geometry textbook from the era of New Math.
see: SmsgGeometry
Geometry by Moise Downs is good but not the only good text around. Adkins/Weeks has a good geometry text as does Jacobs. M-D is my favorite but that shouldn't be taken as the last word by any means! (Barry Garelick)
homeschooling curricula and books
homeschool law
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Jaime Escalante
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middle school math
Mathcounts web site devoted to middle school math; excellent; Mathcounts contests are major events
For late middle school and high school I am impressed by the Dolciani series, Structure and Method (McDougal-Littell). Unfortunately the most advanced Dolciani, the pre-calculus Modern Introductory Analysis, has been allowed to go out of print. Saxon also seems a decent option for the late middle school and early high school years, as does Singapore's New Elementary Mathematics. There may be plenty of other good traditional choices, but I am not familiar with U.S. high school textbook series other than Dolciani. I don't know if the Japanese mathematics textbooks (Translated by UCSMP) could be an option; they are a very strong series for the highest grades. I don't know of U.S. studies that compare outcomes of various high school curricula. Internationally, of course, TIMSS especially has shown the superiority of typical curricula used in Korea, Japan, and Singapore.
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online algebra
online math
multipliers][Donna Young's online lesson in unit multipliers (she has many terrific printable manipulatives as well]] edHelper.com I'll probably join this site (Catherine speaking) - Susan likes it, and it has a phenomenal ability to construct whatever kind of worksheet you need, on the fly $19.99 a year - I've just subscribed, and it's very helpful. The one drawback is that you can't specify value range to the extent I would like. I needed a sheet of integer problems with integers between -20 and 20 (which I could have Christopher solve using Doug Sundseth's number lines), but wasn't able to ask the program to do this. Math for Morons horrible title, but this is probably a good & useful site - includes calculus Webmath.com looks terrific - 1,300 completely solved problems K-12 plus math experts to answer questions Grade Level Math Links K-12 (looks good) printable number lines, 8 to a page all positive numbers, unfortunately long & semi-annotated list of online resources line jumper at FunBrain add & subtract integers on a number line (kids love this site, in my experience--tons of math games)
Here's MathBrain (part of FunBrain) Math baseball at FunBrain The boys in my Singapore Math class loved this game. Lesson Tutor this looks terrific, though I haven't used it yet; seems to be associated with Teachnology, which is associated with FunBrain... interactive math links (haven't use this site as yet)
online tutorial in real analysis by Dr. Bert Wachsmuth of Seton Hall University. Some sections are incomplete, but Barry Garelick says that what is there is impressive.
online geometry
GeometryEuclid have you stumped? Archimedes run rings around your head? Well you've come to the right place. This is where you'll find almost everything you'll ever need to know about Geometry. We have a special page on constructions and plenty of sample problems to help you understand the concepts. Have a blast and don't forget to check out our Glossary - it's huge! (no idea whether this site is useful - let me know)
online story problems
Challenge Index (looks like it may be fun - sample question: How fast can an Arctic tern fly around the world?)
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possibilities
I haven't had time to look around this web page, but on first sight, it appeals to me. It appears to have a mix of problems surrounded by lots of white space (good) and illustrated with clip art that, so far, I find stimulating as opposed to bewildering. (I love Carolyn's line about how the Prentice Hall pre-algebra book is going to make hers & Ben's eyes spin like cartoon characters. No joke.)
If you have reactions, let us know. Catherine
pre-algebra
Pre-Algebra: An Accelerated Course by Mary Dolciani ISBN: 0395591236 (almost certainly an excellent book - I haven't read it closely, but I consult it often & my neighbor's son relied on it to get through the Phase 4 class last year)
3-23-2006: I've now worked my way through all but the last 10 lessons of Saxon Homeschool 8/7, and I love it. Can't possibly praise it highly enough. This is Christopher's 6th grade year, and if he had been using Saxon 8/7 instead of Prentice-Hall Applications, he'd a) know and understand math through pre-algebra, and b) like math through pre-algebra.
pre-algebra workbooks
I've used two, and found both helpful:
Instructional Fair Pre-Algebra by Frank Schaffer is my favorite of the two. (IF workbooks can be hard to track down on the web; no idea where to get the best price.)
pre-algebra worksheets
Glencoe Pre-Algebra Parent and Student Study Guidefree online "The Glencoe Parent and Student Study Guide is designed to help you support, monitor, and improve your child's math performance. These worksheets are written so that you do not have to be a mathematician to help your child." excellent, fantastically helpful
Iím modeling this on Saxon Mathís constant repetition of 4 fact families to teach inverse operations & the commutative property (see next page). Christopher and I both found the 4-fact families terrifically effective.
We'll see how it goes.
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references
Russian Math
No idea what this book is like, but the folks at Mathematically Correct have a link to it, so I finally ordered a copy yesterday. [update: I just got my copy--it's incredible. I'm working my way through it now. 6/05 -- Catherine]
A press release from the translator has this to say:
First published in 1987, Mathematics 6 took the Soviet education establishment by storm, winning the national competition for best new math book that year.
2nd update: I love, love, love this book. I've now worked 100 of the 1100 problems in the book, have learned much, and am going to write numerous posts about it. If we were awarding stars, this MATHEMATICS 6 would have 5. more on this, and on who might want to use it, t/k. 6-12-05
3rd update: I still love this book; am now up to problem number 219. I'll probably have Christopher use this book next summer, between the 6th and 7th grades.
final update: I've studied every lesson in the book, worked every problem. It's brilliant. Makes the Singapore Math books look like overachieving strivers (and those books are terrific). Russian Math category thread here
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Saxon Math
Saxon answer sheets, complete set These are not the answers, but the sheets on which children do their work and write their answers. You can see what they look like here. Terrifically helpful, because Saxon Homeschool Edition does not include a workbook. You may want to write each problem out by hand on these sheets; I did that for Christopher throughout Saxon 6/5, and it was a big help.
Singapore Math placement tests & guidelines
Parker & Baldridge
note: For what it's worth, I would probably skip the instructor's & teacher's guides (see below) and spend my money on Parker & Baldridge & possibly one or both of the Singapore books for parents (links below). However, I've taught only a couple of units—on fractions, ratios, & proportions—using PRIMARY MATHEMATICS, so I'm not the best person to listen to on this. (Catherine)
[update: now that I've gone to the trouble of posting all of the links for Jennifer Hoerst's Home Instructor's Guides at Sonlight.com, I find that these are the same guides sold on SingaporeMath.com, and that Ms. Hoerst runs a Singapore Math forum at Yahoo groups. I'm wondering whether she's the owner of SingaporeMath.com.]
Singapore Math's Teacher's Guides & Home Instructor's Guides
note: The Singapore Math web site offers two guides for each book, the Home Instructor's Guides by Jennifer Hoerst & the Teacher's Guides, written in Singapore. I ordered the Home Instructor's Guide for 3B and found it fairly confusing. That was back when I was first trying to teach Christopher what he'd missed at school and I was feeling pretty confused myself, so I'd probably do better with it today. Nevertheless, the graphic design is poor; every page is crammed with symbols, text, and rules. It's not Page Splatter in the manner of U.S. textbooks, but, for me, it takes a conscious act of will to read even one page. As a matter of fact, it was the 3B Home Instructor's Guide that convinced me to go with Saxon instead of Singapore!
Singapore Math middle school
Singapore Math high school
spelling
Perfect, and reasonably priced ($7 for the teacher's guide, $9.85 for the workbook). Eight books altogether, starting with Book 1 in 4th grade. Even if your child is older, it's probably a good idea to start with Book 1, since the books are sequential, and subsequent books build on the syllabication rules learned in earlier books.
Glencoe Pre-Algebra There are various editions of Glencoe Pre-Algebra available online; I have no idea which is which, or whether any substantial revisions have been made from one book to the next. There's a very funny & very negative Amazon reader review of this edition ....
touch typing
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V
vocabulary
The Vocabulary Workshop series is excellent, IMO. Almost more importantly, Christopher is enjoying the first book he's used, Level A, for grade 6. The books begin in second grade and go through grade 12, one book per year. Grades 2 - 5 are Levels Purple, Green, Orange, & Blue. Sixth grade starts with Level A, and the books go through Level H. The cost is around $10 per book, and you don't need the teacher's edition.
Saxon worksheets are here This is a link to a page with Saxon worksheets, in Word documents, that should download to your desktop. You can print them out for every lesson (every book in the series through 8/7) and write or type the problems in the correct spaces). If you type in the problems, I'd love to get copies to upload to Kitchen Table Math. We'd have a set of Saxon workbooks people could download.
DonnaYoung.org lots of terrific printable worksheets, number lines, graph paper, pie-chart fractions, play money, paper for scale drawing & worksheets with number lines on the top (click on math)
Handwriting for Kids lovely web site maintained by homeschooling mom. The focus is on handwriting, but she has terrific visual math worksheets for kids like Andrew (autistic, nonverbal, bright). Penny Math; visual addition; she also has lots of online worksheets (child types in answer & the worksheet is graded online).
from Carolyn
Sometimes, the kid just isn't up to doing a whole math lesson (or more likely, I'm not up to giving him one, since it's something of a battle).
On those nights, something like these math worksheet generators can come in very handy. There are a lot of these generators around, but this one is very configurable; you can set the number of columns and rows of problems, and the difficulty of the problem, and the numbers of significant digits in the solution, and so forth.
Give the kid a worksheet with a few problems on it, and let him get in a little practice. Resist the urge to give him more than 4 or 5 problems on a sheet; make them easy. The most important thing is to make every learning experience a success -- especially true if this is material he is already supposed to know how to do, and will be doing independently.
But Saxon's problem generator is clean, simple, and compelling. I liked using it myself, and Christopher seemed to like it OK, too.
You decide which facts problems you want to do, how difficult the problems should be, and how many you want to do. You can also do timed or untimed problem sets. Kids love seeing their timing get faster, I find.
So if you need something for your child or student(s) to do while you're getting organized, this is probably a good choice. (I still wouldn't trust computer learning to firm up my child's math facts unless it's clear that he or she really is learning math facts online or using a software program. In our case, even after Christopher had used a little software program I bought, it was clear he wasn't gaining speed or accuracy. He didn't really get his math facts down cold until we started doing the Saxon fast fact worksheets. Interestingly, flash cards didn't work well for us, either. And we spent quite a bit of time with them...)
Saxon online math activities* Now that I've warned everyone against teaching math on a computer, I have to admit I'm kind of addicted to these animated Saxon activities, too.
Here are the 5th grade activities. Apparently the site now tells you which activities to do after which lessons in the book; plus you can download them for use when you are not online. |
Combinations of Operations with Fractions
Summary: This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses combinations of operations with fractions. By the end of the module students should gain a further understanding of the order of operations |
Statistics Bridging Courses
Early in 2013 the Mathematics Learning Centre will offer short bridging courses for students planning to undertake programmes which require the study of statistics, such as Statistics and Research Methods for Psychology, and degrees/diplomas in Public Health or other postgraduate degrees.
These courses are designed for people who lack confidence when faced with mathematical tasks or as a refresher for people who want to brush up on basic mathematical skills. They may also be useful for students who have not studied Mathematics (2 Unit) at school. They are not appropriate for students who have at any time completed the higher levels of mathematics for the Higher School Certificate.
The courses aim to review the basic mathematics needs of students in a statistics course and to develop an intuitive understanding of some fundamental statistical concepts.
The program includes:
use of a scientific calculator, including the use of statistical functions
algebra, including the use of formulae and the solution of simple linear equations
introduction to concepts in probability by means of practical activities |
Course Descriptions
Mathematics Course Descriptions
MAT-designated courses (with the exception of MAT101 and MAT102) qualify as Liberal Arts or Mathematics electives.
MAT101
Elementary Algebra with Lab - 3 Credits
This course develops the fundamental processes of algebraic thinking and provides students with the skills for further study in higher level algebra based courses. This course is integrated with an online mathematics program and mandatory computer lab sessions designed to further enhance the classroom experience. Topics include a study of the real number system, solving and graphing linear equations and inequalities in one and two variables, exponents, scientific notation, operations on polynomials, ratios, proportions, and basic factoring in a problem solving context. Course requires subscription to a supplementary online program. Graphing calculator will be provided for occasional use in class.
Prerequisite: Department recommendation.
MAT102
Intermediate Algebra - 3 Credits
This course builds upon algebraic skills learned in MAT101 or a similar experience and provides students with additional skills needed for further study in higher level algebra based courses. This course is integrated with an online mathematics program designed to further enhance the classroom experience. Topics include further development of the study of linear functions, solving absolute value equations and inequalities, solving linear systems for break-even analysis, working with polynomial functions, and further development of factoring skills, applications of quadratic functions, and simplifying rational and radical expressions. Course requires subscription to a supplementary online program.
