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Abstract Algebra: Theory and Applications
In pre-college mathematics courses, we learned the basic methodology and notions of algebra. We appointed letters of the alphabet to abstractly represent unknown or unspecified quantities. We discovered how to translate real-world (and often complicated) problems into simple equations whose solutions, if they could be found, held the key to greater understanding. But algebra does not end there. Advanced algebra examines sets of objects (numbers, matrices, polynomials, functions, ideas) and operations on these sets. The approach is typically axiomatic: One assumes a small number of basic properties, or axioms, and attempts to deduce all other properties of the mathematical system from these. Such abstraction allows us to study, simultaneously, all structures satisfying a given set of axioms and to recognize both their commonalties and their differences. Specific topics to be covered include groups, actions, isomorphism, symmetry, permutations, rings, and fields. Prerequisites: Calculus I and Discrete Mathematics; enrollment only by consent of the instructor. |
Short description Grades 6, 7 & 8 math eBooks comprise three principle sections. These are, notably: (Read more) math eBooks are produced such as that as well as a Publications Guide, and three principle publications corresponding to the principle sections (Number and Algebra, Geometry and Measures and Handling Data) there are individual modules produced within each principle section which are published as eBooks.
Collecting and Representing Data is a module within the Handling Data principle section of our Grades 6, 7 & 8 publications. It is one module out of a total of four modules in that principle section, the others being: • Probability • Averages • Cumulative Distributions (Less) |
College Geometry : A Discovery Approach - Text Only - 2nd edition
Summary: College Geometry is an approachable text, covering both Euclidean and Non-Euclidean geometry. This text is directed at the one semester course at the college level, for both pure mathematics majors and prospective teachers. A primary focus is on student participation, which is promoted in two ways: (1) Each section of the book contains one or two units, called Moments for Discovery, that use drawing, computational, or reasoning experiments to guide students to an oft...show moreen surprising conclusion related to section concepts; and (2) More than 650 problems were carefully designed to maintain student interest.
Features NEW! Geometer's Sketchpad Projects. A part of each exercise section, and incorporated into selected examples. NEW! Glossary. End of Chapter Material. In addition to the current chapter summary and End of Chapter True/False questions, there are new conceptual exercises to test the students' understanding of the chapter material. Moments for Discovery. Reinforces chapter material by encouraging students to experiment. Historical perspective. Appropriate biographies are written throughout the text, to give context to the material that students are learning. Our Geometric World. Placed throughout each chapter, this feature illustrates the real world application of the material that students are learning |
DiscreteMathematicsIntroduction Saad Mneimneh 1 Introduction College mathematics will often focus on calculus, and while it is true that cal-culus is the most important field that started modern mathematics, it is very
Introduction To DiscreteMathematics Review If you put n + 1 pigeons in n pigeonholes then at least one hole would have more than one pigeon. If n(r−1)+1 objects are put into n boxes, then at least one of the boxes contains r or more of
Introduction: DiscreteMathematics Standard Course of Study Updated 03/01/05 In compliance with federal law, including the provisions of Title IX of the Education Amendments of 1972, NC Department of Public Instruction does not discriminate on the basis of race, sex, religion, color, national or
DiscreteMathematics over the past nine years; this program is funded by the National Science Foundation. ... Introduction to Contemporary Mathematics, by the Consortium for Mathematics and its Applications; and Excursions in Modern Mathematics by P. Tannenbaum and R. Arnold.
Catalog No. MAT 206 2 4. To help students understand the concepts of models, simulation and abstraction in mathematics. 5. To provide students with an appreciation of the inherent beauty of adiscrete structure in
IntroductionDiscreteMathematics is actually the rst kind of mathematics that most children are exposed to in elementary schools. When we learn to count, we learn 1,2,3,4, and it takes a while to even realize that there might be
IntroductionDiscreteMathematics I Dr. Penelope Kirby Welcome Welcome to Florida State University's MAD 2104: DiscreteMathematics I, an Internet-supported course. This course has three main objectives. One objective is to introduce you |
Product Details:
This well-respected text gives an introduction to the theory and application of modern numerical approximation techniques for students taking a one- or two-semester course in numerical analysis. With an accessible treatment that only requires a calculus prerequisite, Burden and Faires explain how, why, and when approximation techniques can be expected to work, and why, in some situations, they fail. A wealth of examples and exercises develop students'' intuition, and demonstrate the subject''s practical applications to important everyday problems in math, computing, engineering, and physical science disciplines. The first book of its kind built from the ground up to serve a diverse undergraduate audience, three decades later Burden and Faires remains the definitive introduction to a vital and practical subject.
Description:
This book provides a broad overview of the basic theory
and methods of applied multivariate analysis. The presentation integrates both theory and practice including both the analysis of formal linear multivariate models and exploratory data analysis techniques. Each chapter ...
Description:
Over recent years, developments in statistical computing have freed statisticians
from the burden of calculation and have made possible new methods of analysis that previously would have been too difficult or time consuming. Up till now these developments have ... |
serv... read more
Challenging Problems in Algebra by Alfred S. Posamentier, Charles T. Salkind Over 300 unusual problems, ranging from easy to difficult, involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms, and more. Detailed solutions, as well as brief answers, for all problems are provided.
Abstract Algebra by W. E. Deskins Excellent textbook provides undergraduates with an accessible introduction to the basic concepts of abstract algebra and to the analysis of abstract algebraic systems. Features many examples and problems.
Elements of Abstract Algebra by Allan Clark Lucid coverage of the major theories of abstract algebra, with helpful illustrations and exercises included throughout. Unabridged, corrected republication of the work originally published 1971. Bibliography. Index. Includes 24 tables and figures.
Product Description:
serve as valuable references. Volume II comprises all of the subjects usually covered in a first-year graduate course in algebra. Topics include categories, universal algebra, modules, basic structure theory of rings, classical representation theory of finite groups, elements of homological algebra with applications, commutative ideal theory, and formally real fields. In addition to the immediate introduction and constant use of categories and functors, it revisits many topics from Volume I with greater depth and sophistication. Exercises appear throughout the text, along with insightful, carefully explained proofs.
Reprint of the W. H. Freeman and Company, San Francisco, 1989 edition |
A reference that provides coverage of first-year college math, including algebraic, trigonometric, exponential, and logarithmic functions and their graphs. It also includes solutions of linear and quadratic equations, analytic geometry...
Covers the fundamentals of algebra and trigonometry. This book also explains the principles of mathematical reasoning Progressions, including arithmetic, finite geometric and infinite geometric progressions. It deals with the theory...
Tough Test Questions? Missed Lectures? Not Enough Time? In this book, each outline presents all the essential course information in an easy-to-follow, topic-by-topic format. It features: the course scope and...
Addresses a focused theme on mathematics education. This title intends to illustrate the diversity within the theme and the research that translates into classroom pedagogies. It illuminates how application and... |
Beschreibung
Hi Guys, Ever wanted to have your teacher sit down with you by his shoulder and help you through your work on differentiation in a simple step by step way. This live worksheet app does just that!
There are four sections. First, powers of x, and linear combinations. Second, we look at evaluation of the derivatives at particular values. In the third section we go on to look at sines and cosines and finally in section four we deal with exponentials and logs.
It contains well over 100 questions and on-line worked video solutions for each one!
The idea, is that you try a question on the worksheet first and then just click on it and a video of the solution plays to show you how its done step by step.
The worksheet is ideal to get into the subject, feeling comfortable and then its just about practice really. There are some fairly tricky problems along the way especially with the log questions, as well as many fairly straightforward ones too.
Every question that I write I will generally put down everything that we need beforehand. So everything we need will be on the page. We'll often use rules for indices and logs so any time we need them I will always write them down.
Along the bottom you see a selection of options. You'll see a mathtip. I can recommend that - its a cartoon for you.
You can reset the page or section thereof so when you have a look at the question video, the question will be ticked, so that you can keep a track of your progress.
Another useful tool is an embedded differentiator which is handy to work out any derivative problem you might be working on.
I've also linked in a film, Brian Cox's "A Night with the Stars" - an interesting programme that was on BBC2 recently and so that's embedded also in this little app.
So I hope you enjoy it and I'm looking forward to making lot's of these. So look out for the next one. This one is on Simple Differentiation and the next one will take things a step further and look at quotients and products and functions of a function and I'll just carry on like that.
So I Hope you enjoy it and any problems just give me a buzz, send me an e-mail and all the best I hope you get on well with it. Cheers, Mark |
Algebra
Lecture 13: Averages
Embed
Lecture Details :
Introduction to averages and algebra problems involving averages.
Course Description :
This is the original Algebra course on the Khan Academy and is where Sal continues to add videos that are not done for some other organization. It starts from very basic algebra and works its way through algebra II. |
The
most concise mathematical expression that describes a continuously
changing physical system is a differential equation, which uses
derivatives to quantify all possible states of an evolving system in one
equation. Topics include first-order differential equations,
second-order linear differential equations, power-series solutions,
Laplace transforms, numerical methods of solution, and systems of
differential equations. (4 credits) Prerequisite: MATH 283 |
Algebra may seem intimidating?but it doesn't have to be. With Teach Yourself VISUALLY Algebra, you can learn algebra in a fraction of the time and without ever losing your cool. This visual guide takes advantage of color and illustrations to factor out confusion and helps you easily master the subject. You'll review the various properties of numbers, as well as how to use powers and exponents, fractions, decimals and percentages, and square and cube roots. Each chapter concludes with exercises to reinforce your skills. |
The user reviews some basic definitions and properties of real numbers. After viewing explanations and examples of the properties, users can interactively test their understanding of the properties o... More: lessons, discussions, ratings, reviews,...
The user reviews the definition of proportions and how to take the cross product. After viewing examples, users can practice finding the cross product to solve for the missing number in the proportion... More: lessons, discussions, ratings, reviews,...
In a beach race, contestants must swim to a point along the beach and then run to reach the finish line. Where should I aim to land on the beach so as to minimize my total time for the race? Stu... More: lessons, discussions, ratings, reviews,...
Euclid's proposition lays out the Pythagorean Theorem - the sum of the squares of the sides of a right triangle equal the square of the hypotenuse. The guide then examines the structure of the proposi |
Patterns
of Change
Develops student ability to recognize and describe important patterns
that relate quantitative variables, to use data tables, graphs, words,
and symbols to represent the relationships, and to use reasoning
and calculating tools to answer questions and solve problems.
Patterns
in Data
Develops student ability to make sense of real-world data through
use of graphical displays, measures of center, and measures of variability.
Topics
include:
Distributions of data and their shapes, as displayed in dot plots,
histograms, and box plots; measures of center including mean and
median, and their properties; measures of variability including interquartile
range and standard deviation, and their properties; and percentiles
and outliers.
Unit
3
Linear
Functions
Develops student ability to recognize and represent linear relationships
between variables and to use tables, graphs, and algebraic expressions
for linear functions to solve problems in situations that involve
constant rate of change or slope.
Vertex-Edge
Graphs
Develops student understanding of vertex-edge graphs and ability
to use these graphs to represent and solve problems involving paths,
networks, and relationships among a finite number of elements, including
finding efficient routes and avoiding conflicts.
Exponential
Functions
Develops student ability to recognize and represent exponential growth
and decay patterns, to express those patterns in symbolic forms,
to solve problems that involve exponential change, and to use properties
of exponents to write expressions in equivalent forms.
Patterns
in Shape
Develops student ability to visualize and describe two- and three-dimensional
shapes, to represent them with drawings, to examine shape properties
through both experimentation and careful reasoning, and to use those
properties to solve problems.
Topics
include:
Triangle Inequality, congruence conditions for triangles, special
quadrilaterals and quadrilateral linkages, Pythagorean Theorem, properties
of polygons, tilings of the plane, properties of polyhedra, and the
Platonic solids.
Topics
include:
Quadratic functions and their graphs, applications to projectile
motion and economic problems, expanding and factoring quadratic expressions,
and solving quadratic equations by the quadratic formula and calculator
approximation.
Unit
8
Patterns
in Chance
Develops student ability to solve problems involving chance by constructing
sample spaces of equally-likely outcomes or geometric models and
to approximate solutions to more complex probability problems by
using simulation. |
MATH LAB, Real World data, TI-84 Graphing Calculator, Prediction EQNs
PDF (Acrobat) Document File
Be sure that you have an application to open this file type before downloading and/or purchasing.
0.22 MB | 7 pages
PRODUCT DESCRIPTION
This is an awesome math lab. It not only allows students to experience some of the really neat features of their TI-83 or TI-84 graphing calculator, but also allows students to:
-practice scatterplots
-formulate a prediction equation
-determine a line of best fit (linear regression)
-write the equation of a line
-find slope
-graph data
-analyze real world data
-students come to their own conclusion based on their processing of data
-students compare their own answers using line of best fit with the graphing calculator's "answers"
Perfect for the block (1 class) or regular class (2 classes). Lab takes approximately 90 minutes. 30-45 minutes is teacher led. It is recommended that teacher walk students through the lab using your home state. Then students work in pairs on another state's data. Some students can then do lab in 30-40 minutes whereas others will need 60 minutes or so. Actual census data (provided) is linear for 42 states and the United States itself. Extension activities include student's creating posters of their results for classroom display and/or computer lab research of census data or a quest for more linear data to analyze.
This lab has worked for me mostly at the algebra 2 level with students of various levels (honors, regular and basic) and is good for algebra 1 too (but access to graphing calculators is more difficult sometimes).
Purchase includes 7 pages:
Page 1 - (available on preview) gives objectives and detailed directions of lab.
Page 2 - (available on preview) gives the student worksheet where student works through data manually and then again with the graphing calculator.
Page 3 - step by step or key by key instructions for the graphing calculator provided.
Page 4 - Questions provided for student response/analysis. And grading rubric for easy on the spot grading of math lab.
Page 5-7 - Real world census data provided for 42 states plus the United States country itself. Decades 1930, 1960, 1980, 1990 and 2000 provided. Students then predict 2010 data (which should come out by next year) and beyond. (2 pages are the original chart of data retyped for clarity on a word doc.)
This is a very user friendly assignment. It's turn-key ready. Students love this. It's such a change of pace and the students are interacting with real data using all the skills they recently learned/reviewed in class. This is a must have lesson. You'll be quite glad you purchased this for years to come.
Product Questions & Answers
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$3.50
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List Price: $5.00
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Algebra / Number Theory / Algebraic Geometry
Graduate students in algebra, number theory, and algebraic geometry courses build upon knowledge first learned in grade school. These are the best math schools for algebra / number theory / algebraic geometry programs. |
books.google.co.jp - The Well,... for dummies
Calculus for dummies
The
Well, the good news is that you can master calculus. It's not nearly as tough as its mystique would lead you to think. Much of calculus is really just very advanced algebra, geometry, and trig. It builds upon and is a logical extension of those subjects. If you can do algebra, geometry, and trig, you can do calculus.
Calculus For Dummies is intended for three groups of readers
li>Students taking their first calculus course – If you're enrolled in a calculus course and you find your textbook less than crystal clear, this is the book for you. It covers the most important topics in the first year of calculus: differentiation, integration, and infinite series
Students who need to brush up on their calculus to prepare for other studies – If you've had elementary calculus, but it's been a couple of years and you want to review the concepts to prepare for, say, some graduate program, Calculus For Dummies will give you a thorough, no-nonsense refresher course
Adults of all ages who'd like a good introduction to the subject – Non-student readers will find the book's exposition clear and accessible. Calculus For Dummies takes calculus out of the ivory tower and brings it down to earth
This is a user-friendly math book. Whenever possible, the author explains the calculus concepts by showing you connections between the calculus ideas and easier ideas from algebra and geometry. Then, you'll see how the calculus concepts work in concrete examples. All explanations are in plain English, not math-speak. Calculus For Dummies covers the following topics and more
li>Real-world examples of calculu
The two big ideas of calculus: differentiation and integratio
Why calculus work
Pre-algebra and algebra revie
Common functions and their graph
Limits and continuit
Integration and approximating are
Sequences and serie
Don't buy the misconception. Sure calculus is difficult – but it's manageable, doable. You made it through algebra, geometry, and trigonometry. Well, calculus just picks up where they leave off – it's simply the next step in a logical progression0
星 1 つ
0
Review: Calculus for Dummies
ユーザー レビュー - John Maynard - Goodreads
This book could use more exercises, can I do the work at the end of it explanations, sure I can do the work, I think , but I really could use exercise. I appreciate the humor in which the book ...レビュー全文を読む
Review: Calculus for Dummies
ユーザー レビュー - Ray - Goodreads
My high school calculus program was kind of weak, so when I entered in college, I was totally doomed. So my professor recommended me solving calculus problems that in the books were used as examples ...レビュー全文を読む
book.store.bg - Calculus for Dummies - Mark Ryan for me there has to be a "calculus for pre-dummies", because "calculus for dummies" is not adequate. i had all the basic math courses in high school and ... import.book.store.bg/ product/ id-0764524984/ calculus-for-dummies.html?printthispage=1 |
OCAD 0800
ELEMENTARY ALGEBRA (4 cr.)
This course is appropriate for you if you have a sound background in basic arithmetic but have not been exposed to algebra or if you need to strengthen your basic algebra skills. Topics may include properties of real numbers, order of operations, linear and quadratic equations, exponents, polynomials, graphing and systems of linear equations. Successful completion of OCAD 0800 ensures placement into MATH 1050, MATH 1070, MATH 1080, MATH 2500, ECON 2200, ECON 2250, or PSYC 2050. You are referred to this course based on your results on the mathematics/statistics placement assessment. See Summary of Financial Procedures for pricing information. Offered under the S/U grading option only. (Note: OCAD credits are not applied to graduation credit requirements.) |
books.google.ca - In,... Variables
Complex Variables: Introduction and Applications
In, and residue calculus and also includes transform methods, ODEs in the complex plane, numerical methods and more. Part II contains conformal mappings, asymptotic expansions, and the study of Riemann-Hilbert problems. The authors also provide an extensive array of applications, illustrative examples and homework exercises. This book is ideal for use in introductory undergraduate and graduate level courses in complex variables.