Prerequisite: C or better in MAT101 or Department PermissionMAT106
Business Mathematics (elective offered in Spring of 2013) - 3 credits
This course, intended for the business major, surveys topics in elementary algebra, personal finance, probability, and statistics and is integrated with an online homework and tutorial program designed to assist students in achieving their goals of high level performance in and out of the classroom. Topics focus on real-life situations, decision making skills, and problem solving. Topics include solving algebraic equations, solving ratio and proportion problems, and applications involving percentage, simple interest, simple discounts, consumer credit, compound interest, future and present value, applied probability, descriptive statistics, investments, mortgages, and taxes. Some working knowledge of elementary algebra is expected. Course requires subscription to a supplementary online program. Scientific or graphing calculator strongly recommended.
A survey of mathematics topics all students need to meet with success in today's society. This course is integrated with a state of the art online homework program designed to assist students in achieving their goals of high level performance in and out of the classroom. Topics include a study of number systems, essential algebraic & geometric principles, sets and logic, counting principles, statistics, graphing, and data analysis. Optional topics may include networks, money, and voting principles. Course requires subscription to a supplementary online program. Scientific calculator recommended. Course is designed to prepare students for success on standard workplace competency assessments.
MAT120
College Algebra - 3 CreditsPrerequisite: C or better in MAT102 or Department Permission.
MAT130
Pre-Calculus and Trigonometry - 3 Credits
This course is a study of functions deeply embedded with real-life activities and integrated with an online mathematics program designed to further enhance the classroom experience. Topics include an overview of algebraic, exponential, logarithmic, rational, radical, and trigonometric functions as they are applied to daily life experiences. Course requires subscription to a supplementary online program. Graphing calculator required.
Prerequisite: MAT120, or MAT102 with Department Permission, or Department Recommendation.
MAT220
Statistics - 3 CreditsMAT223
Statistics II - 3 credits
This course is a continuation of introductory statistics with applications. Topics covered include inferences involving two populations, analysis of variance, linear regression analysis, multiple regression, forecasting, time series analysis, and elements of nonparametric statistics. This course is integrated with a state of the art online program designed to assist students in achieving their goals of high level performance in and out of the classroom. Course requires subscription to a supplementary online program. Scientific or graphing calculator and access to a spreadsheet program is recommended.
Prerequisite: MAT 220 or Department permission.
MAT230
Quantitative Analysis - 3 CreditsPrerequisite: MAT120 College Algebra or MAT130 Pre-Calculus.
MAT250
Calculus I - 3 Credits
This course introduces differential and integral calculus of one variable. Topics include analytic geometry, functions, limits, derivatives, applications of derivatives, and anti-derivatives. This course is integrated with a state of the art online homework program designed to assist students in achieving their goals of high level performance in and out of the classroom. Course requires subscription to a supplementary online program.
Prerequisite: MAT130 Pre-Calculus or Department permission.
MAT251
Calculus II - 3 Credits
This course is a continuation of MAT250. Topics include the definite integral, the Fundamental Theorem of Calculus, exponential and logarithmic functions, techniques of integration, and applications. This course is integrated with a state of the art online homework program designed to assist students in achieving their goals of high level performance in and out of the classroom. Course requires subscription to a supplementary online program. |
Mathematics
Mathematics includes the teaching of algebra, patterns, "number sense" (i.e. is a number too big? too small?), how math is applied to real life, geometry, basic trigonometry, and an introduction to probability and statistics. Our aim at ISU is to use Mathematics as a framework to interpret and manipulate numerical data, as well as apply algebra, geometry, and trigonometry to a variety of real life and theoretical problems. |
This is a common problem; don't let it get to you. You will get at ease with coordinate grids free worksheets 4th grade in a couple of weeks. Till then you can use Algebrator to help you with your assignments.
Algebrator really helps you out in coordinate grids free worksheets 4th grade. I have looked for all Algebra software on the net. It is very user-friendly . You just put your problem and it will generate a complete step-by-step report of the solution. This helped me much with scientific notation, algebra formulas and graphing circles. It helps you understand Math better. I was distressedof paying huge sum to Maths Tutors who could not give me the required time and attention. It is a worthful tool which could change your entire mindset towards math. Using Algebrator would be a pleasure. Take it.
Algebrator is the program that I have used through several algebra classes - Intermediate algebra, College Algebra and College Algebra. It is a really a great piece of algebra software. I remember of going through problems with absolute values, difference of squares and ratios. I would simply type in a problem homework, click on Solve – and step by step solution to my math homework. I highly recommend the program. |
Visualizing Mathematical Ideas With Technologies
Because of the abstractness of mathematics, visualization is an important strategy in helping learners understand mathematical concepts. Such visualization tools are not always computer mediated. For example, Cotter (2000) showed that using Asian forms of visualization (e.g., abacus, tally sticks, and place cards) advanced understanding of place value, addition, and subtraction. Mathematics educators have promoted the use of manipulatives and similar visual comparative devices for many years. Snir (1995) argues that computers can make a unique contribution to the clarification and correction of commonly held misconceptions of phenomena by visualizing those ideas. For instance, the computer can be used to form a representation for the phenomenon in which all the relational and mathematical wave equations are embedded within the program code and reflected on the screen by the use of graphics and visuals. This makes the computer an efficient tool to clarify scientific understanding of waves. By using computer graphics, one can shift attention back and forth from the local to the global properties of the phenomenon and train the mind to integrate the two aspects into one coherent picture (Snir, 1995).
Visualization tools have been developed primarily for mathematics and the sciences. Mathematics is an abstract field of study. Understanding equations in algebra, trigonometry, calculus, and virtually all other fields of math is aided by seeing their plots. Understanding the dynamics of mathematics is aided by being able to manipulate formulas and equations and observe the effects of that manipulation. Programs such as Mathematica ( mathematica/index.html), MathLab ( Statistical Analysis System, and Statistical Package for the Social Sciences are often used to visually represent mathematical relationships in problems so that learners can see the effects of any problem manipulation. Being able to interrelate numeric and symbolic representations with their graphical output helps learners understand mathematics more conceptually. Those tools, because of their power and complexity, are seldom used with K–12 students. Most of the research on these tools has been conducted in universities.
Visualizing Formulas With Graphing Calculators (by Fran Arbaugh)
The National Council of Teachers of Mathematics (NCTM) recommends that mathematics instruction at all grades enable students to create and use representations to organize, record, and communicate mathematical ideas; select, apply, and translate among representations to solve problems; and use representations to model and interpret physical, social, and mathematical phenomena (NCTM, 2000, p. 360). Handheld graphing calculators (such as those made by Casio, Hewlett-Packard, and Texas Instruments) are portable tools that students can use in the classroom or at home to support their mathematical sense making.
Students often have difficulty distinguishing important features of functional relationships. For instance, to build understanding of linear relationships, students can use different representations, generated by the graphing calculator, to make connections between what is happening contextually, numerically, graphically, and symbolically for a particular mathematical relationship.
Students using a graphing calculator can easily move between the symbolic, graphical, and numeric representations of the two functions. They can trace along both functions to find (x, y) values graphically. They can then compare those values to the (x, y) pairs in the table. Students can find x and y intercepts on the graph and table and discuss how to manipulate the symbolic representation to find the same information.
Research indicates that the use of graphing calculators has a positive influence on students' understanding of mathematics (Ruthven, 1990). In addition, Dunham and Dick (1994) report that students who use graphing calculators are more flexible problem solvers, are more persistent when faced with a new problem situation, and are highly engaged in the act of problem solving. As more and more mathematics textbooks incorporate the use of a graphing calculator in learning and teaching high school mathematics, more research needs to be conducted on the impact of this technology on student understanding.
Tinkering With Data Sets
Data analysis and interpretation of statistics are key skills, according to standards published by the NCTM. The Technical Education Research Center in Cambridge, Massachusetts, created a simple-to-use database program called TableTop to support database construction and analysis by school-age children (Hancock, Kaput, & Goldsmith, 1992). Tabletop works with existing databases or with databases students create themselves. Data are visually represented by mobile icons that can be arranged into box plots, cross tabulations, histograms, scatter plots, and Venn diagrams. Students develop mathematical understanding of attributes, logical relationships, place value, and plotting and learn to perceive the stories and patterns that lie within the data they collect.
TableTop has been replaced by new data visualization software called TinkerPlots ( Developed with a grant from the National Science Foundation at the University of Massachusetts, TinkerPlots is data visualization software for grades 4 to 8 that enables students to see different patterns and clusters in statistical data. Students begin by asking a question that requires a prediction or inference (see chapter 3). They collect data (e.g., shoe size and height), assign units to the data (e.g., size and inches), and then represent the data graphically in many ways. With all the data points on a graph, students can group them in clusters, sort them by amount or other sequence, and display them in a seemingly infinite variety of formats. Students are able to use rich data sets or generate their own data sets based on problems they invent and construct their own graphical displays to help them solve the problem. Students learn to reason with data.
Cliff Konold (2006), the designer of TinkerPlots, introduces the use of the software by asking the class whether they think students in higher grades carry heavier backpacks than do students in lower grades. He has them explore a data set to see whether the data support their expectations. To help them answer the question, students can separate the cases into four bins according to the weight of the backpacks. To view the data in different representations, the icons representing each case can be stacked, then separated completely until the case icons appear over their actual values on a number line. By selecting the attribute Grade, the fifth-grade students were separated vertically from the other grades. By pulling out each of the three other grades one by one, students could then see the distributions of PackWeight for each of the four grades in this data set (grades 1, 3, 5, and 7). These different views enable students with different cognitive styles to find a mathematical representation that makes sense to them. TinkerPlots can also import Microsoft Excel spreadsheet files to enable students to visualize data in more ways than those afforded by Excel. Students can assign different icons to the data points and generate numerous comparative plots that Excel cannot.
Fathom Dynamic Statistics Software (by Fran Arbaugh)
Like TinkerPlots for elementary and middle grade students, Fathom Dynamic Statistics Software (Finzer, Erickson, & Binker, 2001) allows high school students access to powerful tools for making sense of large data sets.
Visual Geometry With Geometric Supposer
One of the best-known visualization tools is Geometric Supposer ( math-international/software5.htm), a tool for making and testing conjectures in geometry through the process of constructing and manipulating geometric objects and exploring the relationships within and between these objects (Schwartz & Yerushalmy, 1987). Geometric Supposer allows students to choose a primitive shape, such as a triangle, and construct it by defining points, segments, parallels or perpendiculars, bisectors, or angles (Yerushalmy & Houde, 1986). The program plots and remembers each manipulation and can apply it to similar figures. For example, if the students conjecture that "a median drawn from the vertex of any triangle to the opposite side bisects the angle," they can test it easily by asking Geometric Supposer to measure the angles or by applying the relationship to several other triangles. The students will learn immediately that the conjecture is not true. Constructing these test examples manually would require more effort than students are likely to generate, but the computational power of the computer makes this testing very easy.
Geometry instruction is traditionally based on the application of theorems to prove that certain relationships exist among objects. This top-down approach requires analytic reasoning, which a majority of students find difficult. Geometric Supposer supports the learning of geometry by enabling the student to inductively prove these relationships by manipulating the components of geometric objects and observing the results. Rather than having the student apply someone else's logic, Geometric Supposer makes explicit the relationships between visual properties and the numerical properties of the objects (Yerushalmy, 1990). Rather than using the computer to provide conclusive results, the computer calculates the results of students' experiments. The research results with Geometric Supposer have been consistently positive. |
Math Placement Test Preparation
A review of basic math concepts and skills can significantly raise a student's score on a math placement test. The review options below are designed to help self-motivated students place into an appropriate math class. Please note that these are "self-help" options: no TMCC tutoring or instruction is provided (also note that any specific course information contained in an external link applies to the institution that has set up this link and not to TMCC).
This Pre-Algebra Quick Review (designed to help students place into Math 095) is for students who need only a little brushing up on their pre-algebra math skills.
The extensive pre-algebra review options below are for students who are highly motivated and comfortable teaching themselves math on their own—students testing below Math 095 who need motivation, support, and tutoring to learn math should enroll in the TMCC Skills Center.
ALEKS Online Pre-algebra Course
ALEKS provides an initial assessment of the student's math skills, an individualized curriculum based upon that initial assessment, guided practice problems, worked examples, video tutorials, and regular assessments during the course. The 18-week ALEKS access code to take this class currently costs $67.00 (if purchased online). For details, see ALEKS Pre-Algebra Course.
Free "Pencil and Paper" Pre-algebra Course
This course uses a free, downloadable textbook that provides lessons, worked examples, and practice problems with answers. Video lessons covering many of the course's topics and additional practice problems are also provided. The student works through assigned chapters and sections. For details, see Free Pre-Algebra Course (choose Study Guide for the course outline and instructions). |
Applications of Trigonometry Lesson 7: Graphs of Polar Equations will explore the graphs of polar equations byusing calculators and by pattern recognition of standard equations. The lesson expands basic graphs by having students analyze each curve at a deeper level of understanding. The lesson contains an eight-page "Bound Book" style foldable as a graphic organizer to engage students, a SmartNotes file for presenting the lesson, and a *.PDF file of the completed lesson.