Review: Complex Variables: Introduction and Applications
User Review - mirela Darau - Goodreads
One of my favourite books along with Bender & Orszag's Mathematical Methods. Accessible language, lots of relevant examples, it's definetely a pleasant read. I had a first look into it when struggling ...Read full review |
, algebra 2 and calculus algebra 1, algebra 2 and calculus |
Calculus Revisited: Single Variable Calculus
Calculus Revisited is a series of videos and related resources that covers the materials normally found in a freshman-level introductory calculus course. The series was first released in 1970 as a way for people to review the essentials of calculus. It is equally valuable for students who are learning calculus for the first time.
Is our political ideology simply the result of a genetic coin toss? Mounting evidence suggests that biology may be a factor. In this video, Academic Earth explores some of the key research into the biology of politics. |
Functions and Graphs
Mathcentre provide these resources which cover aspects of functions and graphs and are suitable for students studying mathematics at A Level, as well as those students for whom mathematics is an integral part of their course. Some of the topics covered include an introduction to functions, the hyperbolic, trigonometric and polynomial functions, as well as inverse functions and limits of functions.
Comprehensive notes, with clear descriptions, for each resource are provided, together with relevant diagrams and examples. Students wishing to review, and consolidate, their knowledge and understanding of functions and graphs |
Mastering Essential Math Skills
This exercise book is an excellent resource to practice and review math skills you´ll need to establish a strong foundation and smooth transition into Algebra and other higher math courses. Workbooks are available for 4th – 5th grade and middle school / high school |
The Algebra 2 Tutor teaches students the core topics of Algebra 2 and bridges the gap between Algebra 1 and Trigonometry. It contains essential material to help students do well in advanced mathematics. Many of the topics in this series are used in other Math courses, such as writing equations of lines, graphing equations and solving systems of equations. These skills are used time and time again in more advanced courses such as Physics and Calculus. The Algebra 2 Tutor is a complete 15 lesson series covering all of the core topics in detail. What sets this series apart from other teaching tools is that the concepts are taught entirely through step-by-step example problems of increasing difficulty. It works by introducing each new concept in an easy to understand way and using example problems that are worked out step-by-step and line-by-line to completion. If a student has a problem with coursework or homework, simply find a similar problem fully worked on in the series and review for the steps needed to solve the problem. Students will be able to work problems with ease, improve their problem-solving skills and understand the underlying concepts of Algebra 2. This lesson teaches students how to solve a system of equations using the addition method. In this technique, one equation of the system is added to the other equation in order to eliminate one of the variables. This allows the solution to be found without any graphing required. Numerous examples are presented in order to reinforce this material.
This product is manufactured on demand using DVD-R recordable media. Amazon.com's standard return policy will apply. |
Galore!: Masterclasses, Workshops, and Team Projects in Mathematics and Its Applications for an Amazon.co.uk gift card of up to £1.45, which you can then spend on millions of items across the site. Trade-in values may vary (terms apply). Learn more
Book Description26,"ASIN":"0198507704","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":31.19,"ASIN":"019851493X","isPreorder":0}],"shippingId":"0198507704::jDtbzS1k4NilejNqabL3TYmfAsqltareeSA0Ngnp4NlmFW65dhwH74VPpf4jPQs9rpL6iu2Q9WDVEdyuJ%2BaIqbjhs3Wad6fF,019851493X::68qrV5XaMZYczzymWCDA%2FnmaOZFXULQS6j8jEkA8v7v3F7nPe8n136NvIMuf6FpMWNXsVH7agtb22z5Xgs8C89NR13DPOX book that meets not only the needs of teachers who are involved in the delivery of enrichment material whether it be in the classroom or on a Saturday morning, but also the cravings of those occasional students whose appetite for mathematics is insatiable. (The Mathematical Gazette)
Resources like this deserve a prominent place on the shelf of any mathematics department that is on the look out for ways to enthuse, educate, inspire and challenge. (The Mathematical Gazette)
The main ideas are accessible to children from the age of eleven, while some parts of the book should interest and challenge older school and university students, as well as their teachers and parents. (EMS)
What a good read for anyone interested in mathematics ... historical stories link beautifully to work involving different bases and give good introductory stories for lessons in number work ... Whether you are a teacher in a junior or secondary school this book offers some interesting starting points in areas of mathematics not normally covered in the standard school curriculum ... the author's style is very engaging. (Mathematics TODAY)
"As Obi-Wan Kenobi said about the Light Sabre in Star Wars, a slide-rule is an ancient weapon from a more civilised age" State Budd and Sangwin in their book Mathematics Galore ... placed in the right hands [the book] is a powerful weapon. May the force be strong with readers. was there ever a more civilised age when mathematics was taught as eclectically as this? (Plus Online Magazine)
This is a book which anyone with an interest in mathematics should enjoy, particulary those looking for innovative teaching ideas. (Education in Chemistry)
First Sentence
Unlike most other mathematical problems, the study of mazes and labyrinths takes us into the dark territory of murder, suicide, adultery, passion, intrigue, religion, and conquest. Read the first page |
Topics
Introduction to Functions
In mathematics, a relationship describles one quantity in terms of another. A function is a type of relationship in which for each first component there is one and only one second component. In mathematics, an introduction to functions and how to identify whether or not a relationship is a function is very important building block since a lot of complex topics in upper-level math involve functions. |
Course Content and Outcome Guide for MCH 120
Date:
22-AUG-2011
Posted by:
Curriculum Office
Course Number:
MCH 120
Course Title:
Machine Shop Math
Credit Hours:
2
Lecture hours:
0
Lecture/Lab hours:
20
Lab hours:
0
Special Fee:
$12
Course Description
Covers instruction and practice in working with whole numbers, fractions, decimals, formulas, inch and metric systems, formulas, calculating simple and direct indexing. Introduces how to apply the use of the inch/metric systems, dividing/index head and formulas as they pertain to thread calculations, gear calculations, speed and feed calculations, and taper calculations. Prerequisite: MCH 100. Audit available.
Addendum to Course Description
Applying Shop Math - Math skills are very important to the machinist in his/her daily work. The machinist must be able to calculate accurately and with reasonable speed. This module will provide instruction and practice in working with whole numbers, fractions, and decimals conversions.
Shop Math - Inch & Metric -In the Machine Shop, accurate workmanship depends on accurate measurements. The metric system of measurement is being adopted by many industries in an effort to be competitive in foreign markets. This module will introduce the student to the principles of the inch and metric systems of measurement.
Shop Math/Formulas - The machinists frequently makes calculations to solve for the unknown value needed to produce a part. A formula tells what values using symbols needs; what computations are necessary to combine those values by using operation signs; and what order to combine them by using grouping signs. In this module the student will learn how to apply the use of formulas as they pertain to Thread Calculations and Taper Calculations.
Percent, Charts, Graphs & Angles - There are times when the print given to the technician does not specifically provide all of the required information to allow the machinist to complete the work piece. At these times, the technician may have to use math procedures to calculate the missing information.To produce a superior product in the manufacturing process, machinists need tools to evaluate quality. Statistical Process Control (SPC) includes Percent, Graphs and Charts which are those tools that help the technician interpret whether the process is in or out of control. This module will introduce the student to the tools of SPC. This module will help the student learn these procedures and calculations.
Intended Outcomes for the course
Upon successful completion of this course students will be able to:
Calculate decimal equivalents of fractions noted on blue prints.
Convert inch to metric and metric to inch from dimensions on blue prints.
Apply mathematical formulas as appropriate to thread and taper calculations on shop drawings.
Course Activities and Design
MCH 120
Through direct instruction and practice students use formulas to determine tapers, thread pitch, and depth from shop drawings and blue prints. Students perform calculations in metric and English that include conversion of fractions to decimal equivalents, and conversion form metric to English units. |
MAPLE BASICS
The Maple interface has a long list of palettes and even handwriting recognition for finding symbols and one can edit mathematical expressions to make them look like real mathematics without being limited by the executable Maple syntax. Context sensitive right-click menus allow one to do most elementary mathematical operations without knowing any syntax.
This "Clickable Calculus" makes Maple easier for elementary users. It also has an easily accessible Math Dictionary.
It has a tools menu with Assistants (dialog windows to import and analyze data), Tutors (Java applet windows that guide you through many calculus and algebra routines), and Tasks (that uses Help to guide you in accomplishing a list of mathematical tasks).
In document mode, one can freely create a mathematical report without the constraint of input, output and text regions, much like a MathCAD worksheet.
Worksheet mode allows one to see the input region syntax popped in by right-click menu choices, giving more information about what Maple is doing and allowing easy editing of command parameters.
Math (2d) versus Maple (1d) notation in the input region
When the cursor is in an input region, the"text" and "math" entries in the tool bar will toggle between Standard Math Notation and Maple Notation. Standard Math is preferred for using the (floating, more limited) palettes to input expressions. Maple notation shows you the Maple syntax of the input expression. You can also use the Format Menu and choose convert to change from 2D Math input (the old Standard Math Notation) to 1D Math input = Maple input, if you want to learn the Maple command syntax for a WYSIWYG math expression.
An important tip for 2D Math input is that you must use the right arrow key to continue inputting an expression after raising to an exponent or dividing by a denominator (using the forward slash for division, asterisk for multiplication), in fact you can use all 4 arrows to move around an expression to edit its various pieces, while when entering from the palette, the tab key moves you through the characters to be replaced.
Calculus packages:
Student[Calculus1] is very useful for Calc 1 and Calc 2.
Student[MultivariateCalculus] is helpful for Calc 3 for tasks involving a scalar function of 2 or more independent variables.
Student[VectorCalculus] is helpful for Calc3 for doing vector calculus tasks, i.e., those tasks involving vector functions of one or more independent variables.
VecCalcis an external package to accompany Stewart Multivariable Calculus CalcLabs, available on citrixweb.
Linear algebra packages:
LinearAlgebra utilizes the new way of doing vectors and matrices in Maple, available from the palette insertion.
Student[LinearAlgebra] uses the same structures but aimed at teaching linear algebra with additional Tutor commands. In both cases commands are named by joining together capitalized key words, like "ReducedRowEchelonForm". Here it is useful to use command auto-completion so one can just type the first few characters and then Control, Space Bar to bring up a list of all commands starting with those letters to select from with the mouse (only one starts with "Red"). This feature is case sensitive. |
Algebra II
In this section you'll find study materials for algebra II help. Use the links below to find the area of algebra II you're looking for help with. Each study guide comes complete with an explanation, example problems, and practice problems with solutions to help you learn algebra II.
Introduction to Sequences and Arithmetic
Sequences
A sequence is a series of terms in which each term in the series is generated using a rule. Each value in the sequence is a called a term. The rule of a sequence ... |
Also Available As:
Triangular Arrays with Applications
Thomas Koshy
Description
Triangular arrays are a unifying thread throughout various areas of discrete mathematics such as number theory and combinatorics. They can be used to sharpen a variety of mathematical skills and tools, such as pattern recognition, conjecturing, proof-techniques, and problem-solving techniques.
While a good deal of research exists concerning triangular arrays and their applications, the information is scattered in various journals and is inaccessible to many mathematicians. This is the first text that will collect and organize the information and present it in a clear and comprehensive introduction to the topic. An invaluable resource book, it gives a historical introduction to Pascal's triangle and covers application topics such as binomial
coefficients, figurate numbers, Fibonacci and Lucas numbers, Pell and Pell-Lucas numbers, graph theory, Fibonomial and tribinomial coefficients and Fibonacci and Lucas polynomials, amongst others. The book also features the historical development of triangular arrays, including short biographies of prominent mathematicians, along with the name and affiliation of every discoverer and year of discovery. The book is intended for mathematicians as well as computer scientists, math and science teachers, advanced high school students, and those with mathematical curiosity and maturity. |
Posts I've Made
Brush up / dive in / drown (!) in discrete math and calc I-II. These are the introductory maths courses at college level. Discrete math is a really fun course, you touch on a lot of things, nothing super deep, but it's a great starting point for everything else you will learn, both in maths and CS. Do well in it, and you will reap benefits later on, it's worth studying hard and really grasping each concept. Calc I isn't hard but it's not easy either. Take notes. Work problems. Get very familiar with log, e^x, and the trig identities. Try Khan Academy on if you don't know it, I went there for a crash course in calculus and it sorted me out
From there, if you start to get a good handle on things, calc III, linear algebra, combinatorics, there's loads to learn, and it's all good.
Quote
But the confusing part is, I don't know where to start. It will be stupid of me to just start learning any kind of math.
It's all related man, and worth learning, you can't really start in the wrong place. You will quickly find out when things are beyond you, but it's still good to bang your head against things for a while.
Here's a thing. Project Euler. A whole load of mathy programming problems. See if you can do the first 10. You can use whatever language or program you want, or just pencil and paper. Some of them are quite easy. Some are deceptively hard. Some are obviously hard. Some (many, most) of them have very efficient and simple solutions that you will have to research. My method is to pick a new problem and play around with it on paper for a little while. Sometimes I can work out a solution. Other times I might head on over to Wikipedia and get a feel for what kind of problem it is, maybe (of course!) there is a cool way to do it. You'll get a feel for 'computational complexity', or how 'hard' a problem is to compute. Some of these problems could tie up your computer for a million years to find a solution in the obvious, brute force way. But there happens to be another way that takes 234 milliseconds.
Math is my weak point and It takes me time to catch onto things and it doesnt help when my teacher sucks (too late for me to drop class) If some one could explain to me how to find the answer for this question that would be great and much appreciated.
I need to factor out the GCF of this problem
a(b+7) + 4(b+7)
also if some one could confirm that i did this problem correctly that would be cool
i had the factor the GCF out of this 12p(cubed) - 6p and i got 3p(4p(squared)- 2)i was going off of this tutorial
If there are any other good tutorials please share with me.
For your second problem, following the steps on the page you linked I get this:
12p^3 - 6p
examine the coefficients in each term for common factors
12 (12, 6, 4, 3, 2, 1)
6 (6, 3, 2, 1)
6 is the greatest common factor
examine the variable p in each term, and find the lowest exponent
p^3
p^1 (p^1 = p)
p^1 is greatest common factor
multiply the GCF terms together
6p is the GCF of the expression, and we can re-write it as 6p(2p^2 - 1) - you were close, but you chose 4 as the GCF term, when it was actually 6.
So for your first question:
a(b+7) + 4(b+7)
examine the coefficients for a GCF
a = 1a (1, a)
4 (4, 1)
1 is the GCF of the coefficients
now examine the variables for a GCF
(b + 7)
(b + 7)
they are the same, so the GCF is (b + 7)
multiply the GCF terms together
1(b + 7) = (b + 7)
so the GCF is (b + 7) and you can rewrite the expression as (b + 7)(a + 4)
I think that's the point of using linked lists, to learn how to perform CRUD (create, remove, update, delete) operations on that particular structure, and I'll grant you, it's not particularly fun, but it is an important thing to learn so I would encourage you to keep plugging away at it.
A linked list is quite a simple structure. You've got nodes with pointers to next nodes. To delete a node, you need to make the node behind it point to the node in front of it. To search for a node, you need to iterate through the list one at a time checking your search key. To add to the list, you need to find the right position, and then point an existing node to the new node, and the new node to the next node.
Do one of these operations at a time. Draw it on paper. Make sure you allow for the corner cases (node is first/last, one list is empty, etc).
Once you can perform these operations, and you can , you'll be nearly all the way there. |
Website Detail Page
written by
Gary Gladding
published by
the University of llinois Physics Education Research Group
This resource contains collections of quantitative homework problems for introductory physics, calculus-based physics, Electricity and Magnetism, Optics, and Modern Physics. Each homework problem is accompanied by a Socratic-dialogue "help" sequence designed to encourage critical thinking as users analyze various strategies for solving a problem. Once the initial problem is correctly answered, a recap of the solution is presented in conceptual, strategic, and quantitative contexts. The sequence culminates with follow-up conceptual questions to test understanding. New collections are being developed for Thermodynamics and Quantum Physics.
Disclaimer: ComPADRE offers citation styles as a guide only. We cannot offer interpretations about citations as this is an automated procedure. Please refer to the style manuals in the Citation Source Information area for clarifications. |
Mathematics All AroundTom Pirnot" believes that conceptual understanding is the key to a student' s success in learning mathematics. He focuses on explaining the thinking behind the subject matter, so that students are able to truly understand the material and apply it to their lives. This textbook maintains a conversational tone throughout and focuses on motivating students and the mathematics through current applications. Ultimately, students who use this book will become more educated consumers of the vast amount of technical and mathematical information that th... MOREey encounter daily, transforming them into mathematically aware citizens. In the words of the author, "I have written Mathematics All Around based on the belief that there are three things a student must focus on in order to learn and remember mathematics understanding, understanding, understanding. Instead of simply presenting the students with an equation or method and asking them to repeat the procedure, I explain the thinking behind the subject so they have a better grasp of the material and an easier time with the work. With this approach, one can discuss topics usually considered "too difficult" for liberal arts students. As a result, students end up with an understanding of and positive attitude toward many different and often challenging mathematical topics." |
JOHN WAS RIGHT! - SOME THINGS HAVEN'T CHANGED EVEN AFTER MORE THAN A HUNDRED YEARS!