Compressed Zip File
Be sure that you have an application to open this file type before downloading and/or purchasing.
1891.67 |
Cliffs Quick Review for Geometry - 01 edition
Summary: When it comes to pinpointing the stuff you really need to know, nobody does it better than CliffsNotes. This fast, effective tutorial helps you master core geometry concepts -- from perimeter, area, and similarity to parallel lines, geometric solids, and coordinate geometry -- and get the best possible grade.
At CliffsNotes, we're dedicated to helping you do your best, no matter how challenging the subject. Our authors are veteran teachers and talented wri...show moreters who know how to cut to the chase -- and zero in on the essential information you need to succeed. ...show less
Ed Kohn, MS is an outstanding educator and author with over 33 years experience teaching mathematics. Currently, he is the testing coordinator and math department chairman at Sherman Oaks Center for Enriched Studies.
2001 Paperback Good Our goal with every sale is customer satisfaction, so please buy with confidence. Orders are shipped same or next day. This is a used book and may show some signs of use or wear...show more. ...show lessVeryGood
Coas Books, Inc. NM Las Cruces, NM
2001 |
Help With Math:
Purveyors of MathXpert
MathXpert: software to help you learn mathematics.
MathXpert is software to help people learn algebra, precalculus, or calculus. Here's a typical solution in progress. The student
has already taken three steps. The part of the expression that changed from the previous line is shown in red.
MathXpert displays solutions
in the classical two-column format, with the justification for each step in the right-hand column.
What happens next depends on whether the student knows what to do next. If so, MathXpert provides tools for
carrying out the desired mathematical operation. If not, then the student can get help. You can see both possibilities:
click here to see what happens if the student knows what to do, or
click the Hint, Autostep, Showstep, or AutoFinish button to see the
kinds of help available. |
bravo! 10.02.01 description
A trigonometric and scientific RPN calculator. Mathematic - Solution of triangles - Complex numbers and vectors calculations - Measure converter: 112 different measures grouped in 12 categories - 8 stac-registers that may be seen in a separate window...read more |
It is sometimes characterized as an "algebraic" methodology. All of the points, lines and shapes are discussed and studied but with a different perspective. In this teaching method, there is a stronger emphasis on the use of the formulas for calculating the areas and volumes and less of an emphasis on the theorem-proof method |
College Algebra : A Graphing Approach / With Cd - 2nd edition
Summary: Williams offers a refreshing and innovative approach to college algebra, motivating the topics with a variety of creative applications and thoroughly integrating the graphing calculator. Written in a clear and friendly voice that speaks to students with varying algebra skills, with a rich array of pedagogical devices to support their learning, this text teaches students to look at math from both algebraic and geometric viewpoints. Williams focuses on the underlying c...show moreoncepts, introducing and using the graphing calculator as an integral means, not an end. This new edition is complemented by an outstanding array of innovative supplements (including online tutorials, video lessons on CD-ROM, and powerful course management and testing resources) that facilitate teaching and enhance learning.
Benefits:
NEW!-Many new applications have been added, including examples on the use of cellular telephones and traffic flow through a college campus, and an exploration in the field of cryptography.
NEW!-PreConsulting with professionals in fields such as pharmacology, bacteriology, demography, relativity, and economics, Williams provides creative applications that illustrate concepts such as the consumer awareness and queuing theory. The applications serve to introduce students to the role of math in a variety of fields. Chapter-opening applications motivate the chapter's key topics. More detail is presented later in the chapter, once students have the skills to solve the problem.
Graphing calculators are introduced when useful and integrated throughout this text in a natural way. Students are encouraged to use them to gain geometrical and numerical insight, but without neglecting mastery of basic algebra skills. This approach allows students to explore new concepts from more than one point of view or method, perform tedious computations quickly, and strengthen their problem-solving skills. Many figures show screen output so students learn to use and interpret the results of their graphing calculators quickly and accurately.
Almost 400 examples with detailed solutions, as well as a variety of applications, illustrate the important techniques and concepts.
"Self-check" and "Further Ideas" problems follow many worked examples and are ideal for in-class work. The former reinforces the ideas in the example; the latter extends the example and requires original thinking. Answers to these exercises are given at the end of the section immediately before the exercise set.
The text contains more than 3600 exercises. Each set includes routine drill problems based on the examples, and moves to original and more demanding problems. Answers to odd-numbered exercises are provided in the back of the book.
Historical notes are found at the beginning of each chapter to enrich students' understanding of the field of mathematics.
Explorations found throughout the text encourage students to investigate a mathematical topic or concept using the graphing calculator as a tool.
Section projects and chapter projects extend the theory and/or applications of the chapter and are ideal for group work.
NEW!-Additional graphing calculator material has been added where suggested by reviewers. Data used in applications and exercises has been updated throughout.
"Chapter Highlights" of the key points and references, "Chapter Tests," and "Chapter Review Exercises" are found at the end of each chapter. A "Cumulative Review Test" is provided after every third chapter. Together, these features reinforce the key ideas, test the important skills, and pinpoint areas students should review.
NEW!-Group Discussion Opportunities have been expanded.
NEW!-The review chapter has been condensed, to allow for a quicker start to core material.
NEW!-A free text-specific graphing calculator manual is available on the text's Companion Web site, providing examples and key stroke instructions to help students understand key concepts in the book, using the TI-83, TI-89, and Voyage200.
NEW!-A Resource Integration Guide, found online at the Instructor's Web site, demonstrates how the wide variety of text-specific and stand-alone supplements integrates with and complements the main text.
NEW!-Every new copy of this text is packaged with BCA Tutorial, our suite of online, dynamic, customizable tutorial resources that puts tools for student content mastery at their fingertips. By entering a PIN code packaged with their textbook, students gain access to text-specific tutorials with step-by-step explanations, exercises and quizzes, and vMentor--live, one-on-one online help from an experienced mathematics tutor.
NEW!-For instructors, BCA offers highly customizable testing, course management, and diagnostic online resources that provide a dynamic way to power the course.
NEW!-Our student mastery system also includes the Interactive Video Skillbuilder CD-ROM. Think of it as portable office hours! Free with every copy of this text, the Interactive Video Skillbuilder CD-ROM contains more than eight hours of video instruction and includes MathCue Tutorial Software.New
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Course Descriptions
Mathematics Courses
Pre-Algebra
This course will familiarize students with manipulating numbers and equations and help them understand the general principles at work. Students will understand and use factoring of numerators and denominators and properties of exponents. Students will know the Pythagorean theorem and solve problems in which they compute the length of an unknown side. They will know how to compute the surface area and volume of basic three-dimensional objects and understand how area and volume change with a change in scale. Students will convert between units of measurement. They will know and use different representations of fractional numbers (fractions, decimals, and percents). Students will use ratio and proportion to solve problems, compute percents of increase and decrease, and compute simple and compound interest. They will graph linear functions and understand the idea of slope and its relation to ratio.
Algebra I
Symbolic reasoning and calculations with symbols are central in algebra. Through the study of algebra, a student develops an understanding of the symbolic language of mathematics and the sciences. In addition, algebraic skills and concepts are developed and used in a wide variety of problem-solving situations. Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers. They determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion. Students use properties of the number system to judge the validity of results, to justify each step of a procedure, and to prove or disprove statements. Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.
Geometry
In this course students develop their ability to construct formal, logical arguments and proofs in geometric settings and problems. They identify and give examples of undefined terms, axioms, theorems, and inductive and deductive reasoning. They know and use the triangle inequality theorem and measures of sides and interior and exterior angles of triangles and polygons to classify figures and solve problems. Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures. |
an introduction to integrability and conformal field theory in two dimensions using quantum groups. The book begins with a brief introduction to S-matrices, spin chains and vertex models as a prelude to the study of Yang–Baxter algebras and the Bethe ansatz. The basic ideas of integrable systems are then introduced, giving particular emphasis to vertex and face models. Special attention is given to explaining the underlying mathematical tools, including braid groups, knot invariants and towers of algebra. The book then goes on to give a detailed introduction to quantum groups as a prelude to chapters on integrable models, two-dimensional conformal field theories and superconformal field theories. The book contains many diagrams and exercises to illustrate key points in the text. less |
Algebra II: Polynomials and Radicals
Find study help on polynomials and radicals for algebra II. Use the links below to select the specific area of polynomials and radicals you're looking for help with. Each guide comes complete with an explanation, example problems, and practice problems with solutions to help you learn polynomials and radicals for algebra II. |
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Math 526 Quiz 2Name: Please circle your section number: 001 002 You must abide by the terms of the honor code. No calculators are allowed. 1. Solve the following system of equations using Gaussian elimination on the augmented matrix representation o
Math 526 Quiz 3Name: Please circle your section number: 001 002 You must abide by the terms of the honor code. No calculators are allowed. 1. Let A, B, and C be invertible n-by-n matrices. What is the inverse of the matrix M = ABCB?2. What is the
Math 526Test 1Namc:-=-t_-e-lll'-_Plcasp circle yom sectioll llumber: 001 002 ?\Iake yom answers clear and give the exact answer (71 and not 3.14, or ~ and not O.~3:33). Feel free to use the backs of the pages, but make sure you tell me t
Math 526 Quiz 7Name: Please circle your section number: 001 002 You must abide by the terms of the honor code. No calculators are allowed. 3 -4 ? 2 51. What is the determinant of the matrix2. Let the determinant of the 3-by-3 matrix A be 4. Give
Math 526 Quiz 8Name: Please circle your section number: 001 002 You must abide by the terms of the honor code. No calculators are allowed. 1. Find the eigenvalues and the associated eigenvectors of the matrix A = 3 2 ? 1 47 -2 8 2. What are the
Math 526 Test 3Name: Please circle your section number: 001 002 Make your answers clear. Feel free to use the backs of the pages, but make sure you tell me to look there if you want it graded. No calculators are allowed. 1. Let A = -2 -2 . 1 -4(a)
Math 526 Extra Credit QuizName: Please circle your section number: 001 002 Due at the Final Exam. 1. The Pseudoinverse (Section 7.4) If m > n, it is probable that Ax = b does not have a solution because we have more equations than unknowns. So we lo
Using Movies as a Means of Literary Analysis Presented by Lynn Knowles North Star of Texas Writing Project June 7, 2004 [email protected] Quick WriteWhat is your favorite movie? Brainstorm & Discuss Why do we watch movies? What
Homework 2 Solution Guidelines1. In this problem, "the channel being sampled" gives us the rate at which the state of the channel can be changed. Thus this refers to the sampling of the analog voltage on the line, not the sampling of some analog re
Probability Probability and Random VariablesA Random Variable, X, is a variable whose value depends upon the outcome of a random experiment. Since the outcomes of our random experiments are represented as points S then to each such outcome , we a
CSC 570 Computer NetworksData Link Control - Medium Access ControlPositioning Local Area NetworksSmall size; room, floor, building Small number of computers, dozens, hundreds Manydifferent approaches, standards Ethernet has become de f
OPNET Homework 2 CSC 570-001, Fall, 2006Issued 10/4/06 due date: 11/8/06 1. Go through the "Basic Processes" section in Modeler tutorial. a. Submit the graphs from the "Basic Processes" section showing the number of packets received by the count pr
Case 98-4 Impairment of Write One Pens Write One Company ("Write"), an SEC registrant listed on a stock exchange, is a retailer of high-quality small office equipment such as calculators, phones, desk lamps, and fine pens (e.g., Cross, Mont Blanc, Wa
Ocean 423 Vertical circulation1When we are thinking about how the density, temperature and salinity structure is set in the ocean, there are different processes at work depending on where in the water column we are looking. If we are considering |
Chestnut Mountain Precalculus is built off a healthy curiosity for the world around us. These are concepts that when explained properly can prompt a further desire for learning in the future. Let's get the ball rolling.
...Physical |
The Mathematics Department offers twelve courses which give students the opportunity for a full four-year course of study. Three units of credit are required for graduation. The Advanced Program is offered to accelerate students' study by allowing them to register for AP Calculus in their senior year. All students will be required to purchase a specific graphing calculator at the beginning of their freshman year. This calculator will be used in mathematics and science classes.
318 Advanced Algebra 1
for freshmen with special placement
1 credit
Prerequisites: Placement test and department approval
This accelerated course in Algebra is available to the student who has had an introduction to Algebra in the eighth grade. Advanced Algebra 1 covers the content of the Algebra 1 course in more depth and with more emphasis on applications. In addition, some Algebra 2 topics are covered, including exponential functions, piecewise functions, matrices, linear programming, solving linear equations in three variables, and graphing radical and rational equations.
321 Geometry
required for sophomores
1 credit
Prerequisites: Algebra 1 or Advanced Algebra 1
This course uses undefined terms, definitions, constructions, postulates, theorems and some trigonometry to help students prove statements about geometric figures and relationships between those figures. Additional topics could include coordinate geometry and transformations.