Homeschool educators are constantly faced with the dilemma of deciding whether or not their son or daughter needs to take a separate high school geometry course because some academic institution wants to see geometry on the high school transcript. Or, because the publishers offer it as a separate math textbook in their curriculum - implying it is to be taken as a separate course. Remembering, of course, that selling three different math books brings in thirty-three percent more revenue than selling just two.
John Saxon's unique methodology of combining algebra in the geometric plane and geometry in the algebraic plane all in the same math textbook had solved that dilemma facing home school educators for these past twenty-five years. However, unknown to John, this same problem had been addressed over a hundred years earlier at the University of Chicago.
Knowledge of this information came to me by way of a gift from my wife and her sisters. After their mother's death in 2003, my wife and her sisters spent the next six years going through some sixty years of papers and books accumulated by their parents and stored in the attic and basement of the house they all grew up in. When asked by friends why it was taking them so long, one of the daughters replied "Mom and Dad took more than a half century to fill the house with their memories. It won't hurt to take a couple more years to go through them."
Among some of the treasures they found in the basement were letters to their great-grandfather written by a fellow soldier while both were on active duty serving in the Union Army. One of these letters was written to their great-grandfather while his friend was assigned to "Picket Duty" on the "Picket Line." His friend was describing to their great-grandfather the dreary rainy day he was experiencing. He wrote that he thought it was much more dangerous being on "Picket Duty" than being on the front lines, as the "Rebels" were always sneaking up and shooting at them from out of nowhere.
The treasure they found for me was an old math book that their father had used while a sophomore in high school in 1917. The book is titled "Geometric Exercises for Algebraic Solution - Second Year Mathematics for Secondary Schools." It was published by the University of Chicago Press in October of 1907.
The authors of the book were professors of mathematics and astronomy at the University of Chicago, and they addressed the problem facing high school students in their era. Students who had just barely grasped the concepts of the algebra 1 text, only to be thrown into a non-algebraic geometry textbook and then, a year or more later being asked to grasp the more complicated concepts of an algebra 2 textbook. The book they had written contained algebraic concepts combined with geometry. It was designed as a supplement to a geometry textbook so the students would continue to use algebraic concepts and not forget them.
John never mentioned these authors - or the book - so I can only assume that he never knew it existed. For if he had, I feel certain that it would have been one more shining light for him to shine in the faces of the high-minded academicians that he - as did these authors - thought were wreaking havoc with mathematics in the secondary schools. In the preface of their textbook, the professors wrote:
"The reasons against the plan in common vogue in secondary schools
of breaking the continuity of algebra by dropping it for a whole year
after barely starting it, are numerous and strong ... With no other
subject of the curriculum does a loss of continuity and connectiveness
work so great a havoc as with mathematics ... To attain high educational
results from any body of mathematical truths, once grasped, it is profoundly
important that subsequent work be so planned and executed as to lead the
learner to see their value and to feel their power through manifold uses."
So, should you blame the publishers for publishing a separate geometry textbook? Or is it the fault of misguided high-minded academicians who - after more than a hundred years - still demand a separate geometry text from the publishers? I am not sure, but thankfully, this decision need not yet face the home school educators using John Saxon's math books for the original home school third editions of John Saxon's algebra one and algebra two textbooks still contain geometry as well as algebra - as does the advanced mathematics textbook.
Any home school student using John Saxon's math textbooks who successfully completes algebra one, (2nd or 3rd editions), algebra 2, (2nd or 3rd editions), and at least the first half of the advanced mathematics (2nd edition) textbook, has covered the same material found in any high school algebra one, algebra two and geometry math textbook - including two-column formal proofs. Their high school transcripts - as I point out in my book - can accurately reflect completion of an algebra one, algebra two, and a separate geometry course.
When home school educators tell me they are confused because the school website offers different materials than what is offered to them on the Saxon Homeschool website, I remind them that - unless they want to purchase a hardback version of their soft back textbook - they do not need anything being offered on the Saxon School website. In fact, they are getting a better curriculum by staying on the Homeschool website. You can still purchase the original versions of John Saxon's math textbooks that he intended be used to develop "mastery" as recommended by the University of Chicago mathematics professors over a hundred years ago.
Because many of you do not have a copy of my book, I have reproduced that list from page 15 of the book so you can see what editions of John Saxon's original math books are still good whether acquired used or new. These editions will remain excellent math textbooks for several more decades.
Math 54, 2nd Ed (Hardcover) - or - new 3rd Ed (Softcover).
Math 65, 2nd Ed (Hardcover) - or - new 3rd Ed (Softcover).
Math 76, 3rd Ed (Hardcover) - or - new 4th Ed (Softcover).
Math 87, 2nd Ed (Hardcover) - or - new 3rd Ed (Softcover).
Algebra 1/2, 3rd Ed (Hardcover).
Algebra 1, 3rd Ed (Hardcover).
Algebra 2, 2nd or 3rd Ed (Hardcover) - content is identical.
Advanced Mathematics, 2nd Ed (Hardcover)..
Calculus, 1st or 2nd Ed (Hardcover).
Physics, 1st Ed (Hardcover) - there is no second edition of this book.
"May you have a very Blessed and Merry Christmas."
November 2011
SHOULD YOU GRADE THE DAILY SAXON MATH ASSIGNMENTS?
I continue to see comments on familiar blogs about correcting - or grading - the daily work of Saxon math students. That is a process contrary to what John Saxon intended when he developed his math books. Unlike any other math book on the market today, John's math books were designed to test the student's knowledge every week. Why would you want to have students suffer the pains of getting 100 on their daily work when the weekly test will easily tell you if they are doing well?
I always tell homeschool educators that grading the daily work, when there is a test every Friday, amounts to a form of academic harassment to the student. Like everything else in life, we tend to apply our best when it is absolutely necessary. Students will accept minor mistakes and errors when performing their daily "practice" of math problems. They know when they make a mistake and rather than redo the entire problem, they recognize the correction necessary to fix the error and move on without correcting it. They have a sense when they know or do not know how to do a certain math problem; however, when they encounter that all important test every Friday, - as I like to describe it - they put on their "Test Hat" to do their very best to make sure they do not repeat the same error!
In sports, daily practice ensures the individual will perform well at the weekly game, for without the practice, the game would end in disaster. The same concept applies to daily piano practice. While the young concert pianist does not set out to make mistakes during the daily practice for the upcoming piano recital, he quickly learns from his mistakes. Built into John Saxon's methodology are weekly tests (every four lessons from Algebra 1/2 through Calculus) to ensure that classroom as well as homeschool educators can quickly identify and correct these mistakes before too much time has elapsed.
In other words, the homeschool educator as well as the classroom teacher is only four days away from finding out what the student has or has not mastered during the past week's daily work. I know of no other math textbook that allows the homeschool educator or the classroom teacher this repetitive check and balance to enable swift and certain correction of the mistakes to ensure they do not continue. Yes, you can check daily work to see if your students are still having trouble with a particular concept, particularly one they missed on their last weekly test, which can be correlated to their latest daily assignment. However, as one home school educator stated recently on one of the blogs "Yes, they must get 100 percent on every paper or they do not move on." While this may be necessary in other math curriculums that do not have 30 or more weekly tests, it is a bit restrictive and punitive in a Saxon environment.
John Saxon realized that not all students would master every new math concept on the day it is introduced, which accounts for the delay allowing more than a full week's practice of the new concepts before being tested on them. He also realized that some students might need still another week of practice for some concepts which accounts for his using a test score of eighty percent as reflecting mastery. Generally, when a student receives a score of eighty on a weekly test, it results from the student not yet having mastered one or two of the new concepts as well as perhaps having skipped a review of an old concept that appeared in the assignment several days before the test. When the students see the old concept in the daily work, they think they can skip that "golden oldie" because they already know how to do it! The reason they get it wrong on the test is that the test problem had the same unusual twist to it that the problem had that the student skipped while doing the daily assignment.
In all the years I taught John Saxon's math at the high school, I never graded a single homework paper. I did monitor the daily work to ensure it was done and I would speak with students whose test grades were falling below the acceptable minimum of eighty percent. I can assure you that having the student do every problem over that he failed to do on his daily assignments does not have anywhere near the benefit of going over the problems missed on the weekly tests because the weekly tests reveal mastery - or lack thereof - while the daily homework only reveals their daily memory!
October 2011
SAXON MATH - WHEN USED CORRECTLY - IS STILL THE BEST MATH CURRICULUM!
Over the last twenty-some years, I have heard just about every story told by public and private school classroom teachers, school administrators, and home school educators about how difficult John Saxon's math books are. I believe that home school educators who speak poorly about John Saxon's math books are like the classroom teachers and administrators I encountered who always blamed the math book for students' poor showing. They never became aware that misusing John Saxon's math books was a major contributing factor to the student's difficulty. They never received or asked for any special training on how to correctly use John Saxon's math books. Why should they? After all, isnt one math textbook just like another?
More than a decade ago, while briefing the superintendent of a large school district in Colorado I related to him - from my observations - that the vast majority of the districts math teachers were not properly using John Saxon's math books. His district had been using (rather misusing) John's books for more than five years and the students math scores were getting worse, not better! I told him that it was not the books, but rather this misuse of the books that accounted for the district's failing math scores.
In the middle of my briefing, he stopped me and said, "What I hear you saying Art, is that we bought a new car, and since we already knew how to drive, we saw no reason to read the owner's manual wouldn't you agree?" To which I replied "It's worse than that, sir! You all thought you had purchased a car with an automatic transmission, but Saxon is a stick shift! It is critical that certain procedures be followed, just as well as some be dropped, or you will strip the gears!" I went on to tell him that while I was not the owner of the company, if John Saxon were alive today, standing up here addressing them under these circumstances, he would tell them to either use his books correctly or get rid of them, and blame someone else's textbooks for the failing grades.
On another occasion while briefing administrators at a school district in the state of Missouri whose math teachers were guilty of the same misuse, I promised their superintendent the same results I had promised the superintendent in Colorado that if they would make some adjustments and use the books correctly, they would develop a successful math program and their students math scores would go up. The district decided to implement the changes I had recommended. About eighteen months later, I received a letter from the superintendent. She wrote that their middle school students had scored the highest of any middle school in the state on their end-of-year math exams.
During these past several decades of advising and assisting homeschool parents about curriculum choices for their children, I noticed many of their calls and email to me were the result of having received inaccurate or inadequate - sometimes downright erroneous - advice. This erroneous advice came from other home school parents, discussion groups, well-meaning but uninformed or inexperienced publishing company employees, or from well meaning, but inexperienced employees of homeschool textbook distributors.
With all the new math books and supplemental math products on the market today - and textbook publishers promising every home school parent that if you use their books, your sons and daughters would score well on the ACT or SAT tests - I thought it appropriate to take this opportunity to defend John's math books for the benefit of the home school educators and their students.
I do not sell John Saxon's math books - I never have! But I firmly believe that John's math books remain the best math textbooks on the market today. I also believe that some of these new book fads, advertising how their product makes math fun, will ultimately leave your child short of mastering the requisite fundamentals of mathematics necessary to succeed in the collegiate realm of engineering, architecture, science, medicine, et al.
Students fail calculus - not because they do not understand the calculus - but because they never mastered the fundamentals of algebra, and they will fail a basic algebra course if they have not mastered the concepts of decimals, fractions and percents. John Saxon's math books were designed to create mastery of mathematics at all levels, and the infusion of repetition over time (referred to by Dr. Benjamin Bloom as "automaticity") creates this mastery at every level for every student who uses John Saxon's math books properly.
While home school students have a great deal more academic flexibility than the public or private classroom students do, they can just as easily fall prey to the same difficulties in mathematics as the public classroom students if they are using one of John Saxon's math books incorrectly. Parents of home school students who have displayed poor progress while using John Saxon's math books, generally have unknowingly contributed to the student's poor performance by taking shortcuts and preventing the student from receiving the full benefit of John Saxon's methods.
Earlier this year, in the January and February news articles, I went over the essential Do's and Don't's together with my comments and recommendations on how to correct them and have your child enjoy mathematics and realize mastery of the material using the best mathematics curriculum on the market today - John Saxon's math books!
If you need to discuss a special situation concerning your son or daughter's math progression or difficulty, please do not hesitate to either email or call me at:
Email:art.reed@usingsaxon.com Telephone: 580-234-0064 (CST)
"Do not worry about your difficulties in mathematics; I can assure you that mine are far greater"
Albert Einstein
September 2011
WHAT ARE FORMULA CARDS? WHAT ARE THEY USED FOR?
WHERE CAN I GET THEM?
Having been repeatedly threatened by my high school math teachers that I would be doomed to fail their tests if I did not memorize all those math formulas, I was somewhat surprised later in a college calculus course when the professor handed out "formula cards" containing over ninety geometry, trigonometry identities, and calculus formulas. He explained that they could be used on his tests. He did not bat an eye as he handed them out and reminded us that selecting the correct formulas and knowing how and when to use them was far more important than trying to memorize them or write them on the desk top.
So, when I started teaching at the high school, I announced to the students that they could make "formula cards" by using 5 x 8 inch cards, lined on one side and plain on the other. It never failed. Immediately, one of the students would ask why I did not have them printed off and handed out, saving them a considerable amount of time and money creating their own.
I told my students that whenever they encountered a formula in their textbooks, writing it down would strengthen the connection more than if they just read it and tried to recall it later while working a problem. Reading the formula in the textbook was their first encounter and there would not yet be a strong connection between what they were reading and what they tried to remember. However, when they took the time to create a formula card for that particular formula, they would be strengthening that connection. As they used the card when doing their daily assignments, they would continue the process and eventually place the formula in their long term memory.
So, how can you get formula cards? Simple! Each student makes his own. I allowed my students to use them starting with Math 87 or Algebra 1/2. One young lady in my Algebra 2 class used blue cards for geometry formulas and white cards for the algebra formulas to save her time looking through the cards. The cards should be destroyed after completion of the course, requiring the next student to make his own. Then how do you make formula cards?
Have the students use 5 x 8 cards - and write or print clearly and big. On the plain side of the card they print the title of the formula such as the formula for the area of a sector found on page 16 of the third edition of the Algebra 2 textbook.
So, on the front of the card (the plain side) in the center of the card the student would print::
AREA OF A SECTOR
When you turn the card over, in the upper right hand corner is the page number of the formula to enable the student to immediately go to that page should he need more information (in this case p 16). Recording the page number saves flipping through the book looking for the information and wasting time, especially when the student encounters a difficult problem some twenty lessons later.
After writing down the appropriate page number, they neatly record the formula: (double checking to make sure they have recorded it correctly.)
Area of Sector = Pc/360 times [(pi)(r)]^2 (where the piece (Pc) equals the part of the sector given.)
NOTE: If diameter is given remember to divide by two before squaring the value.
Remember, students may also use the formula cards on tests - and if you watch them - the dog eared cards seldom get looked at after awhile.
For those of you concerned about students taking the ACT or SAT, unless they have changed their policy, students are given a sheet of formulas for the math portion of the test. Again, this requires the student to know which formula to select and what to do with it - rather than remembering all those formulas!
August 2011
IS THERE ANY VALUE TO USING A SEPARATE GEOMETRY TEXTBOOK?
Have you ever seen an automobile mechanic's tool chest? Unless things have changed, auto mechanics do not have three or four separate tool chests. They have one tool chest that contains numerous file drawers separating the tools necessary to accomplish their daily repair work. But the key is that all of these tools are in a single tool chest.
What if the auto mechanic purchased several tool chests thinking to simplify things by neatly separating the specific types of tools from each other into separate tool chests rather than in separate drawers in the one tool chest? Each separate tool chest would then contain a series of complete but distinctly different tools. If mechanics did this, there would now exist the possibility that they would find themselves trying to remember which tool chest contained which tools - and - the extra tool chests would cost them more!
It is somewhat like that in mathematics. Each division of mathematics has its strengths and weaknesses and like the auto mechanic who selects the best tool for a specific job, so the physicist, engineer, or mathematician selects the best math procedure to meet the needs of what they are doing.
But how do we address the argument that geometry provides a distinct and essential thought process unlike that used in algebra? The advent of computers has provided educators with an alternative course titled Computer Programming. A computer programming course teaches students the same methodology or thought process that the two-column proofs of geometry do. Basically, it teaches the student that he cannot go through a door until he has opened it - meaning - the student must use valid statements that are logically and correctly placed to reach a valid conclusion and to prove that conclusion valid by having the computer program work correctly.
Before computers, educators in the United States felt that providing the separate geometry course would benefit those students interested in literature and the arts, who enjoyed the challenge of geometry without the burden of algebra, while still allowing students entering the fields of science and engineering, who had to take more math, to take the course also. When I was in high school, most geometry teachers taught only geometry, they never taught an algebra course - as I soon learned!
I recall encountering that little known fact when I took high school geometry from one such teacher. I was sharply rebuked early in the school year when I kept using the term "equal" to describe two triangles that had identical measures of sides and angles. The first time I said the two triangles that contained identical angles and sides were "equal," she told me I was wrong. She then proceeded to tell me and the class that the only correct term to describe two identical triangles was the term "congruent." She did not say my answer was technically correct, but that in the geometry class, we used the term "congruent" rather than "equal" - she specifically pointed out that I was "wrong."
The next day in geometry class, I really got in trouble when I stood and read Webster's definition of the word congruent.
Just before I was told to go to the office and tell the principal that I was being rude, I asked her why the two triangles could not also be said to be equal since they had identical angles and sides and were equal in size. Then I drove the final nail in my coffin when I proceeded to read Webster's definition of "equal."
Equal - adj. 1) Being the same in quantity or size...
Half a century later, when I taught both the algebra and geometry concepts simultaneously while using John Saxon's math books at a rural high school, I made it clear to the students that while they should become familiar with the terminology of the subject, they were free to interchange terms as long as they were correctly applied. I also made it clear to them that the object of learning geometry and algebra was to challenge and expand their thought processes and for them to understand the strengths and weaknesses of each and apply whichever math tool best served the problem being considered.
While many tout the separate geometry textbook as necessary to enable a child to concentrate on a single subject rather than attempting to process both geometry and algebra simultaneously, I would ask them how a young geometry student can solve for an unknown side in a particular triangle without some basic knowledge of algebraic equations. In other words, if you are going to use a separate geometry textbook, it cannot be used by a student who has not yet learned how to manipulate algebraic equations. This means that a separate geometry book is best introduced after the student has successfully completed an algebra 1 course.
For most students this means placing the separate geometry course between the Algebra 1 and Algebra 2 courses creating a gap of some fifteen months between them. (Two summers off, plus the nine month geometry course). As was true in my high school days, this situation creates a problem for the vast majority of high school students who enter the Algebra 2 course having forgotten much of what they had learned in the Algebra 1 course fifteen months earlier.
So what am I getting at? Must we have a separate geometry textbook for students who cannot handle the geometry and algebra concurrently? Well, let me ask you, if students can successfully study a foreign language while also taking an English course or successfully study a computer programming course while also taking an algebra course, why can't they study algebra and geometry at the same time, as John Saxon designed it?
Successful completion of John Saxon's Algebra 2, (2nd or 3rd editions) not only gives the student a full years' credit for the Algebra 2 course, but it also incorporates the equivalent of the first semester of a regular high school geometry course. I said "Successful Completion" for several reasons. FIRST: The student has to pass the course and SECOND: The student has to complete all 129 lessons.
Whenever I hear home school educators make the comment that "John Saxon's Algebra 2 book does not have any two-column proofs," I immediately know that they stopped before reaching lesson 124 of the book which is where two-column proofs are introduced. The last six lessons of the Algebra 2 textbook (2nd or 3rd editions) contain thirty-one problems dealing with two-column proofs. The following year, in the first half of the Advanced Mathematics textbook, they not only encounter some heavy duty algebra concepts, but they also complete the equivalent of the second semester of a regular high school geometry course. The first thirty of these sixty lessons contain more than forty problems dealing with two-column proofs.
So why then did John Saxon not want to publish a separate geometry textbook? As I mentioned in one of my newsletters several years ago, a group of professors who taught mathematics and science at the University of Chicago bemoaned the fact that educators continued to place a geometry course between basic algebra (Algebra 1) one and the advanced algebra course (Algebra 2) to the detriment of the student. AND THEY WROTE THIS 104 YEARS AGO!
In the preface to their book titled "Geometric Exercises for Algebraic Solution," published in 1907, the professors explained that it is this lengthy "void" that prevents students from retaining the necessary basic algebra concepts learned in basic algebra to be successful when encountering the rigors of advanced algebra.
We remain one of the only - if not the only - industrialized nations that have separate math textbooks for each individual math subject. When foreign exchange students arrive at our high schools, they come with a single mathematics book that contains geometry, algebra, trigonometry, and when appropriate, calculus as well. Is it any wonder why we are falling towards the bottom of the list in math and science?
When students take a separate geometry course without having gradually been introduced to its unique terminology and concepts, they encounter more difficulty than do students using John Saxon's math books The beauty of using John's math books, from Math 76 through Algebra 1 is that students receive a gradual introduction to the geometry terminology and concepts.
If you are going to use John Saxon's math books through Advanced Mathematics or Calculus you do not need a separate geometry book. This means you must use the third editions of John Saxon's Algebra 1 and Algebra 2 books because the current owners of Saxon Publishers (HMHCO) have stripped all of the geometry from the new fourth editions of their versions of Algebra 1 and Algebra 2. And you do not want a student to go from the fourth edition of Algebra 2 to the Saxon Advanced Mathematics textbook.
NOTE: Please Click Here to watch a short video on how to receive credits for Geometry, Trigonometry and Pre-calculus using John Saxon's Advanced Mathematics textbook - and how to record the course titles on the student's transcript.
July 2011
HOW MUCH TIME SHOULD STUDENTS SPEND ON MATH EACH DAY?
One of several arguments advanced by home school educators regarding the efficiency of the Saxon math curriculum is that from Math 54 through Advanced Mathematics the courses require too much time to complete the daily assignment of thirty problems. Their solution to this often takes one of two approaches. Either they allow the student to take shortcuts to reduce the time spent on daily assignments, or they find another math curriculum that takes less time – you know – you've heard them say, "We found another math curriculum that is more fun, easier, and it does not require so much time."
In this year's, January and February newsletters, I addressed some of the ramifications of taking these shortcuts when using John Saxon's math books. In these two articles, I described in detail the effects upon students who used some or all of them, so I will not go over them again here. I would ask you to read those two newsletters if you have not already done so. What I want to discuss here is what may be causing the excessive amount of time taken by the students and also, what constitutes excessive time to an educator who taught in a public classroom using Saxon math books for over a decade.
While I was teaching high school mathematics in a rural Oklahoma high school, I would often go and watch my students who were on the the high school track, basketball, or football teams during their practice sessions after school. I was able to chat with the mothers and fathers who were also watching these practices. This one-on-one conversation often gave me an insight into their priorities regarding their children's education.
While they sometimes complained about the rigors of my math classes, they never once complained about the length of time their sons and daughters were out on the field in the heat or cold - or on the basketball court – practicing – after just spending six academic hours in the classroom. In fact, when coaches were forced to cancel a practice for one reason or another, some of the parents would vocally complain that the practices should continue. They expressed concern that skipping practice would take the "edge" off their son or daughter's playing ability and inhibit their athletic "sharpness" for the next game.
Strange then that some parents would complain the 45 – 60 minutes spent each day on mathematics "practice" would be excessive - and more unusual - that they would seek an easier course of action. They never discussed the ramifications that doing so might take the "edge" off their child's math "sharpness" for the next math course or the state mandated math test. I never heard the high school parents complain about watching the tough daily drills and practices run by the coaches. I never heard a parent complain about the hour spent each day by the students diligently practicing their piano lessons, or having to come in before school early each day to spend 45 minutes in the weight room.
At least several times each week I receive email from home school parents who express concern that their son or daughter was taking an inordinate amount of time on their daily math assignment in one of the books from Math 54 through Advanced Mathematics. The solution to the excessive time spent by students using the Advanced Mathematics textbook is easy to resolve. The solution to that unique situation is explained in a short video clip (Click Here to view that video).
I have interacted with several thousand parents and students in the twelve years that I taught mathematics at that rural high school. I have also advised thousands more home school educators and home school students in the succeeding decade after my retirement while serving as one of the Homeschool Curriculum Advisors (for Math 76 through Calculus and Physics) for Saxon Publishers and later for Harcourt-Achieve who bought the company from John's children. And while every child and home school situation is different, my experiences have shown me that there exist several situations that contribute to excessive time spent on daily work by students, whether home schooled or attending a public or private classroom.
These situations are:
The Student is in The Wrong Level Math Course: If after lesson thirty in any Saxon math book, students continue to receive 80% on the weekly tests of twenty questions, within a maximum of fifty minutes with no partial credit (all right or all wrong) and no calculator (until Algebra 1), then they are in the correct level Saxon math book. If the test scores are constantly below that or if they fall below an 80 on their first five or so tests, then that is a good indication they are in the wrong level Saxon math book. This situation can result from any one or more of the following conditions:
They did not finish the previous Saxon math book.
They took shortcuts in the preceding math book.
Their previous math book was not a Saxon math book.
They did not take the weekly tests in the previous math book, using the daily grade as an indication of their level of proficiency.
Their last five tests in the preceding course were well below 80% (minimal mastery).
The Student is Required to Re-do Math Problems from Yesterday's Lesson: Why do we want students to get 100% on their daily practice for the weekly test? When we grade their daily work and have them go over the ones they missed on the previous day's assignment, nothing is accomplished except to "academically harass" the students. The daily work reflects nothing but the status of the students' temporary learning curve. It is the weekly tests and not the daily work that reveal what the student has mastered from the previous weeks and months of work. Not every student masters every concept the day it is introduced, which is why there is a four to five day delay from when the concept is introduced to when it is tested. In the twelve years that I taught John Saxon's math books in high school, I did not grade one homework paper – but I did grade the weekly tests which reflected what the students had mastered as opposed to their daily work which did not. Remember, John Saxon's math books are the only books I am aware of that use weekly tests to evaluate a student's progress. There are a minimum of thirty weekly tests in every one of John's math books from Math 54 on.
Too Much Time is Spent on The Warm Up Box: From Math 54 through Math 87, there is what used to be called a "Warm Up" box at the top of the first page of every lesson. I recall watching a sixth grade teacher waste almost thirty minutes of class time while three boys took turns giving different opinions as to how the "Problem of The Day" was to be solved – and arguing as to which had the better approach. After class, I reminded the teacher that the original purpose of the box was to get the students settled down and "focused" on math right after the second bell rang. I said to her, "Why not immediately review a couple of the problems from yesterday's lesson at the start of class for the few who perhaps did not grasp the concept yesterday? Then move immediately to the new lesson." This process would take about 10 to 20 minutes and would leave students with about 40 minutes of remaining class time to work on their new homework assignment.
NOTE: In any of John Saxon's math books from Math 54 through Algebra 2, the "A" and "B" students will get their 30 problems done in less than 40-50 minutes. The "C" students will require more than an hour.
The Student is Required to Do All of The Daily Practice Problems: The daily practice problems were created for teachers to use on the blackboard when teaching the lesson's concept so they did not have to create their own or use the homework problems for demonstrating that concept. Many of the lessons from Math 54 through Math 87 have as many as six or more such problems and if the student understands the concept, they are not necessary. If the student has not yet grasped the concept, having the student do six or more additional practice problems of the same concept will only further frustrate him. Remember, not every student grasps every concept on the day it is introduced. The five minutes spent on review each day is essential to many students.
The Student is a Dawdler or a Dreamer: There is nothing wrong with being a "Dreamer," but some students just look for something to keep them from doing what they should be doing. I call these students "Dawdlers." I recall the first year I taught. I had to constantly tell some students in every class to stop gazing out the window at the cattle grazing in the field outside our classroom – and get on their homework. That summer, I replaced the clear glass window and frame with a frosted glass block window - and in the following eleven years I had absolutely no problem with my "Dawdlers."
The Student is Slowed by Distractions: Is the student working on the daily assignment in a room filled with activity and younger siblings who are creating all sorts of distractions? Even the strongest math student will be distracted by excessive noise or by constantly being interrupted by younger siblings seeking attention. Did you leave the student alone in his room only to find he was on his cell phone talking or texting with friends or listening to the radio? Or worse, does he have a television or computer in his room and does he use the computer to search the internet for a solution to his math problems or engage in something equally less distracting by watching the television?
Please do not misinterpret what I have discussed here. If you desire to do all of the above and the student takes two hours to complete a daily assignment, and both you and the student are satisfied, then that is acceptable. But if you are using this excessive time as an excuse for your child's frustration and as an argument against John Saxon's textbooks, I would remind you of what John once told a school district that did everything John had asked them not to do and they were now blaming John's books for their district's low math test scores. John told them, "If you want to continue your current practices, get rid of my books and buy someone else's book to blame."
June 2011
JUST WHAT IS THE DIFFERENCE BETWEEN MATH 87 AND ALGEBRA 1/2 ?
There appear to be varying explanations regarding whether a student should use Math 87 or Algebra 1/2 after completing the third or fourth edition of John Saxon's Math 76 textbook. Let me see if I can shed some light on the best way to determine which one, or when both, should be used.
First, whenever I discuss the Math 76 textbook in this article, I am talking about the third or fourth editions of that book. I am not talking about the old first or second editions of John's Math 76 books. These two older editions have been out of print for almost fifteen years now and their content, while acceptable at the time, would not now enable a math student to proceed successfully through either the second or third editions of Math 87 or the third edition of Algebra 1/2.
Second, whenever I discuss using the Math 87 textbook, I am talking about either the second or third editions of that book and not the older first edition which has also been out of print for more than a decade.
Let me assure you that, except for the new soft cover, the addition of a solutions manual, and the varied numbering of the pages, there is absolutely no difference between the 120 lessons and the 12 Investigations of the hard cover second edition of Math 87 and the new soft cover third edition of Math 87. Oh yes, the new third edition has added a TOPIC A at the end of the book (after Investigation 12) dealing with Roman Numerals and Base 2. And even though the marketing folks at the publishers have added the word "Prealgebra" under the cover title of the soft cover third edition textbook, these two additional topics, while interesting and nice to know, are not pre-algebra material and will not create any shortfall for the student in Algebra 1 or even later in Algebra 2.
Both the Math 87 and Algebra 1/2 textbooks prepare the student for any Algebra 1 course. The main difference between using the Math 87 and the Algebra 1/2 books depends upon the student's success in the Math 76 textbook. The Math 87 book starts out a little slower than the Algebra 1/2 book does because it assumes the student needs the additional review resulting from the student encountering difficulty in the latter half of the Math 76, textbook. Also, If you were to open to any lesson in the Algebra 1/2 textbook, you would immediately notice that the "Warm-Up' box common in all Saxon math books from Math 54 through Math 87, is noticeably absent.
If there exists a math savvy student of John Saxon's Math 76 textbook, who received test grades of 85 or better on the last five tests in Math 76 (50 - 55 minute test period, no calculator, and no partial credit), then that student would be more challenged and, from my teaching experience, much better off in the Algebra 1/2 book. However, if his last five test scores are below 85, then from my experiences, that indicates that student should proceed to Math 87, and upon completion of that book, if his or her last five tests are now 80 or better (minimal mastery), then that student can easily skip Algebra 1/2 and go on to success in Algebra 1.
If however, a student encounters difficulty going through both Math 76 and Math 87, then proceeding through the Algebra 1/2 textbook before attempting Algebra 1 will allow the student to regain his confidence. Doing so will further ensure the student has mastered a solid conceptual base necessary for success in any Algebra 1 course.
Students will fail an Algebra 1 course if they have not mastered fractions, decimals and percents which are emphasized before the student reaches that course. I realize that not every child fits neatly into a specific mold, but John Saxon's Math 76, Math 87, and Algebra 1/2 textbooks allow the Saxon home school educator sufficient flexibility to satisfy every student's needs and to ensure the students' success in any Algebra 1 course.
May 2011
ARE JOHN SAXON'S ORIGINAL MATH BOOKS GOING THE WAY OF THE DINOSAUR?
In the past several weeks I have been asked by some home school educators whether or not I will create my teaching DVD "videos" for the new fourth editions of Algebra 1 and Algebra 2, and the resulting new first edition of Geometry now being sold on the Saxon Homeschool website by the new owners of Saxon Publishers.
The answer is no, I will not do so. My creation of the current DVD video series for John's math books, based upon rock solid editions created by John Saxon, was not to make money. Using my Saxon classroom teaching experiences, I wanted to create a classroom environment for home school students who wanted to master high school mathematics using John's unique math books. However, publishing math textbooks redesigned to be like all the other math textbooks on the market is not what John intended when he created his unique style of math books.
John Saxon would not have sanctioned gutting his Algebra 1 and Algebra 2 textbooks of their geometry to create a separate geometry textbook. He believed that using a separate geometry textbook was not conducive to mastering high school mathematics. More importantly, each of John's math books had an author - an experienced classroom mathematician - behind them. These three new editions, created under his Saxon title, do not.
When Harcourt-Achieve bought John Saxon's dream - Saxon Publishers - from his children, I made the comment that the new owners were certainly smart enough to recognize the uniqueness of John's books. I predicted that they would not change the content of John's books. Certainly, I commented. "They would never take their prize winning bull and grind it up into hamburger" – or so I thought!
Well the new owners of Saxon Publishers appear to have done just that, and the time has come for me to apologize because they are now selling the hamburger on the Homeschool website. I have previously cautioned home school Saxon users not to use the new fourth editions of Algebra 1 and Algebra 2 then offered only on the school website because the company had gutted all geometry from them to enable them to publish a separate geometry textbook desired by the public school system. But they are now selling them on the Homeschool site as well.
Having been affiliated with one of the larger publishing companies - after Saxon Publishers was sold - I observed that the driving force in the company was not so much the education of the children, but the quarterly profit statement. And that is okay, but being around their VP's and upper level executives showed me that to them "a book is a book is a book." I still believe they have not the foggiest idea of just how unique and powerful John's math books are when used correctly. However, I may be wrong, because they may have already observed that it is this "uniqueness" that requires special handling and that requires special training, and that costs money – reducing quarterly profits.
If you are serious about using John Saxon's original math series through high school, I recommend you not buy these new fourth editions of Algebra 1 and Algebra 2. I strongly recommend you immediately acquire the home school editions of John's math books that I discussed in my February 2010 news article - which include the third editions of Algebra 1 and Algebra 2. The news article not only explains the correct editions that will still be good for several more decades, but it explains the correct sequencing of the books as well.
I do not believe the publishing company will long suffer the expense of publishing both the third and fourth editions of Algebra 1 and Algebra 2. It is my opinion they may well stop printing and selling the third editions of Algebra 1 and Algebra 2 when current stocks run out. This will then require that home school educators using Saxon math books buy the separate geometry book also. After all, "Don't you make more money from selling three books than you do from just selling two?"
Maybe I am wrong, and the publishers of John Saxon's math books will not stop printing the third editions of Algebra 1 and Algebra 2 as I am predicting - but then again I could be wrong - again!