328 Advanced Geometry
Sophomores or freshmen, with special placement
1 credit
Prerequisites: Advanced Algebra 1 with no semester grade lower than a B, or special placement, and department approval
This accelerated course in Geometry is available only to students with strong algebra skills and strong reasoning ability. Advanced Geometry covers the content of the Geometry course in more depth and with more emphasis on analysis. Additional topics include right triangle trigonometry, vectors, law of sines and cosines, and parametric equations and projectile motion.
331 Algebra 2
Juniors
1 credit
Prerequisites: Geometry and department approval
This course extends the study of Algebra 2 through two semesters. The course strengthens Algebra 1 skills and develops the concepts of Algebra 2. Topics studied include linear and quadratic equations and inequalities, graphing, polynomial functions, rational expressions, exponents, radicals, irrational and complex numbers. Optional topics include exponential and logarithmic functions, and the binomial theorem.
Algebra 2
Juniors
1 credit
Prerequisites: Geometry or Advanced Geometry, with no semester grade lower than a C in all previous math classes and department approval
This course includes a review of skills from Algebra 1 and all the essential topics for an Algebra 2 course. It also includes the study of Trigonometry. Topics included are quadratic relations, exponential and logarithmic functions, radical expressions, and analytic geometry.
Advanced Algebra 2 with Trigonometry
Juniors or sophomores, with special placement
1 credit
Prerequisites: Advanced Algebra 1 and/or Advanced Geometry, with no semester grade lower than a B in all previous math classes and department approval
This accelerated course is available only to the very capable student intending to enroll in AP Calculus. The course encompasses Algebra 2 with Trigonometry and material from the Pre-Calculus course. Topics included are Quadratic, Polynomial, and Rational Functions; Exponential and Logarithmic Functions; Analytic Geometry; Sequences and Series; Probability and Statistics; Trigonometry, Vectors and Polar Coordinates. Emphasis is placed on applications of the topics covered.
341 Trigonometry
Elective for seniors
½ credit
Prerequisites: Algebra 2 and department approval
This is a first semester course. The students are introduced to the study of trigonometry using triangle trigonometry. Topics covered include solving right triangles, solving general triangles, and applications. The unit circle, radian measurement, basic trigonometric identities, and graphing trigonometric equations are also covered.
343 Topics in Discrete Mathematics
Elective for seniors
½ credit
Prerequisites: Algebra 2 and department approval
This is a second semester course. The students are introduced to the study of probability and statistics and series and sequences. Additional topics may be covered.
342 Pre-Calculus
This course is designed to broaden the student's grasp of mathematics and to provide an ample preparation for the study of college level courses. The following topics are included: complex numbers, polynomial functions, exponential and logarithmic functions, sequences and series, trigonometric functions, and matrices.
345 AP Statistics
Elective for seniors; juniors with special placement
1 credit
Prerequisites: Algebra 2/Trig or Advanced Algebra 2/Trig, no grade below a C in previous math and English classes, a brief writing assignment and department approval.
This accelerated course teaches students the major concepts and tools for collecting, analyzing and drawing conclusions from data and covers the advanced placement curriculum. The four conceptual themes covered are: Exploring Data; Sampling and Experimentation; Probability and Simulations; Statistical Inference.
349 AP Analytic Geometry and Calculus
Elective, 12; 11 with special placement)
1 credit
Prerequisites: Advanced Algebra 2/Trig or Precalculus, no grade lower than a B in all previous math classes and department approval
This course continues the development of advanced mathematics and encompasses a first course in the differential and integral calculus of functions of a single variable. Topics covered are real numbers, analytic geometry and functions, limits and continuity, the derivative and applications of the derivative, the differential, antidifferentiation, and the definite integral. |
Summary
Table of Contents
Review of Real Numbers
Symbols and Sets of Numbers
Fractions
Exponents and Order of Operations
Introduction to Variable Expressions and Equations
Adding Real Numbers
Subtracting Real Numbers
Multiplying and Dividing Real Numbers
Properties of Real Numbers
Reading Graphs
Equation, Inequalities, and Problem Solving
Simplifying Algebraic Expressions
The Addition Property of Equality
The Multiplication Property of Equality
Solving Linear Equations
An Introduction to Problem Solving
Formulas and Problem Solving
Percent and Problem Solving
Further Problem Solving
Solving Linear Inequalities
Graphing
The Rectangular Coordinate System
Graphing Linear Equations
Intercepts
Slope
Graphing Linear Inequalities
Exponents and Polynomials
Exponents
Adding and Subtracting Polynomials
Multiplying Polynomials
Special Products
Negative Exponents and Scientific Notation
Division of Polynomials
Factoring Polynomials
The Greatest Common Factor and Factoring by Grouping
Factoring Trinomials of the Form x2 + bx + c
Factoring Trinomials of the Form ax2 + bx + c
Factoring Binomials
Choosing a Factoring Strategy
Solving Quadratic Equations by Factoring
Quadratic Equations and Problem Solving
Rational Expressions
Simplifying Rational Expressions
Multiplying and Dividing Rational Expressions
Adding and Subtracting Rational Expressions with Common Denominators and Least Common Denominators |
MATHEMATICS
Except for the remedial levels (Integrated Math courses) and Advanced Placement Calculus, the mathematics courses at AlterHigh School are separated into honors B and C levels.
In the C level material is presented with emphasis on review, practice and application. Concepts are developed primarily through example. The student at this level will do exercises designed to check the grasp of the concepts and his/her ability to apply these ideas in basic situations. Some challenging problems will be assigned as the student demonstrates understanding.
In the B level the concepts are developed with some theory and proof (Geometry B uses direct proof fairly extensively). In addition to basic problems the student at this level will do exercises that are more challenging and that call for more sustained application.
In the honors level a rigorous approach is taken to developing mathematical theory. Proof is used as a tool extensively. In addition to basic and intermediate level exercises, the student will do challenging problems requiring higher level thinking skills. Success in handling these problems will depend on the student's ability to evaluate given information, to discover relationships that are not obvious, and to reason out a method of solution. Prerequisites for AP and Honors classes may not be waived.
Placement into freshman classes is determined by the High School Placement Test, grade school curriculum and eighth grade teacher observation of performance. Placement of all non-freshmen is based on the average of the first three quarters in the current math course. However, all Algebra 2 courses carry an additional prerequisite from Algebra I as noted in the individual course descriptions. The present teacher's signature is required to guarantee the prerequisites (minimum stated for each course) are met.
All students are to have a TI84+ graphing calculator.
COMPUTER PROGRAMMING
Grade 11, 12 Elective Full Year 1 Credit
Prerequisite: Enrollment in or completion of Honors or regular (B) Geometry and the computer teacher's signature. This is not a math course, yet is preparation for college courses in computer science and engineering.
Description: This course teaches the computer language C++. Students will be required to write, compile, execute, debug, store, and retrieve programs.
HONORS ALGEBRA 1
Grade 9 Elective Full Year 1 Credit
Prerequisite: Placement determined by the Math Department
Description: This course enriches the Algebra I concepts with an in depth study of theory and problem solving. Additional topics include direct proofs, factoring cubics, simplifying zero and negative integral exponents, solving systems of three equations in three variables, and an introduction to irrational numbers.
ALGEBRA 1 B
Grade 9 Elective Full Year 1 Credit
Prerequisite: Placement determined by the Math Department
Description: In addition to the concepts presented in Algebra I C, this course includes transforming formulas, combined inequalities, absolute value equations/inequalities, and functions and relations.
ALGEBRA 1 C
Grades 9, 10, 11 Elective Full Year 1 Credit
Prerequisite: Grade 9 - Placement determined by Math Department
Grades 10 and 11 – A grade of A or at least a B- in Integrated Math must be attained
Description: This course is an introduction to the study of the structure of the algebra of the real number system. It is designed to help the student recognize the techniques and properties of algebra as reflections of this structure and to be able to apply algebraic concepts and skills to equations, inequalities, and problem solving.
HONORS GEOMETRY
Grade 9, 10 Elective Full Year 1 Credit
Prerequisite: A in Algebra I B and teacher recommendation; C+ in Honors Algebra I
Description: In addition to the concepts presented in Geometry B, this course presents geometry as a mathematical system, uses proof to develop all topics covered, develops the understanding and use of locus and coordinate geometry topicsGEOMETRY B
Grade 9, 10 Elective Full Year 1 Credit
Prerequisite: A- in Algebra I C; C- in Algebra I B; D in Honors Algebra I
Description: In addition to the concepts presented in Geometry C, this course includes use of two column deductive proofs to introduce and explore many topics, an introduction to indirect and paragraph proofs, an introduction to right triangle trigonometry, and area and volumes of 3-dimensional figures.
GEOMETRY C
Grade 10, 11, 12 Elective Full Year 1 Credit
Prerequisite: D in Integrated Algebra 1/Basic Geometry; D in Algebra I C; D+ or D (only) in Algebra I B
Description: This course includes the use and understanding of the language of geometry, spatial relationships of lines and planes, properties of polygons with emphasis on trianglesINTEGRATED ALGEBRA 1
Grade 9 Elective Full Year 1 Credit
Prerequisite: Placement by the Math department
Description: This course paired with Integrated Algebra 1/Basic Geometry is designed to be a two-year course covering Algebra 1 C topics and an introduction to basic Geometry topics. This course is designed for the student who needs to explore basic algebraic concepts at a slower pace than the Algebra 1 C course. Math review topics and pre-algebra topics will be integrated with an introduction to the study of the structure of algebra of the real number system. Emphasis on review of techniques and applications of algebraic concepts will be used.
INTEGRATED ALGEBRA 1 / BASIC GEOMETRY
Grade 10 Elective Full Year 1 Credit
Prerequisite: D or above in Integrated Algebra I
Description: This course is paired with Integrated Algebra 1 to give the student a full year of Algebra and an introduction to basic Geometry topics. It will review and strengthen previously introduced Algebra 1 topics and will introduce new topics to complete an Algebra 1 course. As time allows, Basic Geometry topics will be introduced to help the student prepare for Geometry C.
HONORS ALGEBRA 2 - TRIG
Grades 10, 11 Elective Full Year 1 Credit
Prerequisite: A+ in Geometry B and Algebra I B; C+ in Honors Geometry and Honors Algebra I
Description: In addition to the concepts in the other Algebra 2 courses, this course includes algebraic proofs of real number properties and absolute value, solving linear equations using determinants, working with trigonometric identities and graphs of sine and cosine functions.
ALGEBRA 2 B - TRIG
Grades 10, 11 Elective Full Year 1 Credit
Prerequisite: A in Geometry C and B in Algebra I C; C- in Geometry B and Algebra I B; D in Honors Geometry and C in Honors Algebra I
Description: In addition to the concepts presented in Algebra 2 C, this course includes beginning trigonometry (degree and radian measures on the unit circle, the six basic trigonometric identities, solving triangles, Law of Sines, Law of Cosines) and co-function formulas, and exponential and logarithmic equations.
ALGEBRA 2 C
Grades 11, 12 Elective Full Year 1 Credit
Prerequisite: D in Algebra I C and Geometry C; D in Algebra I B and D in Geometry B
Description: This course reviews and strengthens Algebra I concepts such as solving linear equations and inequalities, solving quadratic equations and inequalities by factoring, linear graphing, and word problem solving. This course includes solving quadratic equations by completing the square and the quadratic formula, radicals and radical equations, linear equations in two variables, zero and negative exponents, and complex numbers.
HONORS PRECALCULUS
Grades 11, 12 Elective Full Year 1 Credit
Prerequisite: C or better in Honors Algebra 2
Description: In addition to concepts presented in the other Precalculus courses, this course will also include coordinate geometry proofs, defining "e" and natural logarithms, polar graphing, power series, mathematical induction, an introduction to derivatives.
PRECALCULUS B
Grade 11, 12 Elective Full Year 1 Credit
Prerequisite: C in Algebra 2 B; D in Honors Algebra 2
Description: This course will include analytic geometry of all conic sections, trigonometric formulas, equations and identities, advanced graphing, polar coordinates with complex numbers, vectors, binomial theorem with probability, first derivative theory and practice, and an introduction to graphing calculators.
Description: This course is paired with Algebra 2 C to give students the opportunity for a complete Algebra 2 course and an introduction to Precalculus. Topics include trigonometry, polynomial functions, exponents, logarithms, conic sections, basic operations with complex numbers, and probability and statistics.
SELECTED MATH TOPICS
Grade 12 Elective Full Year 1 Credit
Prerequisite: C or lower in Algebra 2B
Description: This course is for students who need a fourth year of math, but not at the PreCalculus level. Topics include, but are not limited to: Set Theory, Logic, Number Theory, Probability, and Statistics.
Description: This course covers topics in elementary functions, differential and integral calculus comparable first year courses in colleges and universities. Topics include properties of functions, limits, derivatives of elementary, composite, implicitly defined, inverse, and logarithmic functions, applications of the derivative, techniques of integration and applications of the integral.
ADVANCED PLACEMENT CALCULUS
Grade 12 Elective Full Year 1 Credit
Prerequisite: A+ in Precalculus B; B- in Honors Pre-Calculus
Description: Advanced Placement Calculus emphasizes a multi-representational approach to Calculus with concepts, results and problems being expressed geometrically, numerically, analytically and verbally. Broad concepts and widely applicable methods are emphasized. Technology is used regularly to reinforce the relationships among the multiple representations of functions, to confirm written work, to implement experimentation, and to assist in interpreting results. It is expected that students enrolled in AP Calculus will take the AP Calculus exam in May at the prevailing fee. |
I am very excited to be back at Mann for another year! Algebra is an extremely challenging course for seventh and eighth graders, but also one of the most useful. With hard work we will all finish this year with great scores and a new found respect for math.
All the assignments and updates for my classes are available on Grade Book Wizard at just log-in and select your course.
The Algebra Upgrade program is also available for all students to practice Algebra content at home, just visit
I am here to help and answer any questions, please feel free to ask.
Algebra 1
Algebra 1 is a college preparatory course which satisfies an A-G requirement for college entrance. The basic algebra skills covered in the course are the building blocks for most math classes students will take in the future.
This year we will be exploring the curriculum through the use of the units based on the clusters used for the CST. These include: Number Properties, Operations and Linear Equations; Graphing and Systems of Linear Equations; Quadratics and Polynomials; and Functions and Rational Expressions.
Club Caltech is an after school club where high achieving students learn about higher education. Topics discussed include: college entrance process and requirements, financial aid, career options, and student life. Students in the club sometimes also tutor other students as a way to begin their community service experience. The club is also visited by counselors from Mann and Crawford High who offer information on classes and opportunities at the schools.
In previous years Club Caltech gone on a field trip to UCSD where we explored the campus, visited dorms, and even ate in a dining hall, and participated in the GSDCMC Field Day. We hope to compete in more math competitions this year.
There is a bulletin board with information and meeting dates in the downstairs hallway of the 600 building. Contact Ms. Weaver if you are interested in joining the club! |
EC10153 Core skills for economists: mathematics 2
Credits: 6
Level: Certificate
Semester: 2
Assessment: EX 80%, TE 20%
Requisites:
While taking this unit you must take EC10130
Aims: To extend students' knowledge and understanding of mathematics and the use of mathematical techniques in economic analysis, begun in EC10130. To provide students with knowledge of areas of mathematics that are relevant to undergraduate economics and to prepare them for more advanced units in economics and econometrics.
Learning Outcomes: By the end of the course unit, students should be able to understand key mathematical concepts, solve mathematical problems, and apply mathematics to economic problems.
Skills: Students will develop mathematical skills, specifically as listed below.
Content: |
Trigonometry Smarts!
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 trigonometry. This book is designed for students to use alone or with a tutor or parent, and provides clear lessons with easy-to-learn techniques and plenty of examples.
Whether you are looking to learn this information for the first time, on your own or with a tutor, or you would like to review some trigonometry skills, this book will be a great choice.
show more show less
Edition:
2012
Publisher:
Enslow Publishers, Incorporated
Binding:
Trade Paper
Pages:
64
Size:
6.50" wide x 9 |
buildings, finding the number of people going into 2 or 3 of the buildings ... 7th-8th Middle School Math, Pre-Algebra, Algebra, Geometry ... School MathThematics, Holt Middle School Math, McDougal Littell Algebra, ... What follows is a list of the key ... Mid terms and final exams for Geometry ...... Chapter readiness quizzes ...
They are helpful in planning the year so that all key grade level ... Grade Level Week-by-Week Standards Map – McDougal Littell ... District Benchmark Test and the CST. ... CSTs than a weekly quiz or chapter test (formative). o The District Benchmarks will be given in the last week of Triads 2, 3 and. 4. ..... Mid Chapter Test. 4 ...
8th GRADE CURRICULUM TRINITY LUTHERAN SCHOOL 824 ...
Projects Memorize and understand key Bible passages for Christian living. ... Text American History – McDougal-Littell, c. ... is read and selected questions at the end of the section are answered in ... Quizzes throughout a chapter, and chapter tests, and daily work provided ... MATHEMATICS PRE-ALGEBRA ... Page 3 ...
HIGH SCHOOL COURSE OUTLINE
Algebra CD SDC is designed specifically for the needs of students with mild/moderate ... The * designates the key standards that comprise a minimum of 70% of the ... orally in some content area reading strategies (especially pre-reading, KWL, and ..... Cumulative Review. McDougal Littell. Chapter Readiness Quiz. Quizzes ...
Effective Programs in Middle and High School Mathematics A Best ...
secondary math achievement is a key predictor of a nation's long-term ... of mathematics programs for middle and high schools to find answers to these ... tematically comparing the evidence bases supporting alternative programs in mid- .... ditional commercial textbooks, such as McDougal-Littell and Prentice Hall, that are ...
Feb 7, 2012 – Sign-in and sign-outs are limited to three (3) per quar- .... Service Coordinator, can answer any questions you .... J.P. Taravella's DECA chapter has been hard at work organizing this year's Public Relations ... The project focuses on three main points a Gi- .... Pre-Algebra, Holt McDougal, Florida Pre-Algebra ...
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Practical Problems in Math for Automractical Problems in Math for Automotive Technicians
Comprehensive and easy-to use, this updated edition covers every type of practical math problem that automotive technicians will face on the job. The subject matter is organized in a knowledge-building format that progresses from the basics of whole number operations into percentages, linear measurements, ratios, and the use of more complex formulas. Complete coverage of fundamentals, as well as more advanced computations make this book suitable for both beginning and advanced technicians. With a special section on graphs, scales, test meters, estimation, and invoices used in the workplace, this book is tailor-made for any automotive course of study |
The fundamental tools of linear algebra are vectors and matrices, which are addressed in the chapter, Mathematical Objects. This chapter deals with the operations that can be carried out on vectors and matrices and other functions that take them as arguments.
The number of columns in the first operand must be the same as the number of rows in the second. In WIRIS,
all vectors are row vectors, but this is not a restriction. In order to multiply a matrix by a row vector, the vector is considered as a column vector as long as this permits multiplying.
The symbol * always appears as · in accordance with typographical convention.
A square matrix can be raised to a whole number power. If we raise it to a negative power and the matrix can be inverted, the inverse of the matrix is raised to the absolute value of the exponent. If the matrix cannot be inverted, an error is returned.
Given a square matrix, A and two integers i and j, this calculates the minor corresponding to the position Aij of the matrix. This minor is the determinant of the matrix obtained by eliminating, from A the row i and the column j.
powered by WIRIS (c) maths for more sl. All rights reserved. Legal notice |
Precalculus
9780321531988
ISBN:
0321531981
Edition: 4 Pub Date: 2008 Publisher: Pearson
Summary: - By Judith A. Penna - Contains keysroke level instruction for the Texas Instruments TI-83 Plus, TI-84 Plus, and TI-89 - Teaches students how to use a graphing calculator using actual examples and exercises from the main text - Mirrors the topic order to the main text to provide a just-in-time mode of instruction - Automatically ships with each new copy of the text |
Differential Geometry, Gauge Theories, and Gravity
Using a self-contained and concise treatment of modern differential geometry, this book will be of great interest to graduate students and researchers in applied mathematics or theoretical physics working in field theory, particle physics, or general relativity. The authors begin with an elementary presentation of differential forms. This formalism is then used to discuss physical examples, followed by a generalization of the mathematics and physics presented to manifolds. The book emphasizes the applications of differential geometry concerned with gauge theories in particle physics and general relativity. Topics discussed include Yang-Mills theories, gravity, fiber bundles, monopoles, instantons, spinors, and anomalies |
Basic College Mathematics, Books a la Carte Edition, 4th Edition
Description
This edition features the exact same content as the traditional text in a convenient, three-hole- punched, loose-leaf version. Books à la Carte also offer a great value—this format costs significantly less than a new textbook.
Elayn Martin-Gay firmly believes that every student can succeed, and her developmental math textbooks and video resources are motivated by this belief. Basic College Mathematics, Fourth Edition was written to help readers effectively make the transition from arithmetic to algebra. The new edition offers new resources like the Student Organizer and now includes Student Resources in the back of the book to help students on their quest for success. |
Attention
Grades 6–8 Mathematics—Introduction to Connected Mathematics
The educators of the Connected Mathematics Project (CMP) have a collective, overarching goal: to help students understand how important it is to be proficient in the various disciplines of mathematics. Students the world over will one day compete for resources to get ahead. With technological advances and global commerce framing their paths to success, students who have insight and a creative attitude, and who have been disciplined in mathematical reasoning and communication will be better positioned respond to the needs of a global economy.
Specifically, educators of Connected Mathematics seek to guide students to proficiency in these areas of mathematics: reason and communication, vocabulary, forms of representation, materials, tools, techniques, intellectual methods.
Connected Mathematics is a comprehensive middle school mathematics curriculum that provides students with multiple opportunities to develop knowledge and fluency with skills and concepts across mathematical strands. Because the program's mathematical ideas develop and deepen over the course of three years, students must have opportunities to study mathematics in each strand every year.
Support for Connected Mathematics is demonstrated by these results in 10 years of testing:
CMP is an effective middle school curriculum that is accessible to all students.
CMP students do as well as, or better than, non-CMP students on tests of basic skills, and outperform non-CMP students on tests of problem- solving ability, conceptual understanding, and proportional reasoning.
CMP students can use basic skills to solve important mathematical problems and are able to communicate their reasoning and understanding.
By the end of grade 8, CMP students show considerable ability to solve non-routine algebra problems and demonstrate a strong understanding of linear functions and a beginning understanding of exponential and quadratic functions. |
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Calculus for Scientists and Engineers: Early Transcendentals, CourseSmart eTextbook
Description
For a three-semester or four-quarter calculus course covering single variable and multivariable calculus for mathematics, engineering, and science majors.
Briggs/Cochran is the most successful new calculus series published in the last two decades. The authors' decades of teaching experience resulted in a text that reflects how students generally use a textbook—i.e., they start in the exercises and refer back to the narrative for help as needed. The text therefore builds from a foundation of meticulously crafted exercise sets, then draws students into the narrative through writing that reflects the voice of the instructor, examples that are stepped out and thoughtfully annotated, and figures that are designed to teach rather than simply supplement the narrative. The authors appeal to students' geometric intuition to introduce fundamental concepts, laying a foundation for the rigorous development that follows.
To further support student learning, the MyMathLab course features an eBook with 700 Interactive Figures that can be manipulated to shed light on key concepts. In addition, the Instructor's Resource Guide and Test Bank features quizzes, test items, lecture support, guided projects, and more.
This book is a special version of Calculus: Early Transcendentals by the same authors, with an entire chapter devoted to differential equations, additional sections on other topics, and additional exercises in most sections. See the "Features" section for more details.