April 2011
WHY IS THERE A "LOVE – HATE" RELATIONSHIP WITH SAXON MATH BOOKS?
Over the past twenty-five years, I have noticed that parents, students, and educators I have spoken to, either strongly like or, just as strongly, dislike John Saxon's math books. During my workshops at home school conventions, I am often asked the question about why this paradigm exists. Or, as one home school educator put it, "Why is there this Love – Hate relationship with Saxon math books?" It is easy to understand why educators like John's math books. They offer continuous review while presenting challenging concepts in increments rather than overwhelming the student with the entire process in a single lesson. They allow for mastery of the fundamentals of mathematics.
In an interview with William F. Buckley on the FIRING LINE in 1983, John Saxon responded to educators who were labeling his books as "blind, mindless drill." He accused them of misusing the word "drill." John reminded the listeners that:
"Van Cliburn does not go to the piano to do piano drill. He practices - and - Reggie Jackson does not take batting drill, he takes batting practice."
John went on to explain that
"Algebra is a skill like playing the piano, and practice is required for learning to play the piano. You do not teach a child to play the piano by teaching him music theory. You do not teach a child algebra by teaching him advanced algebraic concepts that had best be reserved till his junior year in college when he has mastered the fundamentals."
As John would say, "Doing precedes Understanding - Understanding does not precede doing."
It is my belief that, "John Saxon's math books remain the best math books on the market today for mastery of math concepts!" Successful Saxon math students cannot stop telling people how they almost aced their ACT or SAT math test, or CLEP'd out of their freshman college algebra course. And those who misuse John Saxon's math books, and ultimately leave Saxon math for some other "catchy – friendly" math curriculum, rarely tell you that their son or daughter had to take a no-credit algebra course when they entered the university because they failed the entry level math test. Yes, they had learned about the math, but they did not master or retain it.
Just what is it that creates this strong dislike of John Saxon's math books? During these past twenty-five years I have observed there are several general reasons that explain most of this strong dislike. Any one of these – or a combination of several – will create a situation that discourages or frustrates the student and eventually turns both the parent and the student against the Saxon math books.
Here are several of those reasons:
ENTERING SAXON MATH AT THE WRONG LEVEL: Not a day goes by that I do not receive an email or telephone call from frustrated parents who cannot understand why their child is failing Saxon Algebra 1 when they just left another publisher's pre-algebra book receiving A's and B's on their tests in that curriculum. I explain that the math curriculum they just left is a good curriculum, but it is teaching the test, and while the student is learning, retention of the concepts is only temporary because no system of constant review is in place to enable mastery of the learned concepts.
Every time I have encountered this situation, I have students take the on-line Saxon Algebra 1 placement test - and without exception, these students have failed that test. That failure tends to confuse the parents when I tell them the test the student just failed was the last test in the Saxon Pre-Algebra textbook. Does this tell you something? This same entry level problem can occur when switching to Saxon at any level in the Saxon math series from Math 54 through the upper level algebra courses; however, the curriculum shock is less dynamic and discouraging when the switch is made after moving from a fifth grade math curriculum into the Saxon sixth grade Math 76 book.
MIXING OUTDATED EDITIONS WITH NEWER ONES: There is nothing wrong with using the older out-of-print editions of John Saxon's original math books so long as you use all of them – from Math 54 to Math 87. However, for the student to be successful in the new third edition of Algebra 1, the student has to go from the older first edition of Math 87 to the second or third edition of Algebra ½ before attempting the third edition of the Saxon Algebra 1 course.
But when you start with a first edition of the Math 54 book in the fourth grade and then move to a second or third edition of Math 65 for the fifth grade; or you move from a first or second edition of the sixth grade Math 76 book to a second or third edition of the seventh grade Math 87 book, you are subjecting the students to a frustrating challenge which in some cases does not allow them to make up the gap they encounter when they move from an academically weaker text to an academically stronger one.
The new second or third editions of the fifth grade Saxon Math 65 are stronger in academic content then the older first edition of the sixth grade Math 76 book. Moving from the former to the latter is like skipping a book and going from a fifth grade to a seventh grade textbook. Again, using the entire selection of John's original first edition math books is okay so long as you do not attempt to go from one of the old editions to a newer edition. If you must do this, please email or call me for assistance before you make the change.
SKIPPING LESSONS OR PROBLEMS: How many times have I heard someone say, "But the lesson was easy and I wanted to finish the book early, so I skipped the easy lesson. That shouldn't make any difference." Or, "There are two of each type of problem, so why do all thirty problems? Just doing the odd numbered ones is okay because the answers for them are in the back of the book." Well, let's apply that logic to your music lessons.
We will just play every other musical note when there are two of the same notes in a row. After all, when we practice, we already know the notes we're skipping. Besides, it makes the piano practice go faster. Or an even better idea. When you have to play a piece of music, why not skip the middle two sheets of music because you already know how they sound and the audience has heard them before anyway.
My standard reply to these questions is "Must students always do something they do not know how to do? Can they not do something they already know how to do so that they can get better at it? The word used to describe that particular phenomenon is "Mastery!"
USING A DAILY ASSIGNMENT GRADE INSTEAD OF USING THE WEEKLY TEST GRADES: Why would John Saxon add thirty tests to each level math book if he thought they were not important and did not want you to use them? Grading the daily assignments is misleading because it only reflects students' short term memory, not their mastery. Besides, unless you stand over students every day and watch how they get their answers, you have no idea what created the daily answers you just graded.
Doing daily work is like taking an open book test with unlimited time. The daily assignment grades reflect short term memory. However, answering twenty test questions - which came from among the 120 – 150 daily problems the students worked on in the past four or five days - reflects what students have mastered and placed in long term memory. John Saxon's math books are the only curriculum on the market today that I am aware of that require a test every four or five lessons. Grading the homework and skipping the tests negates the system of mastery, for the student is then no longer held accountable for mastering the concepts.
MISUSE OF THE SAXON PLACEMENT TESTS: When students finish one Saxon level math book, you should never administer the Saxon placement test to see what their next book should be. The placement tests were designed to see at what level your child would enter the Saxon series based upon what they had mastered from their previous math experiences. They were not designed to evaluate Saxon math students on their progress. The only valid way to determine which the next book to use would be is by evaluating the student's last four or five test scores in their current book. If those test scores are eighty or better, in a fifty minute test – using no partial credit – then they are prepared for the next level Saxon math book.
In March of 1993, in the preface to his first edition Physics textbook, John wrote about "The Coming Disaster in Science Education in America." He explained that this was a result of actions by the National Council of Teachers of Mathematics (NCTM). He went on to explain that the NCTM had decided, with no advance testing whatsoever, to replace testing for calculus, physics, chemistry and engineering with a watered-down mathematics curriculum that would emphasize the teaching of probability and statistics and would replace the development of paper-and-pencil skills with drills on calculators and computers. John Saxon believed that this shift in emphasis ". . . would leave the American student bereft of the detailed knowledge of the parts that permit comprehension of the whole."
If you use the books as John Saxon intended them to be used, you will join the multitude of other successful Saxon users who value his math books. I realize that every child is different. And while the above situations apply to about 99% of all students, there are always exceptions that justify the rule. If your particular situation does not fit neatly into the above descriptions, please feel free to email me at art.reed@thesaxonteacher.com or call me at (580) 234-0064 (CST). If you email me, please include your telephone number and I will call you at my expense.
March 2011
ARE THE NEW SAXON MATH BOOKS BETTER THAN THE OLD EDITIONS?
Some of you may remember that in the summer of 2004, the Saxon family sold Saxon Publishers to Harcourt Achieve. Just to put everything in perspective, Harcourt Achieve, Inc. was then owned by the Harcourt Corporation which in turn was later acquired by the multi-billion dollar conglomerate Reed-Elsevier who then sold Harcourt, Inc. to Houghton Mifflin creating the current company (that owns Saxon Publishers) which is now the Houghton-Mifflin Harcourt Company also known as HMHCO. It all reminds me of when the Savings and Loan Companies got the nickname "Velcro banks" because they changed names so often before they disappeared the way of the dinosaurs.
When I published my June 2007 news article, I told readers "Not to worry!" As I had said earlier when Harcourt acquired John Saxon's publishing company in 2004, the new sale should not affect the quality of John's books. I asked the obvious question, "Why would anyone buy someone's prize-winning 'Blue Ribbon Bull' to make hamburger with?" I did not believe that this new sale would change John's books much either, and I told the readers that if these changes became more than just cosmetics, I would certainly keep them informed.
Well, it is time to mention that some of the changes are no longer cosmetic. Some of the new editions are not what John Saxon had intended for his books. These new editions are vastly different, and both home school educators as well as classroom teachers must be aware of these changes and be selective about what editions and titles they should and should not use if they desire to continue with John Saxon's methods and standards.
Initially, these revised new editions were offered only to the public and private schools and not to the home school community. However, introduction of their new geometry textbook to the home school web site tells me that it may not be long before the new fourth editions of Algebra 1 and Algebra 2 replace the current third editions now offered on the website.
I could be wrong. Perhaps they added the geometry textbook to the home school website because some home school parents were unaware that a full year of high school geometry was already offered within the Algebra 2 textbook (first semester of geometry) and the first sixty lessons of the Advanced Mathematics textbook (second semester of geometry). Additionally, placing the geometry course in between the Saxon Algebra 1 and Saxon Algebra 2 textbooks is a sure formula for student frustration in Saxon Algebra 2 since the new geometry book does not contain algebra content. The only reference to "Geometry" in the new fourth edition of Saxon Algebra 1 is a reference in the index to "Geometric Sequences" found in lesson 105. That term is not related to geometry. It is the title given to an algebraic formula dealing with a sequence of numbers that have a common ratio between the consecutive terms.
It would be my hope that the senior executives at HMHCO would recognize the uniqueness and value of the current editions of John Saxon's math books that continue his methods and standards. However, to ensure you have the correct editions of John Saxon's math books, as he published them, you can go to my February 2010 news article where I list the correct editions to use from Math 54 through Calculus. The editions I referenced in that article will be good for many more decades.
February 2011
What are some of the main causes for student frustration or failure when using John Saxon's math books? (Part 2)
Last month we discussed the ESSENTIAL DO'S when using John Saxon's math books.
This month we will go over the ESSENTIAL DONT'S:
Don't Skip the First 30 – 35 Lessons in the Book. Many home school parents still believe that because the first thirty or so lessons in every Saxon math book appear to be a review of material in the last part of the previous textbook, they can skip them. Let's review the two elements of automaticity. The two critical elements are: repetition - over time!
Yes, some of the early problems in the textbook appear similar to the problems found in the last part of the previous textbook. They have, however, been changed from the previous textbook to ensure that the student has mastered the concept. Remember, part of the concept of mastery involves leaving the material for a period of time and then returning to it. Students are supposed to have sixty to ninety days off in the summer to rest their thought processes. They need this review to reinstate that thought process! Additionally, while the first lessons in the books do contain some review, they also contain new material as well.
I would add what I have asked thousands of home school parents these past nine years. "Must students always have to do something they do not know how to do? Why can't they do something they already know how to do? What is wrong with building or reinforcing their confidence in mathematics through review?"
Don't Skip Textbooks. Skipping a book in Saxon is like tearing out the middle pages of your piano sheet music and then attempting to play the entire piece while still providing a meaningful musical presentation. In my book, under the specific textbook descriptions, I discuss any legitimate textbook elimination based upon specific abilities of the individual students. However, these recommendations vary from student to student depending upon their background and ability.
Don't Skip Problems in the Daily Assignments. When students complain that the daily workload of thirty problems is too much, it is generally the result of one of the following conditions:
Students are so involved in a multitude of activities that they cannot spend the thirty minutes to an hour each day required for Saxon mathematics.
Students are at a level above their capabilities and unable to adequately process the required concepts in the allotted time because of this difficulty.
The student is either a dawdler or just lazy!
Doing just the odd or just the even numbered problems in a Saxon math book is not the solution to those difficulties. As I mention in one of the early chapters in my book, there are two of each type of problem for several reasons - and doing just the odd or even is not one of those reasons!
Don't Skip Lessons. Incremental Development literally means introducing complicated math concepts to the students in small increments, rather than having them tackle the entire concept all at once. It is essential that students do a lesson a day and take a test every four to five lessons, depending on what book they are using. So what happens when you skip an easy lesson or two?
Very simply, the student cannot process the new material satisfactorily without having had a chance to read about it, and to understand its characteristics. Some students attempt to fix this shortcoming by then working on several lessons in a single day, to catch up to where they should be in the book. This technique is also not recommended. As I have told my classroom students on numerous occasions, "The only way to eat an elephant is one bite at a time."
While my book goes into more detail, I believe these few simple rules about what TO DO and what NOT TO DO to ensure success when using John's math books will benefit home school educators who use, or are contemplating using, Saxon math books.
So long as you use the books and editions I referenced in my book, and later re-iterated in my February 2010 news article, you will find that Saxon math books remain the best math books on the market today - if used correctly! Those referenced books and editions will be good for your child's math education - from fourth grade through their senior year in high school - for several more decades – or longer!
January 2011
What are some of the main causes for student frustration or failure when using John Saxon's math books? (Part 1)
The unique incremental development process used in John Saxon's math textbooks,; coupled with the cumulative nature of the daily work make them excellent textbooks for use in either a classroom or home school environment. If the textbooks are not used correctly, however, they will eventually present problems for the students.
The uniqueness of John Saxon's method of incremental development, coupled with the cumulative nature of the daily work in every Saxon math textbook, requires specific rules be followed to ensure success – and ultimately mastery!
In the next several news articles, we will discuss the ESSENTIAL DO'S and DON'T'S when using John Saxon's math books.
This month we will discuss the ESSENTIAL DO'S.
Do Place the Student in the Correct Level Math Book. Probably the vast majority of families who dislike John Saxon's math books do so because the student is using a math book above his or her capability. Since all of John's math books were written at the appropriate reading level of the student (or a grade level below), the problem is not one of students not being able to read the material presented to them, but their not being able to comprehend the math concepts being presented to them. This frustration is then interpreted as being created by the book and not by incorrect placement of the student.
Do Always Use the Correct Edition. Using the wrong edition of a Saxon math book can quickly lead to insurmountable problems. For example, moving from the first or second edition of Math 76 to the second or third edition of Math 87, or the third edition of Algebra ½ would be like moving from Math 65 to Algebra ½ in the current editions. For more information on which editions of John's books are still valid, read the earlier published February 2010 Newsletter, or read pages 15 – 18 in my book.
Do Finish The Entire Book. Finishing the entire textbook is critical to success in the next level book. I know, parents and teachers often ask me, "Why finish the last twenty or so lessons when much of that same material is presented in the first thirty or so lessons of the next level textbook?" While the first twenty or so lessons of the next level Saxon book may appear to cover the same concepts as the last thirty or so lessons in the previous book, the new textbook presents the review concepts in different and more challenging ways. Additionally, there are new concepts mixed in with them. The review is used to enable a review of necessary concepts while building the student's confidence back up after a few months off during the summer. Then comes the argument from some home school educators, "But we do not take any break between books – we go year round, so the review is not necessary."
My only reply to that is "Why must students always do something they do not know how to do? Can't they sometimes just review to build their confidence by doing something they already know how to do? If they are continuing year round, and already know how to do some of the early concepts in the next textbook, then it won't take them long to do their daily assignment. I once had a public school superintendant ask me "Which is more important, mastery or completing the book?" To which I replied, "They are synonymous."
Do All of the Problems - Every Day. There is a reason the problems come in pairs, and it is not so the student can do just the odd or even problems. The two problems are different from each other to keep the student from memorizing the procedure, as opposed to mastering the concept. Students who cannot complete the thirty problems each day in about an hour are either dawdling, or are at a level of mathematics above their capabilities, based upon their previous math experiences.
Do Follow the Order of the Lessons. I am often asked by parents at workshops and in email "Why study both lessons seventeen and eighteen?After all, they both cover the same concept?"Why not just skip lesson eighteen and go straight to lesson nineteen?" Why do both lessons? Well, because the author took an extremely difficult math concept and separated it into two different lessons. This allowed the student to more readily comprehend the entire concept, a concept which will be presented again in a more challenging way later in lesson twenty-seven of that book!
Do Give All of the Scheduled Tests – On Time. In every test booklet, in front of the printed Test 1 is a schedule for the required tests. Not testing is not an option! I have often heard home school parents say, "He does so well on his daily work; why test him?" To which I reply, "The results of the daily work reflect memory – the results of the weekly tests reflect mastery!" The results of the last five tests in every book give an indication of whether or not the student is prepared for the next level math book. Scores of eighty or better on any test reflect minimal mastery achieved. Scores of eighty or better on the last five tests in the series tell you the student is prepared to advance to the next level.
In the February newsletter, we will discuss the ESSENTIAL DON'T'S when using John's books. |
MATHEMATICS: GCSE: Shape, Space, Statistics and Probability (164 pages) provides a detailed study of shapes, their properties and measurement, statistics and probability . The book contains a wealth... More > of worked examples and exercises accompanied by worked answers. The content material is appropriate for study from GCSE level (and upwards) in mathematics and statisticsLinear Algebra I is a book for university students of any university branch of science. You will find summaries of theory and exercises solved, of the following topics: Matrices, Resolution of Linear... More > Systems Equations, Vector Spaces, Linear Transformations, Diagonalization of endomorphism, and Bilinear and Quadratic Forms.
I have 20 years of experience teaching mathematics at the university level. And, as a teacher of Algebra, Calculus, Statistics, etc., of university students, and, as a result of the needs that I have seen in my students, I have written this book.