Table of Contents
1. Functions
1.1 Review of functions
1.2 Representing functions
1.3 Inverse, exponential, and logarithmic functions
1.4 Trigonometric functions and their inverses
2. Limits
2.1 The idea of limits
2.2 Definitions of limits
2.3 Techniques for computing limits
2.4 Infinite limits
2.5 Limits at infinity
2.6 Continuity
2.7 Precise definitions of limits
3. Derivatives
3.1 Introducing the derivative
3.2 Rules of differentiation
3.3 The product and quotient rules
3.4 Derivatives of trigonometric functions
3.5 Derivatives as rates of change
3.6 The Chain Rule
3.7 Implicit differentiation
3.8 Derivatives of logarithmic and exponential functions
3.9 Derivatives of inverse trigonometric functions
3.10 Related rates
4. Applications of the Derivative
4.1 Maxima and minima
4.2 What derivatives tell us
4.3 Graphing functions
4.4 Optimization problems
4.5 Linear approximation and differentials
4.6 Mean Value Theorem
4.7 L'Hôpital's Rule
4.8 Newton's Method
4.9 Antiderivatives
5. Integration
5.1 Approximating areas under curves
5.2 Definite integrals
5.3 Fundamental Theorem of Calculus
5.4 Working with integrals
5.5 Substitution rule
6. Applications of Integration
6.1 Velocity and net change
6.2 Regions between curves
6.3 Volume by slicing
6.4 Volume by shells
6.5 Length of curves
6.6 Surface area
6.7 Physical applications
6.8 Logarithmic and exponential functions revisited
6.9 Exponential models
6.10 Hyperbolic functions
7. Integration Techniques
7.1 Integration Strategies
7.2 Integration by parts
7.3 Trigonometric integrals
7.4 Trigonometric substitutions
7.5 Partial fractions
7.6 Other integration strategies
7.7 Numerical integration
7.8 Improper integrals
8. Differential Equations
8.1 Basic ideas
8.2 Direction fields and Euler's method
8.3 Separable differential equations
8.4 Special first-order differential equations
8.5 Modeling with differential equations
9. Sequences and Infinite Series
9.1 An overview
9.2 Sequences
9.3 Infinite series
9.4 The Divergence and Integral Tests
9.5 The Ratio, Root, and Comparison Tests
9.6 Alternating series
10. Power Series
10.1 Approximating functions with polynomials
10.2 Properties of Power series
10.3 Taylor series
10.4 Working with Taylor series
11. Parametric and Polar Curves
11.1 Parametric equations
11.2 Polar coordinates
11.3 Calculus in polar coordinates
11.4 Conic sections
12. Vectors and Vector-Valued Functions
12.1 Vectors in the plane
12.2 Vectors in three dimensions
12.3 Dot products
12.4 Cross products
12.5 Lines and curves in space
12.6 Calculus of vector-valued functions
12.7 Motion in space
12.8 Length of curves
12.9 Curvature and normal vectors
13. Functions of Several Variables
13.1 Planes and surfaces
13.2 Graphs and level curves
13.3 Limits and continuity
13.4 Partial derivatives
13.5 The Chain Rule
13.6 Directional derivatives and the gradient
13.7 Tangent planes and linear approximation
13.8 Maximum/minimum problems
13.9 Lagrange multipliers
14. Multiple Integration
14.1 Double integrals over rectangular regions
14.2 Double integrals over general regions
14.3 Double integrals in polar coordinates
14.4 Triple integrals
14.5 Triple integrals in cylindrical and spherical coordinates
14.6 Integrals for mass calculations
14.7 Change of variables in multiple integrals
15. Vector Calculus
15.1 Vector fields
15.2 Line integrals
15.3 Conservative vector fields
15.4 Green's theorem
15.5 Divergence and curl
15.6 Surface integrals
15.6 Stokes' theorem
15.8 Divergence theorem
Appendix A. Algebra Review
Appendix B. Proofs of Selected Theorems |
A student should take MATH 090 or MATH 091 to prepare for Intermediate Algebra. Topics investigated in both MATH 090 and MATH 091 include properties and operations of the real number system, algebraic expressions, solving equalities and inequalities, graphical representation of equations, data analysis, graphs, and properties and operations of polynomials. This course does not meet the General Studies requirement in Skills and University Requirements and does not count toward total units needed for graduation. Prerequisite: appropriate score on APU mathematics placement test or SAT 430/ACT 18 math score |
Title
Resource Type
Views
Grade
Rating
In this limits and continuity test, learners solve 8 multiple choice questions. They define the words limits and continuity. Students determine the limits of 8 functions. Learners find the value for a constant in one function, and prove one function is continuous at x=0. 4 questions require students to graph functions. There are 25 questions in all (plus one extra credit question).
In this calculus worksheet, students complete a chart of values using limits and continuity. They use the test of continuity to solve most of the problems and match their answers to the correct answers. There are 18 matching questions with an answer key.
Students read a description of how to evaluate limits then solve problems both with and without their graphing calculators. In this evaluating limits lesson, students evaluate 9 limits problems without their graphing calculators. Answers are checked using the calculator.
In this calculus instructional activity, students work problems containing functions, limits and dealing with continuity. They evaluate functions and use the limits theorem to help find the correct answer. There are 26 questions.
Students investigate limits and continuity of functions. In this limits and continuity of functions lesson, students find the limit as a function approaches a given value. Students find the domain of functions.
Twelfth graders examine limits. In this Calculus lesson plan students use the symbolic capacity of the TI-89 calculator to explore limits. Students examine the tables and graphs and use the information to support their answers.
Twelfth graders investigate limits. In this Calculus activity, 12th graders use the Ti-89 calculator to explore limits. Students examine the tables and graphs to approach limits from a numerical point of view.
In this continuity activity, students examine six functions for continuity. Students find values to make a peice-wise function continuous, state domains, use limits, and the Intermediate Value Theorem. |
2. Objectives (expected learning outcomes) In this first term course you obtain the skills and knowledge that is necessary to understand and master the mathematics lessons, in the second term. This course is optional. It is however in particular recommended to take it if you have a poor background in mathematics or if you feel insecure about the subject.
3. Course content The course consists of five chapters:
1 Set theory (elementary notions) 2 Numbers (the 5 number fields, and the reason why we need them) 3 Plane geometry (stress on the algebraic treatment, as opposed the the Euclidean axiomatics) 4 trigonometry (learn to work with formulae) 5 real functions (elementary functions and working with polynomials). |
Numbers: Rational and Irrational
Ivan Niven
A fine job of presenting the materials at a level which is attainable for the intended reading public. — The Mathematics Teacher
A superb development that starts with the natural numbers and carries the reader through the rationals and their decimal representations to algebraic numbers and then to the real numbers. Along the way, you will see characterizations of the rationals and of certain special (Liouville) transcendental numbers. This material is basic to all of algebra and analysis.
Professor Niven's book may be read with profit by interested high school students as well as by college students and others who want to know more about the basic aspects of pure mathematics. |
In modern society there are very few areas of knowledge and practice in which mathematics does not play a part. These increasingly include areas which affect our quality of life, such as health-related studies and environmental issues, as well as the contributions mathematics continues to make in commerce, science and technology. Consequently, as a subject of study, mathematics possesses great diversity, and it offers a wide range of opportunities to identify areas, which relate to your own interests, concerns, and aspirations.
TEACHING AND ASSESSMENT
Small tutorial groups in which problems are considered and individual work discussed, form an integral part of each course along with larger formal lectures, 'surgeries' and problem classes are held to deal with specific individual difficulties. To encourage an increasingly independent approach to learning, courses are delivered through lectures only, and individual tutorial assistance is given by lectures on the student's initiative. Current methods of student assessment include conventional written examinations, a variety of coursework assignments and, in some cases, a combination of these methods.
SKILLS AND CAREERS
As well as the specific expertise and skills relating to course content, students will continually be developing the kind of logical and analytical thinking which characterizes the discipline of mathematics. It is this quality which marks out the mathematics graduate, not only as a skilled practical scientist, but also as a potential strategic planner and decision maker in any complex situation. Therefore there are many opportunities open to well qualified mathematicians in industry, commerce, finance, education and research. About three-quarters of our graduates enter careers associated with computing, statistics, operational research, actuarial and insurance fields, accountancy and teaching. |
This book is a guided tour of geometry, from Euclid through to algebraic geometry. It shows how mathematicians use a variety of techniques to tackle problems, and it links geometry to other branches of mathematics. It is a teaching text, with a large number of exercises woven into the exposition. Topics covered include: ruler and compass r s1tructions, transformations, triangle and circle theorems, classification of isometries and groups of isometries in dimensions 2 and 3, Platonic solids, conics, similarities, affine, projective and Mobius transformations, non-Euclidean geometry, projective geometry, the beginnings of algebraic geometry.
Stock Availability:
This title will be ordered from the publisher and usually ships by us within 15 days. Allow a few extra days for delivery |
Pasadena, TX PhysicsMatlab is mainly used in colleges to teach algorithms including Runge Kutta for integrating differential equations. I use Mathematica mostly in heavily formulated physics problems such as molecular spins and fractional calculus where equations are concise but complex. It is always advisable for a student to be conversant in both languages |
Used by more than half a million students each year!Actual Regents Examsdevelop your subject knowledge and test-taking skills and show you where you need more study.Answers to All Questionsprovide the guidance you need to learn on your ow
Sequential Math III Power Pack
Editorial review
When students and teachers purchase Let's Review: Sequential Math III in combination with Barron's Regents Exams and Answers: Sequential Math III (the "Red Book"), they save $2.95 over the cost of both books purchased separately.
Algebra I (Cliffs Study Solver)
Editorial review
Basic Math and Pre-Algebra (Cliffs Study Solver)
Editorial review
Algebra II (CliffsStudySolver)
Editorial review
CliffsQuickReviewMath Word Problems (Cliffs Quick Review (Paperback))
Editorial review
Karen Anglin, a mathematics instructor at Blinn College in Brenham, Texas, since 1990, regularly presents workshops to teachers on best practices for teaching math word problems. She holds an MS in Statistics and a BS in Mathematics from
Algebra for Dummies
Editorial review
Reviewed by Aaron S. Rutledge, (Kalamazoo, MI)
this is definitely the book for you. If you want to learn algebra, look elsewhere.
Reviewed by "nguido", (Tampa, FL USA)
ry for Dummies a 5, since Geometry has always been my favorite subject and Algebra has not...
Reviewed by a reader
I had gone back to college and had not been in an algebra class in about 16 years...this book helped me tremendously! The book is very easy to follow and I found it short and to the point.
Reviewed by a reader, (Prince Frederick, MD United States)
Even though there are a lot of pages in this book, the number of concepts covered is extremely small. This would be better titled "Pre-Algebra for Dummies"; in fact, you'd be hard pressed to pass an Algebra I class with the mate |
Mike Davies: Coping with Maths – The jump from GCSE Maths to A Level Maths
The transition between GCSE and A-Level Mathematics is one of the largest jumps a school student can make. . There is no getting around it: A-Level Maths can be difficult! I am often called to tutor children who were flying at GCSE level with A or A* grades, only to start really struggling within months of starting an A-Level course. This guide is intended for anyone wanting to help support a student on an A-Level Mathematics course.
Content and exam format
The problem isn't helped by the size of the learning curve at A-Level. The early modules like C1 and S1 (the first modules in pure mathematics and statistics, respectively) tend to start off with relatively straightforward and familiar content that quickly gets very difficult. For example, the first unit in S1 kicks off with "Representing Data", where students are taught the use of statistical devices like histograms, stem-and-leaf diagrams and boxplots (I have taught some of these to able year 7 pupils in the past!). From this the traditional next step is a whistle-stop tour of probability, normally taking them up until Christmas or so using a standard A-Level progression, and again likely to be very familiar from previous work. Then, boom! Difficult topics with exciting names like "discrete random variables", "binomial probability functions" and "bivariate data" follow in quick succession. Core/Pure mathematics follows much the same pattern, moving quickly from familiar concepts like graphs and co-ordinate geometry into new ideas like calculus.
This increase in difficulty is matched by the fairly brutal markscheme on A-Level papers. An A-grade requires 80%, whilst an E needs 40%; the other grades are staggered equally between these in steps of 10%. Papers for Edexcel, the most popular exam board for Mathematics A-Level, are typically marked out of 75, with 8 or so questions of somewhere between 7-10 marks available for each. Missing just one of these out is enough to drop a whole grade! To stand a chance of accessing the top grades, students really need to be understanding and answering every single question.
I am certainly not saying that students shouldn't be challenged to this degree or recap on key concepts at the start of a course; just that they should be mentally prepared for the difficulty level of what is going to come next. In my experience working as a tutor, this is not always the case.
The differences between A level and GCSE
The key differences between A-Level and GCSE Mathematics are certainly not just about content. One of the most common things my students say to me is their confusion with all the new symbols and terminology. They are expected to look at something like Σ10+2r (r = 10, n =30), identify that they are meant to use the formula S = n/2(2a + (n-1)d) and quickly work out the answer is 987. Assuming this is a question worth 3 marks, they will have no more than a few minutes to do all this. Students are expected to be fully conversant in the meanings of equations and terms within them. Statements like "integrate y=2/√x , x > 0", whilst short, contain a lot of implicit meaning that it will take both time and confidence to understand. Formula books are handed out in exams, but relying on these is like trying to write an essay in a French exam entirely from a dictionary.
I have tutored several students who were able to get top grades at GCSE by rote-learning solutions and correct methods, then bombed at A-Level as they couldn't handle the increase in required conceptual understanding. As with anything, the best way to handle the new concepts is to keep track of them as they arise. I recommend the use of a mathematical dictionary, allowing students to look up terms as they go through the course, and perhaps even get students to compile their own list of key terms as they go along.
Study skills and practice
The best way to study any science is by doing, and so it is good to get students in the habit of practicing the use and application of Mathematics from day one. This doesn't just mean questions from a text book; it extends to understanding the origin of key formulas, deriving one equation from another, making up your own problems, and the old chestnut of doing past papers. It is worth getting students to frankly assess their study skills at the START of any course, and look at how to improve these. On more than one occasion I've asked an A-Level student "how do you revise?", only to be told "I never have". It sounds obvious to an adult, but students often aren't taught effective revision techniques by their school. Take some time to assess what they can do already and then augment this with other good practice. Don't be surprised if this extends right down to concepts like keeping class notes in an organised, logical order!
When to use a tutor
There will be times when students struggle with the material at A-Level Maths. One way of overcoming this is bringing in a tutor to address specific content issues. A good tutor will quickly be able to spot barriers to progress, and with even a short amount of dedicated one-to-one time they will put practical steps in place to address these difficulties. Given the difficulty of the subject, you really want a subject specialist to do this, and so I would recommend looking at Adrian Beckett tutors (a specialist Maths tuition), or Owl Tutors (my own agency).
In a nutshell, I believe the most important success criteria for any student's successful transition to A-Level Maths is a positive, "can-do" mindset. Mathematics (and certainly Further Mathematics) is probably the hardest A-Level choice. Apart from the junior Stephen Hawkings of the world, all students will struggle at times. By being ready for this, and by learning to recognise a difficulty as a positive obstacle to overcome, students will be in a much stronger position to deal with the challenges ahead.
Get into good habits early. Keep all notes in a sensible place, start practicing and doing Maths from an early stage, and start thinking about how to revise from day one
Keep on top of new concepts and definitions as they arise by using a Mathematical dictionary
Encourage and develop positive ways of thinking from day one!
Don't be afraid to call in a tutor to address specific subject concerns
About Michael Davies
I'm the Director of Education at Owl Tutors, a tuition agency based in Clapham. Before this job I taught Maths for 5 years in both London and Manchester. When I'm not tutoring or blogging, I love reading, cycling and football, and can be found playing the bass around town for my band. |
This undergraduate text introduces the fundamentals of neural networks in a gentle but practical fashion with minimal mathematics. It should be of use to students of computer science and engineering, and graduate students in the allied neural more... |
I achieved A* in all subjects including full marks in the Economics papers. I even got a prize from the exam board!"
Mathematics
Mathematics
GCSE/IGCSE
Why study Mathematics?
Questions often arise asking about the need to learn Mathematics, the application of algebra and other skills obtained whilst studying the subject and its usefulness in our daily life and future careers.
The skills that you learn in any Mathematics course may be applicable in life even if you are not studying to become an engineer or an accountant. Many entry-level jobs require employees to have some knowledge of Mathematics. Even understanding the basic mathematical functions can be advantageous.
Here is a list of important skills obtained from learning Mathematics:
develop your knowledge and understanding of mathematical concepts and techniques;
acquire a foundation of mathematical skills for further study in the subject or in related areas;
enjoy using and applying mathematical techniques and concepts, and become confident in using Mathematics to solve problems;
appreciate the importance of Mathematics in your study, in society and in employment.
How is it assessed?
The course is designed to meet the requirements of Edexcel IGCSE Mathematics syllabus. Assessment comprises two written papers, each of two hours. There is no coursework.
Mostly we prepare our students for the higher tier curriculum, which will give you the best chance of gaining grades A* - C. We also offer the course at foundation level for those who feel more comfortable with that. The highest grade achievable at foundation level is grade C. The exam is offered in both January and June of each year.
Related Careers/University courses
A good grounding in Mathematics is vital if you wish to enter university or embark on a career. A grade C or better in IGCSE or GCSE Maths provides evidence that you have the numeracy skills to succeed. |
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In this tutorial, we cover the idea of the slope of a line. We also think about how slope relates to the equation of a line and how you can determine the slope or y-intercept given some clues.\n\nThis tutorial is appropriate for someone who understands the basics of graphing equations and want to dig a bit deeper. 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Mathematical proof is the gold standard of knowledge. Once a mathematical statement has been proved with a rigorous argument, it counts as true throughout the universe and for all time. Imagine, then, the thrill of being able to prove something in mathematics. But you don't have to imagine the exhilaration of constructing a proof—you can do it! Prove It: The Art of Mathematical Argument initiates you into this thrilling discipline in 24 lectures by Professor Bruce H. Edwards of the University of Florida. This course is suitable for everyone from high school students to the more math-savvy.
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Mathematics Describing the Real World: Precalculus and Trigonometry
Professor Bruce H. Edwards
Finally make sense of the mysteries of precalculus and trigonometry in the company of master educator and award-winning Professor Bruce Edwards. In the 36 intensively illustrated lectures of Mathematics Describing the Real World: Precalculus and Trigonometry, he takes you through all the major topics of a typical precalculus course taught in high school or college. You'll gain new insights into functions, complex numbers, matrices, and much more. The course also comes complete with a workbook featuring a wealth of additional explanations and problems.
Algebra II
Professor James A. Sellers
Make sense of Algebra II in the company of master educator and award-winning Professor James A. Sellers. Algebra II gives you all the tools you need to thrive in a core skill of mathematics. In 36 engaging half-hour lectures, Professor Sellers walks you through hundreds of problems, showing every step in their solution and highlighting the most common missteps made by students. Designed for learners of all ages, this course will prove that algebra can be an exciting intellectual adventure and not nearly as difficult as many students fearSave Up To $175Save Up To $175Conquer the mechanics and applications of junior-high and high-school math in this two-course set designed by award-winning Penn State Professor James A. Sellers. In Mastering the Fundamentals of Mathematics, you'll gain proficiency in the key skills necessary to unlock the door to more advanced areas of study—such as algebra, geometry, and calculus—and discover new levels of confidence in dealing with the math of everyday life. Next, Algebra I makes the concepts of first-year algebra—including variables, order of operations, and functions—easy to grasp.
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Everyone from high school students to the more math-savvy will enjoy this two-course set from University of Florida professor Bruce H. Edwards. Prove It: The Art of Mathematical Argument initiates you into the thrilling discipline of solving proofs. And Understanding Calculus: Problems, Solutions, and Tips covers all the major topics of a full-year calculus course in high school at the College Board Advanced Placement AB level or a first-semester course in college. |
Linear Algebra
This course is an introduction to linear algebra. It has been argued that linear algebra constitutes half of all mathematics. Whether or not everyone would agree with that, it is certainly true that practically every modern technology relies on linear algebra to simplify the computations required for Internet searches, 3-D animation, coordination of safety systems, financial trading, air traffic control, and everything in between.
Linear algebra can be viewed either as the study of linear equations or as the study of vectors. It is tied to analytic geometry; practically speaking, this means that almost every fact you will learn in this course has a picture associated with it. Learning to connect the facts with their geometric interpretation will be very useful for you.
The book which is used in the course focuses both on the theoretical aspects as well as the applied aspects of linear algebra. As a result, you will be able to learn the geometric interpretations of many of the algebraic concepts in this subject. Additionally, you will learn some standard techniques in numerical linear algebra, which allow you to deal with matrices that might show up in applications. Toward the end, the more abstract notions of vector spaces and linear transformations on vector spaces will be introduced.
In college algebra, one becomes familiar with the equation of a line in two-dimensional space: y = mx+b. Lines can be generalized to planes and "hyperplanes" in many-dimensional space; these objects are all described by linear relations. Linear transformations are ways of rotating, dilating, or otherwise modifying the underlying space so that these linear objects are not deformed. Linear algebra, then, is the theory and practice of analyzing linear relations and their behavior under linear transformations. According to the second interpretation listed above, linear algebra focuses on vectors, which are mathematical objects in many-dimensional space characterized by magnitude and direction. You can also think of them as a string of coordinates. Each string may represent the state of all the stocks traded in the DOW, the position of a satellite, or some other piece of data with multiple components. Linear transformations change the magnitude and direction of vectors—they transform the coordinates without changing their fundamental relationships with one another. Linear transformations are often written in a compact and easily-readable way by using matrices.
Linear algebra may at first seem dry and difficult to visualize, but it is one of the most useful subjects you can learn if you wish to become a business-person, a physicist, a computer-programmer, an engineer, or a mathematician.
Remember, the prerequisite of this course is one variable calculus course and a reasonable background in college algebra.
Requirements for Completion: In order to complete this course, you will need to work through each unit and all of its assigned materials. You will also need to complete assignments for Unit 1 through Unit 6 as well as the final exam.
Note that you will only receive an official grade on the Final Exam. However, in order to adequately prepare for this exam, you will need to work through the assignments and all the reading material in the 135.75 25.5 hours. Perhaps you can sit down with your calendar and decide to complete all of Unit 0 (a total of 1.25 hours) and half of subunit 1.1 (a total of 3 hours) on Monday night; the rest of subunit 1.1 (a total of 3 hours) on Tuesday; half of subunit 1.2 (a total of 3 hours) on Wednesday; etc.
Tips/Suggestions: It will likely be helpful to have a calculator on hand for this course.
Make sure you have a solid understanding of the pre-requisite topics outlined in Unit 0 before moving on to other units in the course. As you read, take careful notes on a separate sheet of paper. Mark down any important equations, formulas, and definitions that stand out to you. It will be useful to use this "cheat sheet" as a review prior to completing the Final Exam.
Preliminary Information
Open Textbook Challenge Winner: Elementary Linear Algebra
Elementary Linear Algebra was written and submitted to the Open Textbook Challenge by Dr. Kenneth Kuttler of Brigham Young University. Dr. Kuttler wrote this textbook for use by his students at BYU. According to the introduction of Elementary Linear Algebra, "this is intended to be a first course in linear algebra for students who are sophomores or juniors who have had a course in one variable calculus and a reasonable background in college algebra." A solutions manual for the textbook is included.
To learn linear algebra, you must have knowledge of some topics from elementary algebra. In this unit, you will review these topics. Specifically, the unit begins with a brief review of set notation and then moves to a review of complex numbers. This is especially important in linear algebra, since polynomial equations with real coefficients often have complex numbers as roots. The quadratic formula, which is the next topic you will review, is a good example of this phenomenon.
Instructions: Please click on the link above, and read the indicated sections on pages 11–15. Section 1.1 briefly discusses set notation; Sections 1.2 and 1.3 provide a brief review of functions. This reading should take approximately 30 minutes to complete.
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This unit begins with a review of vectors. You will learn the geometric meaning of vectors, which is especially significant in R2 and R3. Next, you will learn the geometric meaning of vector addition and scalar multiplication. Finally, you will apply study vectors in the context of physics to model force and other physical vectors like velocity.
In the next chapter, you will begin learning about vector products. There are two ways of multiplying vectors, both of which are of great importance in applications. The first type of a product is called the dot product, also called the scalar product or the inner product. You will then study the geometric significance of the dot product and applications of dot product by studying the concepts of work and projections. Next, you will begin the study of cross products. The cross product is the other way of multiplying vectors, and it is different from the dot product in fundamental ways. You will learn both the geometric meaning of the cross product and the description in terms of coordinates. Both descriptions of the cross product are important; the geometric description is necessary to understand the applications to physics and geometry while the coordinate description is necessary to actually compute the cross product. You will then learn techniques, which will allow you to discover vector identities and simplify expressions involving cross and dot products in three dimensions.
Next, you will begin exploring systems of linear equations. The basic idea is to study situations where there are several different variables that are related in multiple ways. These linear equations could describe budget constraints in a business, physical constraints in an engineering problem, or any number of other situations. The key is that these constraints can be described by linear equations. The geometric interpretation of these constraints is that each equation describes a line or plane where potential solutions to the problem must lie. The task then is to figure out what combination of variable values solves all of the different linear equations at the same time. Geometrically, this is where all of the lines or planes intersect. Just as is the case with the problems that the equations may be modeling, the system of equations will sometimes have no solution, will sometimes have a single solution, and will sometimes have an infinite number of solutions. Finally, you will learn about matrices andhow to write a system of linear equations as a matrix equation. While this may have at first appeared to be merely a way of putting your coefficients in a table, matrices in fact have many interesting (but not immediately obvious!) properties.
Instructions: Please click on the link above, and read the indicated sections on pages 23–27. Section 2.1 introduces you to algebraic operations done with elements of Fn. In Section 2.2, you will explore the geometric meaning of vectors, and in Section 2.3, you will study the geometric interpretation of vector addition. These readings should take you approximately 1 hour to complete.
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Instructions: Please click on the link above, and read the indicated sections on pages 27–31. In Section 2.4, you will study how distance is defined between two points in Rn. In Section 2.5, you will explore the geometric meaning of scalar multiplication. These readings 31 to Section 2.6, and complete problems 1, 2, 4, and 5. Next, click on "Solutions" (PDF) and check your answers on pages 5–6. This assessment should take you approximately 1 hour to complete.
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Instructions: Please click on the link above, and read Section 2.7 on pages 32–36. In this section, you will learn about the concept of force. This reading 36, and complete problems 2, 3, 7, 9, 10, and 11. Next, click on "Solutions" (PDF) and check your answers on pages 6–8. This assessment should take you approximately 2 hours to complete.
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Instructions: Please click on the link above, and read the indicated sections on pages 39–47. Section 3.1 will provide the definition and properties of the dot product. Section 3.2 will discuss the geometric meaning of the dot product and then apply the ideas to the concepts of work and projection. These readings 47, and work on problems 1, 2, 4, 6, 10, 14, 15, 17, 20, and 21. Next, click on "Solutions" (PDF) and check your answers on pages 8–10. This assessment should take you approximately 2 hours and 30 minutes to complete.
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Instructions: Please click on the link above, and read Section 3.4 on pages 48–54. Section 3.4 will provide the definition, properties, and the geometric meaning of the cross product. This reading should take you approximately 1 hour to complete.
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Instructions: Please click on the link above, and read Section 3.5 on pages 54–56. Section 3.5 will introduce a technique that will allow you to discover vector identities and simplify expressions involving cross and dot products in three dimensions. This reading should take you approximately 30 minutes to complete.
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Instructions: Please click on the link above to open the PDF. Scroll down to page 56, and complete problems 1, 4, 6, 7, 8, 9, 10, 13, 16, 18, and 20. Next, click on "Solutions" (PDF) and check your answers on pages 11–14 4.1 on pages 59–61. Section 4.1 will explore how to find solution(s) for a system of linear equations by graphing. This reading should take you approximately 30 minutes to complete.