This book is characterized by being practical and didactic. It is also useful as a guide for the student.
I hope it will be useful to you, above all.< Less
Applied Discrete Structures, Part II - Algebraic Structures, is an introduction to groups, monoids, vector spaces, lattices, boolean algebras, rings and fields. It corresponds with the content of... More > Discrete Structures II at UMass Lowell, which is a required course for students in Computer Science. It presumes background contained in Part I - Fundamentals, which is the content of Discrete Structures I at UMass Lowell.
Applied Discrete Structures has been approved by the American Institute of Mathematics as part of their Open Textbook Initiative. For more information on open textbooks, visit Less
This collection of my digital artwork from 2004 to 2007 includes digital collage, algorithmic art and vector art, and combinations of all three. Many of these images are 'found art' made... More > by composing and selecting from large 'image spaces'. My work ranges from abstract to representational, and even some almost straightforward photographic work in my Flower Portraits. Each pair of facing pages includes a complete image on the right, and a full scale detail from that image on the left. In this way I try to show large, detailed images in the small pages of this book. The book is 'perfect bound' (traditional paperback) for easier thumbing through pages.< Less |
According to OER Commons, 'These are the lecture notes of a one-semester undergraduate course which we taught at SUNY...
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According to OER Commons, 'TheseThis is a free, online textbook for an introductory course in complex analysis. General topics include Complex Numbers,...
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This is a free, online textbook for an introductory course in complex analysis. General topics include Complex Numbers, Complex Functions, Elementary Functions, Integration, Cauchy's Theorem, More Integration, Harmonic Functions, Series, Taylor and Laurent Series, Poles, Residues, and All That, and Argument Principle. Each chapter from the book can be downloaded as a free pdf file.
This is a free, online textbook offered by Bookboon.com. Topics include: 1. Some simple theoretical results concerning...
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This is a free, online textbook offered by Bookboon.com. Topics include: 1. Some simple theoretical results concerning power series, 2. Simple Fourier series in the Theory of Complex Functions, 3. Power series, 4. Analytic functions described as power series, 5. Linear differential equations and the power series method, 6. The classical differential equations, 7. Some more difficult differential equations, 8. Zeros of analytic functions, 9. Fourier series, and 10. The maximum principle.
This is a free, online textbook offered by Bookboon.com. "This is the fifth textbook you can download for free containing...
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This is a free, online textbook offered by Bookboon.com. "This is the fifth textbook you can download for free containing examples from the Theory of Complex Functions. In this volume we shall consider the Laurent series and their relationship to the general theory, and finally the technique of solving linear differential equations with polynomial coefficients by means of Laurent series.״
"This is a text for a two-term course in introductory real analysis for junior or senior mathematicsmajors and science...
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"This is a text for a two-term course in introductory real analysis for junior or senior mathematicsmajors and science students with a serious interest in mathematics. Prospectiveeducators or mathematically gifted high school students can also benefit from the mathematicalmaturity that can be gained from an introductory real analysis course.The book is designed to fill the gaps left in the development of calculus as it is usuallypresented in an elementary course, and to provide the background required for insight intomore advanced courses in pure and applied mathematics. The standard elementary calculussequence is the only specific prerequisite for Chapters 1–5, which deal with real-valuedfunctions. (However, other analysis oriented courses, such as elementary differential equation,also provide useful preparatory experience.) Chapters 6 and 7 require a workingknowledge of determinants, matrices and linear transformations, typically available from afirst course in linear algebra. Chapter 8 is accessible after completion of Chapters 1–5."
This is a free, online textbook. According to the author, "This text carefully leads the student through the basic topics of...
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This is a free, online textbook. According to the author, "This text carefully leads the student through the basic topics of Real Analysis. Topics include metric spaces, open and closed sets, convergent sequences, function limits and continuity, compact sets, sequences and series of functions, power series, differentiation and integration, Taylor's theorem, total variation, rectifiable arcs, and sufficient conditions of integrability. Well over 500 exercises (many with extensive hints) assist students through the material. For students who need a review of basic mathematical concepts before beginning "epsilon-delta״-style proofs, the text begins with material on set theory (sets, quantifiers, relations and mappings, countable sets), the real numbers (axioms, natural numbers, induction, consequences of the completeness axiom), and Euclidean and vector spaces; this material is condensed from the author's Basic Concepts of Mathematics, the complete version of which can be used as supplementary background material for the present text.״ |
Syllabus:We
will cover the book sequentially through about the midpoint of
Chapter 5, and finish with Chapter 7.
The central purpose of this course is to introduce you to
careful
use of language in the context of mathematical reasoning and
proof. The course is meant to make you think about
mathematics in
a completely new way, in a more mature way. It
should set
you on the path to becoming a mathematical producer rather than
mathematical consumer.
As part of this venture, we will discuss the basic principles
of
logic and various proof techniques, applying them in the context
of the
essential building blocks of mathematical structures: sets,
relations
(including orderings and equivalence relations), functions,
etc.
While the class will introduce you to some new mathematics, the
emphasis of the course is on process rather than content.
I
rarely lecture; you and your fellow students will prove
virtually all
the theorems yourselves and present them to each other in a
seminar
setting. Thus I hope that the most important lines of
communication will be between students rather than instructor to
student as is the case in many classes.
Class work:
Foundations is very likely somewhat different from other math
courses
you have had. Because the purpose of the class is to
change the
way that you think and reason about mathematics, it is essential
that
you become immersed in the work of the course. It is not
enough
to respond to what an instructor does or tells you. You
and your
fellow students are the ones that make things happen in
class.
Without your active participation, nothing will happen.
Perhaps
more than in any class you take, you will get benefit out of the
course
in direct proportion to how much effort you put in. Thus
class
work is the most substantial portion of the grade. It has
several
components: written assignments, class presentations and class
participation generally. (This last includes contributing
to
class discussions, asking good questions, and active
participation when
another student is presenting work at the board.) And, I should
add,
attendance. If you don't attend you can't
participate. You
are expected to be in class; if you aren't your grade will be
adversely
affected.
Written Assignments:
Since
Foundations is primarily a language course, you will be expected
to
learn clearly and precisely to express mathematical ideas in
writing.
Several times during the semester you will be asked to write up
and
turn in the proof of some theorem. Each proof will be
assigned
two grades---one grade for content and one grade for form.
The
content grade will reflect the extent to which the appropriate
ideas
are expressed in your write-up. That is, whether you
understood
the mathematical ideas required for the proof. The grade
for form
will take into consideration clarity of expression,
completeness,
proper usage of both English and mathematical grammar, and
whether you
really said what you meant to say.
Of course, form and content cannot be entirely divorced.
If
your writing is sufficiently muddled that the reader cannot tell
what
you meant to say, both grades will suffer. Likewise, if
you
really don't understand what it is you are trying to say, the
writing
will be fuzzy and unclear. However, it is not impossible
to
distinguish the factors; the grades will be separated so you can
see
where improvement is needed.
When you write up an assignment, you are expected to include
sufficiently many details to enlighten someone who does not
already
know what you are trying to say. This may require that you
restate a definition or previous theorem and say how it is used
in your
proof. Do not be afraid to include too many details.
If you
are in doubt about whether or not to say something that you feel
is
pertinent, always do so!
Class Presentations: I have
said
that most of the class will consist of students presenting work
to each
other. You will be expected to do your share in
this. Most
of the time I rely on volunteers to make presentations.
This
makes it possible for students to present the work about which
they
feel most confident. But the fact that so much of the
grade
depends on this participation means that all students must
volunteer on
something like a regular basis. Don't assume that because
others
volunteer, you (or your grade) are off the hook. The good
news is
that you probably won't end up having to get every problem
assigned
during the semester. If you don't get it, someone else
will, and
you will get to see the fruits of their labors.
The person who is presenting his or her work at the board is
not the
only person with responsibilities in a presentation. The
students
sitting at their desks have as central a role to play.
Students
presenting their work are not meant to replace a seasoned
polished
lecture that would be given by an experienced instructor. Nor
should
they be made to. They are counting on their fellow students to
help
them by making clarifying suggestions and asking
questions. I
will feel free to ask questions of persons who are sitting down.
In-class exams: The purpose of
these
exams will be to encourage everyone to gain a command of the
basic
mathematical facts that are discussed in class. The
questions
will be straightforward for anyone who has been digesting the
material
along the way. Typical questions will ask you to define
important
terms, answer true/false and short answer questions on the basic
material and perhaps state an important theorem or two.
You may
be asked to give a simple proof of a fact that has already been
presented and discussed in the class.
Takehome examinations: Both
midterm
examinations and a portion of the final examination will be
take-home
exams. You will be required to construct proofs for
theorems that
you have not seen before. You are on your honor not to
discuss
take-home exams with anyone but me until all exams have been
turned
in. You may not consult any books except the textbook, but
you
are free to use any class notes, any previously proved theorems,
and
anything that is distributed in class. All guidelines for
written
assignments also apply to take-home exams.
Academic Honesty: You are encouraged to work with other
students on everything except exams. (It has been my experience
that
most students who thrive in this course are part of a small
group of
2-4 students who work together regularly outside of class.
I
think this also makes the class more fun.) It is, however,
understood that all written work that you turn in must finally
be your
own expression. For further information see the student
handbook
or consult with me.
Disabilities: If you have a physical,
psychological, or learning disability that may impact your
ability to
carry out assigned course work, feel free to discuss your
concerns in
private with me, but you should also consult the Office of
Disability
Services at 5453. The Coordinator of Disability Services, Erin
Salva
(salvae@kenyon.edu), will review your concerns and determine,
with you,
what accommodations are appropriate. (All information and
documentation
of disability is confidential.) It is Ms. Salva that has the
authority
and the expertise to decide on the accommodations that are
proper for
your disability. Though I am happy to help you in any way I can,
I
cannot make any special accommodations without proper
authorization
from Ms. Salva. |
books.google.com - ".... Mathematics from an Advanced Standpoint
". His three-part treatment begins with topics associated with arithmetic, including calculating with natural numbers, the first extension of the notion of number, special properties of integers, and complex numbers. Algebra-related subjects constitute the second part, which examines real equations with real unknowns and equations in the field of complex quantities. The final part explores elements of analysis, with discussions of logarithmic and exponential functions, the goniometric functions, and infinitesimal calculus. 1932 ed. 125 figures.
Very good book, advanced explanations for many things either taken for granted or new perspectives to look at things. Interesting things like impossibility to inscribe heptagon using compass and ...Read full review |
a three-level mathematics series covering the lower secondary grades and designed for children in English-medium schools, for whom English is not the first language. |
Galois Theory (Universitext)
Book summary
A clear, efficient exposition of this topic with complete proofs and exercises, covering cubic and quartic formulas; fundamental theory of Galois theory; insolvability of the quintic; Galoiss Great Theorem; and computation of Galois groups of cubics and quartics. Suitable for first-year graduate students, either as a text for a course or for study outside the classroom, this new edition has been completely rewritten in an attempt to make proofs clearer by providing more details. It now begins with a short section on symmetry groups of polygons in the plane, for there is an analogy between polygons and their symmetry groups and polynomials and their Galois groups - an analogy which serves to help readers organise the various field theoretic definitions and constructions. The text is rounded off by appendices on group theory, ruler-compass constructions, and the early history of Galois Theory. The exposition has been redesigned so that the discussion of solvability by radicals now appears later and several new theorems not found in the first edition are included. [via] |
A Graphical Approach to has evolved to address the needs of today ' s student.& While maintaining its unique table& of contents and functions-based approach, the text now includes additional components to build skill, address critical thinking, solve applications, and apply technology to support traditional algebraic solutions. & It continues to incorporate an open design, helpful features, careful explanations of topics, and a comprehensive package of supplements and study aids to provide new and relevant opportunities for learning and teaching.
Polynomial Equations and Inequalities; Further Applications and Models
p. 251
Polynomial Equations and Inequalities
Complex nth Roots
Applications and Polynomial Models
Reviewing Basic Concepts (Sections 3.6-3.8)
p. 259
Chapter 3 Summary
p. 260
Chapter 3 Review Exercises
p. 263
Chapter 3 Test
p. 267
Chapter 3 Project: Creating a Social Security Polynomial
p. 268
Rational, Power, and Root Functions
p. 270
Rational Functions and Graphs
p. 271
The Reciprocal Function
The Rational Function Defined by f(x) = 1 / x[superscript 2]
More on Graphs of Rational Functions
p. 277
Vertical and Horizontal Asymptotes
Graphing Techniques
Oblique Asymptotes
Graphs with Points of Discontinuity
Rational Equations, Inequalities, Applications, and Models
p. 291
Solving Rational Equations and Inequalities
Applications and Models of Rational Functions
Inverse Variation
Combined and Joint Variation
Reviewing Basic Concepts (Sections 4.1-4.3)
p. 305
Functions Defined by Powers and Roots
p. 306
Power and Root Functions
Modeling Using Power Functions
Graphs of f(x) = [characters not reproducible]
Graphing Circles and Horizontal Parabolas Using Root Functions
Equations, Inequalities, and Applications Involving Root Functions
p. 318
Equations and Inequalities
An Application of Root Functions
Reviewing Basic Concepts (Sections 4.4 and 4.5)
p. 328
Chapter 4 Summary
p. 329
Chapter 4 Review Exercises
p. 331
Chapter 4 Test
p. 335
Chapter 4 Project: How Rugged Is Your Coastline?
p. 336
Inverse, Exponential, and Logarithmic Functions
p. 338
Inverse Functions
p. 339
Inverse Operations
One-to-One Functions
Inverse Functions and Their Graphs
Equations of Inverse Functions
An Application of Inverse Functions
Exponential Functions
p. 350
Real-Number Exponents
Graphs of Exponential Functions
Exponential Equations (Type 1)
Compound Interest
The Number e and Continuous Compounding
An Application of Exponential Functions
Logarithms and Their Properties
p. 363
Definition of Logarithm
Common Logarithms
Natural Logarithms
Properties of Logarithms
Change-of-Base Rule
Reviewing Basic Concepts (Sections 5.1-5.3)
p. 373
Logarithmic Functions
p. 374
Graphs of Logarithmic Functions
Applying Earlier Work to Logarithmic Functions
A Logarithmic Model
Exponential and Logarithmic Equations and Inequalities
p. 384
Exponential Equations and Inequalities (Type 2)
Logarithmic Equations and Inequalities
Equations and Inequalities Involving Both Exponentials and Logarithms
Formulas Involving Exponentials and Logarithms
Reviewing Basic Concepts (Sections 5.4 and 5.5)
p. 393
Further Applications and Modeling with Exponential and Logarithmic Functions
p. 394
Physical Science Applications
Financial Applications
Biological and Medical Applications
Modeling Data with Exponential and Logarithmic Functions
Chapter 5 Summary
p. 408
Chapter 5 Review Exercises
p. 411
Chapter 5 Test
p. 414
Chapter 5 Project: Modeling Motor Vehicle Sales in the United States (with a lesson about the careless use of mathematical models)
p. 415
Analytic Geometry
p. 417
Circles and Parabolas
p. 418
Conic Sections
Equations and Graphs of Circles
Equations and Graphs of Parabolas
Translations of Parabolas
An Application of Parabolas
Ellipses and Hyperbolas
p. 432
Equations and Graphs of Ellipses
Translations of Ellipses
An Application of Ellipses
Equations and Graphs of Hyperbolas
Translations of Hyperbolas
Reviewing Basic Concepts (Sections 6.1 and 6.2)
p. 445
Summary of the Conic Sections
p. 445
Characteristics
Identifying Conic Sections
Eccentricity
Parametric Equations
p. 454
Graphs of Parametric Equations and Their Rectangular Equivalents
Alternative Forms of Parametric Equations
An Application of Parametric Equations
Reviewing Basic Concepts (Sections 6.3 and 6.4)
p. 458
Chapter 6 Summary
p. 459
Chapter 6 Review Exercises
p. 461
Chapter 6 Test
p. 463
Chapter 6 Project: Modeling the Path of a Bouncing Ball
p. 464
Systems of Equations and Inequalities; Matrices
p. 466
Systems of Equations
p. 467
Linear Systems
Substitution Method
Elimination Method
Special Systems
Nonlinear Systems
Applications of Systems
Solution of Linear Systems in Three Variables
p. 480
Geometric Considerations
Analyttic Solution of Systems in Three Variables
Applications of Systems
Curve Fitting Using a System
Solution of Linear Systems by Row Transformations
p. 488
Matrix Row Transformations
Row Echelon Method
Reduced Row Echelon Method
Special Cases
An Application of Matrices
Reviewing Basic Concepts (Sections 7.1-7.3)
p. 499
Matrix Properties and Operations
p. 500
Terminology of Matrices
Operations on Matrices
Applying Matrix Algebra
Determinants and Cramer's Rule
p. 513
Determinants of 2 x 2 Matrices
Determinants of Larger Matrices
Derivation of Cramer's Rule
Using Cramer's Rule to Solve Systems
Solution of Linear Systems by Matrix Inverses
p. 524
Identity Matrices
Multiplicative Inverses of Square Matrices
Using Determinants to Find Inverses
Solving Linear Systems Using Inverse Matrices
Curve Fitting Using a System
Reviewing Basic Concepts (Sections 7.4-7.6)
p. 536
Systems of Inequalities and Linear Programming
p. 537
Solving Linear Inequalities
Solving Systems of Inequalities
Linear Programming
Partial Fractions
p. 547
Decomposition of Rational Expressions
Distinct Linear Factors
Repeated Linear Factors
Distinct Linear and Quadratic Factors
Repeated Quadratic Factors
Reviewing Basic Concepts (Sections 7.7 and 7.8)
p. 554
Chapter 7 Summary
p. 554
Chapter 7 Review Exercises
p. 557
Chapter 7 Test
p. 561
Chapter 7 Project: Finding a Polynomial Whose Graph Passes through Any Number of Given Points
p. 562
Trigonometric Functions and Applications
p. 565
Angles and Their Measures
p. 566
Basic Terminology
Degree Measure
Standard Position and Coterminal Angles
Radian Measure
Arc Lengths and Areas of Sectors
Angular and Linear Speed
Trigonometric Functions and Fundamental Identities
p. 582
Trigonometric Functions
Quadrantal Angles
Reciprocal Identities
Signs and Ranges of Function Values
Pythagorean Identities
Quotient Identities
An Application of Trigonometric Functions
Reviewing Basic Concepts (Sections 8.1 and 8.2)
p. 595
Evaluating Trigonometric Functions
p. 596
Definitions of the Trigonometric Functions
Trigonometric Function Values of Special Angles
Cofunction Identities
Reference Angles
Special Angles as Reference Angles
Finding Function Values with a Calculator
Finding Angle Measures
Applications of Right Triangles
p. 608
Significant Digits
Solving Triangles
Angles of Elevation or Depression
Bearing
Further Applications of Trigonometric Functions
Reviewing Basic Concepts (Sections 8.3 and 8.4)
p. 620
The Circular Functions
p. 620
Circular Functions
Applications of Circular Functions
Graphs of the Sine and Cosine Functions
p. 629
Periodic Functions
Graph of the Sine Function
Graph of the Cosine Function
Graphing Techniques, Amplitude, and Period
Translations
Determining a Trigonometric Model Using Curve Fitting
Reviewing Basic Concepts (Sections 8.5 and 8.6)
p. 646
Graphs of the Other Circular Functions
p. 646
Graphs of the Cosecant and Secant Functions
Graphs of the Tangent and Cotangent Functions
Addition of Ordinates
Harmonic Motion
p. 657
Simple Harmonic Motion
Damped Oscillatory Motion
Reviewing Basic Concepts (Sections 8.7 and 8.8)
p. 660
Chapter 8 Summary
p. 661
Chapter 8 Review Exercises
p. 665
Chapter 8 Test
p. 670
Chapter 8 Project: Modeling Sunset Times
p. 671
Trigonometric Identities and Equations
p. 672
Trigonometric Identities
p. 673
Fundamental Identities
Using the Fundamental Identities
Verifying Identities
Sum and Difference Identities
p. 683
Cosine Sum and Difference Identities
Sine and Tangent Sum and Difference Identities
Reviewing Basic Concepts (Sections 9.1 and 9.2)
p. 692
Further Identities
p. 692
Double-Number Identities
Product-to-Sum and Sum-to-Product Identities
Half-Number Identities
The Inverse Circular Functions
p. 704
Review of Inverse Functions
Inverse Sine Function
Inverse Cosine Function
Inverse Tangent Function
Remaining Inverse Trigonometric Functions
Inverse Function Values
Reviewing Basic Concepts (Sections 9.3 and 9.4)
p. 717
Trigonometric Equations and Inequalities (I)
p. 717
Equations Solvable by Linear Methods
Equations Solvable by Factoring
Equations Solvable by the Quadratic Formula
Using Trigonometric Identities to Solve Equations
Trigonometric Equations and Inequalities (II)
p. 724
Equations and Inequalities Involving Multiple-Number Identities
Equations and Inequalities Involving Half-Number Identities
An Application of Trigonometric Equations
Reviewing Basic Concepts (Sections 9.5 and 9.6)
p. 730
Chapter 9 Summary
p. 731
Chapter 9 Review Exercises
p. 733
Chapter 9 Test
p. 736
Chapter 9 Project: Modeling a Damped Pendulum
p. 737
Applications of Trigonometry; Vectors
p. 739
The Law of Sines
p. 740
Congruency and Oblique Triangles
Derivation of the Law of Sines
Applications of Triangles
Ambiguous Case
The Law of Cosines and Area Formulas
p. 754
Derivation of the Law of Cosines
Applications of Triangles
Area Formulas
Vectors and Their Applications
p. 764
Basic Terminology
Algebraic Interpretation of Vectors
Operations with Vectors
Dot Product and the Angle between Vectors
Applications of Vectors
Reviewing Basic Concepts (Sections 10.1-10.3)
p. 777
Trigonometric (Polar) Form of Complex Numbers
p. 778
The Complex Plane and Vector Representation
Trigonometric (Polar) Form
Products of Complex Numbers in Trigonometric Form
Quotients of Complex Numbers in Trigonometric Form
Powers and Roots of Complex Numbers
p. 787
Powers of Complex Numbers (De Moivre's Theorem)
Roots of Complex Numbers
Reviewing Basic Concepts (Sections 10.4 and 10.5)
p. 793
Polar Equations and Graphs
p. 793
Polar Coordinate System
Graphs of Polar Equations
Classifying Polar Equations
Converting Equations
More Parametric Equations
p. 804
Parametric Equations with Trigonometric Functions
The Cycloid
Applications of Parametric Equations
Reviewing Basic Concepts (Sections 10.6 and 10.7)
p. 811
Chapter 10 Summary
p. 811
Chapter 10 Review Exercises
p. 814
Chapter 10 Test
p. 817
Chapter 10 Project: When Is a Circle Really a Polygon?
p. 818
Further Topics in Algebra
p. 820
Sequences and Series
p. 821
Sequences
Series and Summation Notation
Summation Properties
Arithmetic Sequences and Series
p. 831
Arithmetic Sequences
Arithmetic Series
Geometric Sequences and Series
p. 839
Geometric Sequences
Geometric Series
Infinite Geometric Series
Annuities
Reviewing Basic Concepts (Sections 11.1-11.3)
p. 849
The Binomial Theorem
p. 850
A Binomial Expansion Pattern
Pascal's Triangle
n-Factorial
Binomial Coefficients
The Binomial Theorem
rth Term of a Binomial Expansion
Mathematical Induction
p. 857
Proof by Mathematical Induction
Proving Statements
Generalized Principle of Mathematical Induction
Proof of the Binomial Theorem
Reviewing Basic Concepts (Sections 11.4 and 11.5)
p. 863
Counting Theory
p. 863
Fundamental Principle of Counting
Permutations
Combinations
Distinguishing between Permutations and Combinations
Probability
p. 872
Basic Concepts
Complements and Venn Diagrams
Odds
Union of Two Events
Binomial Probability
Reviewing Basic Concepts (Sections 11.6 and 11.7)
p. 881
Chapter 11 Summary
p. 882
Chapter 11 Review Exercises
p. 886
Chapter 11 Test
p. 888
Chapter 11 Project: Using Experimental Probabilities to Simulate Family Makeup
p. 889
Reference: Basic Algebraic Concepts
p. 892
Review of Exponents and Polynomials
p. 893
Rules for Exponents
Terminology for Polynomials
Adding and Subtracting Polynomials
Multiplying Polynomials
Review of Factoring
p. 899
Factoring Out the Greatest Common Factor
Factoring by Grouping
Factoring Trinomials
Factoring Special Products
Factoring by Substitution
Review of Rational Expressions
p. 906
Domain of a Rational Expression
Lowest Terms of a Rational Expression
Multipling and Dividing Rational Expressions
Adding and Subtracting Rational Expressions
Complex Fractions
Review of Negative and Rational Exponents
p. 914
Negative Exponents and the Quotient Rule
Rational Exponents
Review of Radicals
p. 920
Radical Notation
Rules for Radicals
Simplifying Radicals
Operations with Radicals
Rationalizing Denominators
Chapter R Test
p. 928
Geometry Formulas
p. 929
Deciding Which Model Best Fits a Set of Data
p. 931
Vectors in Space
p. 936
Polar Form of Conic Sections
p. 942
Rotation of Axes
p. 946
Answers to Selected Exercises
p. 1
Index of Applications
p. 1
Index
p. 5
Table of Contents provided by Ingram. All Rights Reserved.
John Hornsby- When John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics, education, or journalism. His ultimate decision was to become a teacher, but after twenty-five years of teaching at the high school and university levels and fifteen years of writing mathematics textbooks, all three of his goals have been realized; his love for teaching and for mathematics is evident in his passion for working with students and fellow teachers as well. His specific professional interests are recreational mathematics, mathematics history, and incorporating graphing calculators into the curriculum.
JohnMarge Lial has always been interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, is now affiliated with American River College.
Marge is an avid reader and traveler. Her travel experiences often find their way into her books as applications, exercise sets, and feature sets. She is particularly interested in archeology. Trips to various digs and ruin sites have produced some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan.
Gary Rockswold- Dr. Gary Rockswold has been teaching mathematics for 33 years at all levels from seventh grade to graduate school, including junior high and high school students, talented youth, vocational, undergraduate, and graduate students, and adult education classes. He is currently employed at Minnesota State University, Mankato, where he is a full professor of mathematics. He graduated with majors in mathematics and physics from St.OlafCollege mathematics, he enjoys spending time with his lovely wife and two children. |
Wednesday, September 25, 2013
Algebra is like a terrible disease - I want to stay as far away from it as possible. If I hadn't decided to become a homeschool mom, I'd truly be one of those people who could say, "See, I told you I'd never have to use Algebra in real life!"
Anyway, I've experienced a little deja vu as I've watched my oldest struggle in math a little ever since he started algebra. He definitely doesn't struggle as much as I did, but I know he's not completely mastering it. I usually don't like to divert from our math curriculum, however, I asked my son if he'd like to try something new when VideoText Interactive offered Schoolhouse Review Crew members the opportunity to review two of their online courses, Algebra: A Complete Course or Geometry: A Complete Course.
My son said he did want to try something new, so here we are reviewing Algebra: A Complete Course.It's a complete course becausewhen your child finishes the program, he can claim credits for Pre-Algebra, Algebra 1, and Algebra 2. Even though my son is in 9th grade, has already taken Pre-Algebra, and is actually almost finished with Algebra I, he is starting at he beginning of this program. While tempting to try and jump ahead, we both feel that it wouldn't be wise.
The method of teaching in this course is not the method traditionally taught in school. In this course, your child will start at the beginning of Algebra and finish at the end of Algebra. There won't be any gaps in between what is commonly referred to as Algebra 1 and Algebra 2, so there won't be any need for lots of review and overlapping. This program teaches Algebra analytically, and its goal is MASTERY! Click to watch a video explaining what makes this program unique.
The complete online course includes:
176 Video Lessons - Each lesson takes about 5-10 minutes.
360 pages of Course Notes - These notes repeat what was shown in the video lesson allowing your child to review the development of a concept.
590 pages of Student Work Text - Examples and exercises are provided here for review of what was taught in each lesson.
Solutions Manuals - These give step-by-step answers to all problems in Student Work Text.
Progress Tests - These tests are given at the end of one or more lessons to determine understanding of concepts.
While Algebra is not my thing and reading all of the resources for instructors just about gave me a full-on headache, I will say that once you get started on the lessons this course is extremely user-friendly. You and your child will have separate log in information. Your child can access the videos, course notes, student work text, and solutions to the work text. You will have access to all of that plus tests and solutions to tests. It is also important that you look at all of the resources which are provided for the instructor before your child begins the course. These resources include: Program Overview, Scope and Sequence Rationale, Course Schematic, Quick Reference Guide, Progress Checklists, Course Outline, Student Reference Tables, and Graph Paper Templates.
*To see a detailed program overview and a few of the resources mentioned above, please visit the website. There is no way I can completely and effectively describe the details of the program, what is taught, and how it is taught because, frankly, I don't understand all of it myself.
What I do understand is how to use the program, so that is what I am going to show you! It really is easy. First, I log in. After that, I click on Algebra: A Complete Course shown below.
As you can see, this Algebra course is divided into 10 different units. Once you've finished reading through all of the resources for instructors, your child will begin with Unit I - The Structure of Mathematics.
Each unit is broken down further into parts and lessons. This screen shot is from my page so it's showing quizzes and solutions (instructors guide). Your child will be able to click on Part A - Lesson 1 - Mathematical Parts of Speech to begin the course.
Once your child clicks on the lesson, he will watch the video for that lesson. It is recommended that you, the teacher, watch the videos with your child for at least the first few lessons. After the presentation, your child can print off the Course Notes to review concepts taught. It is NOT recommended that your child follow along with the notes or take notes while he watches the videos so that he can be completely focused on what is being taught. Next, he can print the Student Work Text and work through the problems. Finally, you can use the Solutions Manual to check answers, but then you should let your child find and correct his own mistakes which will help him to establish his own error analysis skills.
My son's first lesson when like this:
Watched video
Printed Course Notes
Printed worksheet and completed 20 problems
Checked work
Took a quiz the next day
I watched the first several lessons with my son and found that the lessons are clearly presented by an instructor and include computer generated visual aids. Examples are given on the screen while the instructor continues to teach. Videos seem to follow the same format for each lesson: Title, Objective, and Video Presentation.
After each lesson, my son prints the Course Notes and worksheets. He works through all of the problems and grades his own work. He waits until the next day to take the quiz. I print off the quiz he needs, and I grade the quiz.
A note about quizzes: there are two versions of each quiz, and they can be used several different ways. Form A could be used as extra practice while Form B could be the graded quiz, or Form A could be used as a graded quiz. Form B could be used as a retest if your child didn't score well on Form A. We choose to do the latter of the two. I've made my son take the second quiz a couple of times just to make sure he'd mastered the concept. He's never failed a quiz, but even if he misses a couple of problems, I usually make him take the second quiz. Sometimes more than one lesson is covered before there is a quiz.
Unit tests are treated the same way. There are two versions, and they can be used in the same manner as the quizzes.
We are currently following the Two-Year Plan for this Algebra course. So, that means my son is basically doing a lesson every other day. Hopefully, by the beginning of his junior year in high school he will be ready to start Geometry!
My son says he wants to continue using VideoText Interactive for Algebra. He likes the simplicity of the lessons, and so far he is doing well. It's kind of hard to tell, though, since most of what he is learning right now is familiar to him. I am hoping as he delves deeper into more difficult Algebra concepts, it will finally click!
If your child is ready for Pre-Algebra, then you might want to consider starting out on the right track with this not-traditional Algebra program. I don't think I can give a specific age range for this course since children will be ready at different ages. For instance, my middle son who is in sixth grade started Pre-Algebra this year, but my oldest son didn't begin Pre-Algebra until he was in seventh grade. You can watch the short video below to help you determine if your child is ready for this course.
Algebra: A Complete Course (the online version) can be purchased on the website for $299. This price includes licensing for 2 students, and remember, the course includes Pre-Algebra, Algebra 1, and Algebra 2. An additional student in your family can be added for $49. The license expires three years from the activation date. In the event that you are not satisfied, the online program offers a 30-day money back guarantee.
2 comments:
Good luck in your teaching. :) I am a homeschooler too, but I participate in a public school program for homescoolers. I teach my first and fifth grader. They all go to school twice a week. The school provides the curriculum. They have also taken over all the schooling for my middle school child. That is good because I would struggle to teach the math. The only bad part is you are provided secular materials. If you want Christian material you have to pay for it. Oh and my middle school daughter goes twice a week and does online learning. It's not a program of choice for everyone though. Wish you all the best in your efforts.
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About Me
Brandi is the wife of the one and only Ragamuffinwriter and home school mom to three precious children. She lived in Memphis, TN for 21 years, but now resides in the hot, dry Arizona desert.
Autumnfawn Lane is a place for her to store her thoughts, archive her family's life, share her faith, reminisce days gone by, compile yummy recipes, review amazing products, and write about all things homeschool. |
Mathematics
MATHEMATICS PHILOSOPHY
The MacDuffie mathematics curriculum is a program in which students can develop an understanding of the meaning of mathematical concepts and gain proficiency with the mechanics of mathematics. The curriculum provides experiences designed to help students move along the continuum from concrete to abstract mathematical representations. These experiences include continued development of arithmetic, algebra, geometry, and advanced concepts with a further goal of training students in the "language" of mathematics, thus preparing them for future work in math and science. MacDuffie's math program treats problem-solving as an ongoing process, designed to help students bridge the gap between the theory of mathematics and its applications in the real world. Problems are presented in a manner which requires students to use their knowledge and understanding to resolve new situations. The introduction of historical references is designed to show students that mathematics is a human endeavor and to lead them towards a greater appreciation of the power of pure mathematical thinking. All math classes at MacDuffie encourage independent thinking and the willingness to take academic risks.
Although the school encourages students to study mathematics during all of their UpperSchoolyears, all candidates for graduation from MacDuffie must take at least three math courses in grades 9 – 12. The three courses must include the equivalent of Algebra I, Geometry, and Algebra II. If the required distributional courses are completed before a student has taken three courses in grades 9 – 12, he or she must continue to advanced math courses. Honors courses are offered as options for Algebra I, Algebra II, Geometry and Pre-calculus to provide capable students with opportunities for more in-depth work at each level. Those students who are ready to take a college-level calculus course may take AP Calculus. Students must have a year grade of at least C- to advance to the next level of mathematics. Students enrolled in Algebra I Honors and in other math courses from Algebra II on, are required to have a TI-83 or TI-84 graphing calculator.
Note on math placement: Students entering MacDuffie are tested for math proficiency. Math placement is based on the test results and previous math achievement.
MIDDLE SCHOOL
1300 – Math 6
Grade 6
This course is designed to promote an understanding of the decimal numeration system along with mastery of the basic operations with whole numbers, fractions and decimals. The course also introduces integers, percents and statistical analysis. The use of variables combined with the creation and solution of simple equations sets the foundation for abstract thinking. Various problem-solving techniques are introduced and utilized in all aspects of the course.