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Instructions: Please click on the link above, and read Section 4.2 on pages 61–72. Section 4.2 will explore how to find solution(s) for a system of linear equations using elementary operations, Gaussian elimination, and other algebraic procedures 72, and complete problems 1, 6, 12, 13, 17, 19, 22, 30, 35, and 36. Next, click on "Solutions" (PDF) and check your answers on pages 14–20 5.1 on pages 77–91. Section 5.1 will provide an overview of matrices and matrix arithmetic. This reading should take you approximately 3 hours to complete.
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Despite the complicated definition of determinants, they are very useful because they allow you to determine, using only one number, whether or not a matrix is invertible. They also are helpful for computing eigenvalues, which you will learn about later. In this unit, you will learn about ways to find the determinants and to use determinants to compute the inverse of a matrix.
You will learn about the rank of the matrix, a very important concept in linear algebra. You will begin by studying the row-reduced echelon form of a matrix and proving that the row-reduced echelon form for a given matrix is unique. This is useful, because you can logically deduce important conclusions about the original matrix by examining its unique row-reduced echelon form. You will then learn that the rank of a matrix is related to the number of linearly independent columns or rows of that matrix; it describes the dimensionality of the space. It is also very important in the use of matrices to solve a system of linear equations, because it tells you whether Ax = 0 has zero, one, or an infinite number of solutions.
Finally, you will learn how matrices also arise in geometry, especially while studying certain types of linear transformations. You will learn that a mxn matrix can be used to transform vectors in Fn to vectors in Fm via matrix multiplication. As you will see, these types of transformation arise quite naturally in linear algebra and are important for applications in mathematics, physics, and engineering.
Instructions: Please click on the link above, and read Section 6.1 on pages 97–104. Section 6.1 will provide an introduction to determinants and techniques for finding them. This reading should take you approximately 1 hour to complete.
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Instructions: Please click on the link above, and read Section 6.2 on pages 104–109. Section 6.2 will introduce some applications, including Cramer's rule. This reading should take you approximately 1 hour to complete.
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Instructions: Please click on the link above, and read Section 8.1 on pages 129–134. Section 8.1 will introduce the elementary matrices, which result from doing a row operation to the identity matrix2 on pages 135–139. Section 8.2 will review the description of the row-reduced echelon form3 on pages 139–142. Section 8.3 will define rank and explain how to find the rank4 on pages 142–152. Section 8.4 will introduce linear independence and bases. This reading should take you approximately 2 hours to complete.
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Instructions: Please click on the link above, and read Section 8.5 on pages 153–156. Section 8.5will introduce the Fredholm Alternative for the case of real matrices here. This reading 156, and complete problems 2, 5, 7, 10, 12, 16, 18, 25, 32, 34, 45, 50, and 54. Next, click on "Solutions" (PDF) and check your answers on pages 38–49. This assessment should take you approximately 4 hours to complete.
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Instructions: Please click on the link above, and read Sections 9.1 and 9.2 on pages 163–173. Section 9.1 and Section 9.2 will introduce linear transformations. These readings should take you approximately 3 hours to complete.
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Instructions: Please click on the above link to open the PDF. Scroll down to page 173, and work on problems 2, 7, 9, 14, 17, 20, 23, 28, 32, 47, and 51. Next, click on "Solutions" (PDF) and check your answers on pages 49–59. This assessment should take you approximately 4 hours to complete.
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We have seen that matrix A corresponds to a linear transformation, T, i.e. T(x) =Ax. If the matrix is square, then those nonzero vectors, any of which are transformed to a multiple of themselves, are called eigenvectors of the matrix, and the mutliples by which they are transformed are called eigenvalues (eigenis the German word for characteristic). The set of eigenvalues is called the spectrum of A and plays an important role in linear algebra. In this unit, you will study the spectrum of a square matrix in detail.
The first thing that we will see is that the eigenvalues of an nxn matrix correspond to the roots of an nth degree polynomial, called the characteristic polynomial of A. As you know from algebra, roots of a polynomial can have multiplicity larger than 1. For eigenvalues, the multiplicity of a root is called the algebraic multiplicity of the eigenvalue, while the dimension of the set of vectors for which it is an eigenvalue is called the geometric multiplicity of the eigenvalue. If these two multiplicities are the same for all eigenvalues, then you will see that A is similar to a matrix with nonzero entries only along the main diagonal, that is A=S-1DS for an invertible matrix S. In fact, the diagonal entries of D are the eigenvalues of A, and the columns of S are a basis of Rn consisting of eigenvectors. Since solving polynomial equations can be difficult, you will study methods of estimating eigenvalues just by looking at the matrix.
You will then consider situations where the eigenvalues are known to be real and the matrix S, which diagonalizes A, can take a special form. If the matrix A is symmetric, that is aij=aji for all i,j, then you will see that A can be diagonalized, that is, all roots of the characteristic polynomial are real numbers. Further, you will learn how to choose the basis of eigenvalues, which comprise S so that the rows and columns each are unit vectors and are mutually perpendicular. Such matrices are called orthogonal and have the property that S-1=ST, where ST is the matrix obtained from S by interchanging its rows and columns. Since not all square matrices are diagonalizable, you will need one of the most important theorems in the spectral theory of matrices: Schur's Theorem, which is useful for analyzing the structure of matrices.
In linear algebra, you usually want to see whether or not Ax = b has any solutions. Often Ax = b has no solution because there are more equations than unknowns, that is, the linear system is inconsistent and b is not in the column space of A. In this case, you can try to find an approximation using a very important technique of the least square approximation. Another thing you want to do is to characterize when Ax = b has a solution, that is, construct conditions for solvability of the system. One way of doing this is by using Fredholm's Alternative, which is discussed in this unit. Fredholm's Alternative is important, because it can be generalized to more general vector spaces, where the concept of rank of a determinant is not defined. Finally, this unit discusses an important result known as the singular value decomposition, which gives a factorization of a matrix.
Instructions: Please click on the link above, and read Section 12.1 on pages 215–231. Spectral Theory refers to the study of eigenvalues and eigenvectors of a matrix, which is introduced in Section 12.1. This reading should take you approximately 2 hours to complete.
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Instructions: Please click on the link above and read Section 12.3 on pages 236–237. Section 12.3 introduces Gerschgorin's Theorem, which provides a way to estimate where the eigenvalues are just from looking at the matrix. This reading should take you approximately 30 minutes to complete.
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Instructions: Please click on the above link to open the PDF. Scroll down to page 237, and complete problems 3, 5, 8, 11, 13, 20, 25, 28, 43, 48, and 54. Next, click on "Solutions" (PDF) and check your answers on pages 76–84. This assessment should take you approximately 4 hours and 30 minutes to complete.
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Instructions: Please click on the link above, and read Section 13.1 on pages 245–255. Section 13.1 will introduce symmetric and orthogonal matrices2 on pages 255–262. Sections 13.2 will discuss several results including the Gram-Schmidt process and the Schur's Theorem3 on pages 263–266. Sections 13.3 discusses a very important technique known as the Least Square Approximation. This reading should take you approximately 1 hour to complete.
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Instructions: Please click on the link above, and read the indicated sections on pages 267–274. Sections 13.4–13.7 will introduce several important topics and results. Please work through these sections carefully 274, and work on problems 2, 5, 10, 14, 19, 24, 28, 32, 37, 39, 43, 48, 52, and 57. Next, click on "Solutions" (PDF) and check your answers on pages 88–106. This assessment should take you approximately 4 hours to complete.
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This unit discusses vector spaces and linear transformations. The first topic you will study in this unit is that of an abstract vector space. You will see that a vector space is a collection of vectors that satisfies a set of axioms. Next, you will study ideas such as subspaces, linear independence, and bases in the context of vector spaces. Remember to think of R or C if you are confused. Next, you will construct abstract fields and vector spaces. You will begin this by first reviewing some basic algebra relating to polynomials. This is both interesting and important, because it provides the basis for constructing different kinds of fields. Finally, you will look at inner product spaces, which are vector spaces that also have an inner product, before moving on to linear transformations, which is the second topic of study in this unit.
Linear transformations have many applications within mathematics as well as in fields outside of mathematics, such as physics. You will study the basic definitions of linear transformations and properties and relations between these and matrices.
Instructions: Please click on the link above, and read Section 16.1 on page 323 and section 16.2.1 on pages 325–330. Section 16.1 will provide the definition of a vector space, and Section 16.2.1 will discuss subspaces, linear dependence, and bases 330, and complete problems 1, 2, 3, and 4. Next, click on "Solutions" (PDF) and check your answers on pages 124–125. This assessment should take you approximately 2 hours to complete.
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Instructions: Please click on the link above, and read Section 16.3 on pages 330–343. Section 16.3 will discuss vector space and fields. This reading should take you approximately 3 hours and 30 minutes to complete.
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Instructions: Please click on the link above to open the PDF. Scroll down to page 243, and work on problems 2, 4, 10, 12, 16, 20, 24, and 29. Next, click on "Solutions" (PDF) and check your answers on pages 125–135. This assessment should take you approximately 4 hours to complete.
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Instructions: Please click on the link above, and read Section 16.5 on pages 348–361. Section 16.5 will discuss vector spaces with inner products. This reading should take you approximately 3 hours and 30 minutes to complete.
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Instructions: Please click on the above link to open the PDF. Scroll down to page 361, and complete problems 1, 4, 7, 12, 15, 17, and 22. Next, click on "Solutions" (PDF) and check your answers on pages 135–150. This assessment should take you approximately 4 hours to complete.
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Instructions: Please click on the link above, and read the indicated sections on pages 367 and 368. Sections 17.1 and 17.2 will discuss linear transformations and vector spaces. These readings should take you approximately 30 minutes to complete.
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Instructions: Please click on the above link, and read Section 17.3 on pages 369–373. Section 17.3 will discuss finding eigenvalues and eigenvectors of linear transformations. This reading should take you approximately 1 hour and 30 minutes to complete.
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Instructions: Please click on the link above, and read Section 17.4 on pages 373–377. Sections 17.4 will discuss linear transformations, which will result by multiplication by n × n matrices. This reading should take you approximately 1 hour to complete.
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Instructions: Please click on the link above, and read Section 17.5 on pages 377–386. Section 17.4 will discuss matrices of linear transformations. This reading should take you approximately 2 hours to complete.
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Instructions: Please click on the link above, and read Section 17.6 on pages 386–391. Section 17.6 will introduce fundamental matrices, matrices whose entries are differentiable functions 391, and work on problems 1, 3, 8, 12, 15, 18, and 21. Next, click on "Solutions" (PDF) and check your answers on pages 151–157. This assessment should take you approximately 4 hours to complete |
WINTER 2011
Math 10 Practice for Exams
As part of your studying for quizzes, you should review homeworks and do more practice problems.
As part of your studying for exams, you should review homeworks and quizzes and do more practice problems.
Many sources of practice problems, and practice exams and quizzes are listed on this page. Many of the problems here have come from actual old exams. |
Product Reviews
Saxon Math 76 Home Study Kit Fourth Edition
4.9
5
41
41
Do you want your child overly prepared?
The Saxon Curriculum prepares your child years above their public school counterparts. After Algebra II in this program for my daughter I put her in public school for Advanced Math. She was so far ahead of where they were and where they were going that I pulled her out and ordered Saxon Advanced Math for her to complete at home. The curriculum prepares our children far ahead of the same curriculum taught elsewhere. You will not be disappointed. I will never stray again. My daughter is now in Calculus in the College and my son will be following in her footsteps because of Saxon.
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September 21, 2012
One of our favorite years!
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August 21, 2012 |
Course Description: This course emphasizes the principles of Algebra 1 at a rigor and pace reflective of an Honors program.
Teacher's Goals, Expectations, and Student Participation: Students are expected to be on time to class and prepared for the class activities. Class will usually start with a "Do Now" problem which is to be completed at the start of class. I expect classroom rules, as well as school wide rules to be followed in class. There will be homework almost every night, and you should expect a quiz every 2 to 3 sections. A test will be given at the end of each Chapter.
Course Materials:You will need a notebook with 3 sections; one for classwork and "Do Now " problems, one for notes, and one for homework. You should bring this notebook to class every day along with a writing utensil and any homework due that day. You should also have your own scientific calculator as it is difficult to provide a full class set and I cannot guarantee that I will have enough to go around.
Assessment Procedures and Policies:
MP1:
Summer Assignment and First Test - 20%
Tests – 50%
Quizzes – 20%
Homework/ Class work/Class Participation – 10%
MP2, MP3, MP4:
Tests – 60%
Quizzes – 30%
Homework/Class work/Class Participation – 10%
Each Marking Period is 22% of your Y1 grade, the other 12% is the Final Exam.
Contact Information:
Email Address: [email protected]
Extra Help is available by appointment before and after school as well as during the day if arranged ahead of time. See me if you need help!!! |
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