1302 – Math 7
Grade 7
This course is designed so that students can gain mastery of the basic operations of integers and rational numbers. More emphasis is placed on abstract thinking. The students learn to create and solve two-step equations and inequalities along with how to represent linear functions graphically on a coordinate system. Percents are presented through ratios and proportions as well as equations. In addition to basic problems, various applications of percents are studied. Students continue to do statistical analysis. Geometry skills include measurement and the development and use of formulas for calculating perimeter, circumference, area and volume. Problem-solving techniques continue to be developed and reinforced.
1312 – Algebra 1
Grades 8 – 10
This course analyzes the basic arithmetic concepts in an abstract way. The content includes integers and rational numbers, solving equations, operations with polynomials, graphing, systems of equations, ratios and proportions, factoring, quadratic equations, rational expressions, and radicals. The course introduces the students to the language of mathematics and teaches them how to translate from words to symbols. Continued emphasis is given to problem-solving and critical thinking. This course is normally followed by Geometry.
1314 – Algebra 1 (Honors)
Grades 7 – 8
Department Approval Only
This is an Algebra 1 course designed for Middle School students who have solid arithmetic skills and whose pre-algebra introduction included manipulation of integers as well as positive and negative rational numbers. The content covers traditional first-year algebra material in greater depth. It also introduces students to topics from an
Algebra II curriculum. Emphasis is on developing analytical skills through the use of problem-solving, proof and mathematical readings.
UPPER SCHOOL
1330 -Geometry
Grades 9 – 11
Geometry allows students to analyze their physical world mathematically as they are introduced to the language and symbolism pertaining to the subject. The content includes parallel and perpendicular lines, polygons, congruent triangles, ratios and proportions, Pythagorean Theorem, circles and arcs, as well as perimeters, areas and volumes. The mastery of these geometric concepts provides an excellent opportunity for utilizing algebraic skills. This course is normally followed by Algebra II.
1332 – Geometry (Honors)
Grades 8 – 11
Department Approval Only
The content for the honors level Geometry is similar to that of regular geometry but goes more in-depth and has a greater emphasis on the theoretical. Students learn to use inductive and deductive reasoning to develop logical chains of thought and to construct paragraph and two-column proofs. This course is normally followed by Algebra II with Trigonometry (Honors Level).
1316 – Algebra II
Grades 10 – 12
This course includes a study of the real number system and its properties, the complex number system, linear equations and inequalities, relations and functions, polynomials, rational expressions, and quadratic functions. Students are also introduced to exponential and logarithmic functions, and trigonometric functions, identities, and graphs. Practice in analyzing and solving word problems is given throughout the course. This course is normally followed by Pre-calculus or Introductory Statistics.
1318 – Algebra II & Trigonometry (Honors)
Grades 10 – 12
Department Approval Only
This course is designed for students who showmathematical aptitude and interest and would benefit from a faster paced curriculum. In addition to the regular content of a second-year algebra course, students do more in-depth work in trigonometry. The development of analytical skills is a continuous process with emphasis on problem-solving and the communication of mathematical ideas. Successful completion of the course may allow students to take Pre-AP Calculus.
1360 – Pre-Calculus
Grades 11 – 12
The content and skills of this course are designed to prepare students for the study of calculus and advanced mathematics. Students also gain an appreciation for the use of mathematics in such areas as business and the social and biological sciences. Topics include trigonometry, functions (including exponential and logarithmic), analytic geometry, sequences and series, and an introduction to calculus. The purpose of this course is to gain an understanding of the development of mathematical concepts and theorems as well as the ability to interpret real-life situations using the symbolic and graphic languages of mathematics. Emphasis is placed on the skills of analysis and synthesis of mathematical ideas. Students learn to draw on a variety of past experiences as a means of creating mathematical models.
1364 – Pre-AP Calculus(Honors)
Grades 11 – 12
Department Approval Only
This course is designed to prepare students for the AP Calculus course. Emphasis is on functions and graphing. Topics include polynomial and rational functions, trigonometric functions, exponential and logarithmic functions and analytic geometry. Students in this course focus on the development of mathematical concepts and theorems. The curriculum is rigorous and provides students with a broad, but in-depth, foundation for advanced study in mathematics. The final quarter of the year will be spent on an introduction to calculus, including limits and derivatives.
1366 – Calculus(Honors)
Grades 11 – 12
Department Approval Only
Students who have successfully completed Pre-Calculus may opt to take this introductory Calculus course. Students in this course learn to find derivatives and study definite and indefinite integrals. Emphasis is on how basic calculus concepts can be applied to business, economics, the life sciences, and other fields.
1368 – Advanced Placement Calculus AB (AP)
Grades 11 – 12
Department Approval Only
Following the recommendations from the "Advanced Placement Course Description" published by the College Board, this course includes: differentiation of polynomials, exponential and logarithmic functions, explicit and implicit differentiation, applications of the derivative including curve sketching, maxima-minima problems, motion problems, and related rates.
The Fundamental Theorem of Calculus and techniques of integration are covered as well as applications of the definite integral including area under the curve, volume, and differential equations.
Students are required to take the AP exam at the conclusion of the course.
1370 – BC and Multivariable Calculus – (AP) (Full year course)
Grades 11 – 12
(Prerequisite: AP Calculus)
Department Approval Only
This AP level course will cover topics from the BC AP Calculus syllabus: parametrized curves, polar and vector functions, Euler's Method for solutions of differential equations and L'Hospital's Rule. Applications of integrals will be included, as well as polynomial approximations and series, most notably the Taylor Series. The course will continue with an introduction to Multivariable Calculus: partial derivatives, multiple integrals, and ultimately vector calculus.
Students are required to take the AP exam at the conclusion of the course.
1380 – Introductory Statistics
Grades 11 – 12
(Prerequisite: Algebra II)
Statistical ideas and statistical reasoning and their relevance in our world today are the focus of this course. Students learn to collect, organize, and display data; to use appropriate statistical methods to analyze that data; and to develop and evaluate inferences and predictions that are based on the data.
1382 – Advanced Placement Statistics (AP)
Grades 11 – 12
Department Approval Only
This course follows the syllabus recommendations published by the College Board. The course is divided into four major units: Organizing Data, Producing Data, Probability, and Statistical Inference. The first unit, Organizing Data, covers graphing and data presentation along with descriptive statistics, correlation, and regression. The unit on Producing Data delves into the processes involved in sampling, surveys, experiments, and simulation. The Probability unit discusses the rules of general probability and randomness, and how these apply to the most common types of variable distributions. The last unit, Statistical Inference, ties all these ideas together by showing how to make conclusions with confidence based on available data.
Students are required to take the AP exam at the conclusion of the course. |
Prentice Hall Mathematics maintains the quality content for which Prentice Hall is known, with the research-based approach students need. Daily, integrated intervention and powerful test prep help all students master the standards and prepare for high-stakes assessments.
Building on the solid foundation established in Connected Mathematics, over 15,000 students and 300 teachers contributed to the revision. Students will learn mathematics through appealing and engaging problems. The three-step Launch, Explore, Summarize approach helps students develop mathematical thinking and reasoning while practicing and maintaining skills.
Give students the tools they need to practice standards-based skills and to excel on the state exam.
Comprehensive content reviews, hundreds of practice questions, and full practice exams make these complete review
guides the perfect solution for lesson supplements, remediation, and ongoing practice and review.
Unlocking the key to history, government, and economics for California students!
Learn more about the outstanding Prentice Hall California programs including our 6-8 series (Ancient Civilizations, Medieval and Early Modern Times, and America: History of our Nation), World History: The Modern World, America's Journey, United States History: Modern America, Magruder's American Government, and Economics: Principles in Action plus a wide range of titles for AP, Honors, and Electives. |
Barron's Review CourseI used this book to home school my son while we were out of the country. It contained several topics tested by New York Regents exams which were not covered in his Algebra/Trig textbook, so it was quite useful. The examples were clear and easy to understand. My only complaint is that it needs better proofreading; I found several errors.
5 of 5 people found the following review helpful
4.0 out of 5 starsGood Review BookNov. 7 2010
By Cuishii - Published on Amazon.com
Format:Paperback|Amazon Verified Purchase
This book is very helpful for reviewing purposes, not so much for learning Algebra 2 as a new topic. It's great for refreshing your memories on stuff you learned for the regents.
6 of 7 people found the following review helpful
5.0 out of 5 starsA good buyAug. 28 2011
By carolina11buyer - Published on Amazon.com
Format:Paperback|Amazon Verified Purchase
The book is an in depth review of Algebra and Trig with good examples and problems with answers. I would recommend it to anyone needing a review and practice solving problems. |
According to OER Commons, 'These are the lecture notes of a one-semester undergraduate course which we taught at SUNY...
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According to OER Commons, 'These are the lecture notes of a one-semester undergraduate course which we taught at SUNY Binghamton. For many of our students, Complex Analysis is their first rigorous analysis (if not mathematics) class they take, and these notes reflect this very much. We tried to rely on as few concepts from real analysis as possible. In particular, series and sequences are treated "from scratch." This also has the (maybe disadvantageous) consequence that power series are introduced very late in the course.'
This is a free, online textbook for an introductory course in complex analysis. General topics include Complex Numbers,...
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This is a free, online textbook for an introductory course in complex analysis. General topics include Complex Numbers, Complex Functions, Elementary Functions, Integration, Cauchy's Theorem, More Integration, Harmonic Functions, Series, Taylor and Laurent Series, Poles, Residues, and All That, and Argument Principle. Each chapter from the book can be downloaded as a free pdf file. |
Mathematics
We believe that problem solving (investigating, conjecturing, predicting, analyzing, and verifying), followed by a well-reasoned presentation of results, is central to the process of learning mathematics, and that this learning happens most effectively in a cooperative, student-centered classroom. Classes are designed to broaden students' knowledge and skills and to prepare them for higher level mathematics and engineering courses. With offerings from Algebra to AP Calculus and beyond, students are taught to master the fundamental processes while their problem-solving abilities are challenged with increasingly complex material. Placement is determined by the needs and talents of each individual. |
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Geometry: With Geometry Explorer
Publisher:
McGraw-Hill
Number of Pages:
463
Price:
103.44
ISBN:
0-07-312990-9
Given the number of high quality geometry texts published within the past ten years or so, one could be forgiven for assuming that the subject has undergone some sort of renaissance within mathematics education. In reality, however, geometry still has no coherent presence within school mathematics and it continues to play only a minor role within undergraduate mathematics.
So here is a book whose overall aim is to 'develop an intuitive feel for geometry whilst also establishing sound understanding of underlying proofs and abstractions'. This, of course, is the common challenge faced by authors of university geometry texts, who necessarily have the two-fold task of laying foundations that should have been provided at school, whilst simultaneously transporting students into the realm of advanced geometric topics. But having taught geometry to undergraduate students, I long ago ceased to be amazed by their lack of basic geometric knowledge, and I have sometimes spent more time going backwards than forwards.
In addressing this dilemma, Michael Hvidsten has invoked the use of new technology in the form of Geometry Explorer (provided with the book). This, of course, is not the only way in which geometric intuition can be strengthened, and it can't be expected to totally compensate for many previous years of geometric neglect. Nonetheless, although employed in a supplementary fashion, I very much like the use to which it is put. For example, in the very first exercise project, students use it to explore many properties of the Golden Rectangle. Much later on, it is used to investigate the tiling of the hyperbolic plane, and there are many other 'projects' that also involve the application of this software. In addition, students may be inclined to experiment with it of their own volition — and the more the better.
Anyway, the book begins with a stimulating chapter on axiomatic methods, with historical commentary running throughout. It considers the strengths and weaknesses of various sets of axioms including those of Euclid, Hilbert and Birkhoff. These are considered in the context of consistency, independence and completeness, followed by some explanation of Gödel's Incompleteness theorem. Chapters 2 to 6 are respectively devoted to Euclidean Geometry, Analytic Geometry, Constructions, Transformation Geometry and Symmetry.
Chapters 7 and 8 provide a cogent introduction to Non-Euclidean Geometry and Non-Euclidean Transformations and I particularly liked the author's treatment of all this material. Initial motivation comes from a re-examination of Euclid's axioms and the history of the parallel postulate. Also, Project 2 (in the very first chapter) requires the use of Geometry Explorer to test the validity of Euclidean properties in hyperbolic geometry, thereby setting the scene for later major investigation of the Poincaré model. The Klein model is also introduced and shown to be structurally equivalent to that of Poincaré. Marvellous stuff!
The last chapter provides an appealing introduction to Fractal Geometry together with discussion of many relevant ideas such as contraction mappings, algorithmic geometry and space-filling curves. And Geometry Explorer is again brought into action via 'Projects' on Snowflake Curves, Complex Branching Systems and IFS Ferns.
Intended for use with mathematics students at 'junior or senior collegiatelevel', the book requires a background in geometry provided by elementary high school and some expertise with matrix algebra and groups is also recommended. Generally, I very much like this book but, for the following reasons, I have considerable reservations regarding its use with such a target group.
Treatment of much of the material, although soundly formulated, could be very demanding for those with weak geometric backgrounds (the majority of undergraduate students, of course).
There is a rather sudden transition from the synthetic/axiomatic approach of Euclid to the transformational approach of Klein. And, although isometries are applied to analysis of symmetry and tiling patterns etc, this algebraic machinery is not employed to reveal a range of geometric results akin to the theorems of Euclid. At a very basic level, for example, if two triangles have equal sides, one can find an isometry that maps one onto the other, thus linking the ideas of Euclidean and Kleinian congruence.
The exercises are predominantly of an investigative nature and many of them require reports to be written by students. This is all very well, except that students need considerable preparation to meet the demands of such a research-based approach to learning.
Of course, no review is complete without mention of one or two minor quibbles. Firstly, it was not the Arabs who introduced symbols such as x2, and I still shudder on seeing expressions like 1/0 = ∞. Finally, no history of vector analysis is complete without mention of Willard Gibbs!
However, if only for the chapters on axiomatics, non-Euclidean and fractal geometry, this book should be regarded as a very valuable addition to the existing literature. Moreover, it is suitable for use with a much wider readership than specified by the author, but it wouldn't be my first choice as a self-tuition manual for those with weak geometric backgrounds.
Peter Ruane is retired from university teaching and now dabbles in as many creative diversions as possible. |
Computational Tools in A Unified Object-Oriented Approach
Emphasizing the connection between mathematical objects and their practical C++ implementation, this book provides a comprehensive introduction to both the theory behind the objects and the C and C++ programming. Object-oriented implementation of three-dimensional meshes facilitates understanding...
Theory and Applications
Decomposition Methods for Differential Equations: Theory and Applications describes the analysis of numerical methods for evolution equations based on temporal and spatial decomposition methods. It covers real-life problems, the underlying decomposition and discretization, the stability and...
A Thorough Overview of the Next Generation in Computing
Poised to follow in the footsteps of the Internet, grid computing is on the verge of becoming more robust and accessible to the public in the near future. Focusing on this novel, yet already powerful, technology, Introduction to Grid Computing...
Known for its versatility, the free programming language R is widely used for statistical computing and graphics, but is also a fully functional programming language well suited to scientific programming.
An Introduction to Scientific Programming and Simulation Using R teaches the skills needed to...
Collects the Latest Research Involving the Application of Process Algebra to Computing
Exploring state-of-the-art applications, Process Algebra for Parallel and Distributed Processing shows how one formal method of reasoning—process algebra—has become a powerful tool for solving design and...
This textbook presents a variety of applied mathematics topics in science and engineering with an emphasis on problem solving techniques using MATLAB®. The authors provide a general overview of the MATLAB language and its graphics abilities before delving into problem solving, making the book...
An Introduction to Experimental Mathematics
Keith Devlin and Jonathan Borwein, two well-known mathematicians with expertise in different mathematical specialties but with a common interest in experimentation in mathematics, have joined forces to create this introduction to experimental mathematics. They cover a variety of topics and examples...
Plausible Reasoning in the 21st Century
This revised and updated second edition maintains the content and spirit of the first edition and includes a new chapter, "Recent Experiences", that provides examples of experimental mathematics that have come to light since the publication of the first edition in 2003. For more examples and...
This textbook introduces several major numerical methods for solving various partial differential equations (PDEs) in science and engineering, including elliptic, parabolic, and hyperbolic equations. It covers traditional techniques that include the classic finite difference method and the finite... |
Synopses & Reviews
Publisher Comments:
This unique text provides students with a single-volume treatment of the basics of calculus and analytic geometry. It reflects the teaching methods and philosophy of Otto Schreier, an influential mathematician and professor. The order of its presentation promotes an intuitive approach to calculus, and it offers a strong emphasis on algebra with minimal prerequisites.
Starting with affine space and linear equations, the text proceeds to considerations of Euclidean space and the theory of determinants, field theory and the fundamental theorem of algebra, elements of group theory, and linear transformations and matrices. Numerous exercises at the end of each section form important supplements to the text.
Synopsis:
This unique text provides students with a basic course in both calculus and analytic geometry. It promotes an intuitive approach to calculus and emphasizes algebraic concepts. Minimal prerequisites. Numerous exercises. 1951 edition.
Synopsis:This unique text provides students with a basic course in both calculus and analytic geometry. It promotes an intuitive approach to calculus and emphasizes algebraic concepts. Minimal prerequisites. Numerous exercises. 1951 edition.
"Synopsis"
by Firebrand, |
Course Detail
Links
Exploring Mathematical Ideas
Instructor
Staff
Survey of abstract mathematical ideas that deepen understanding of patterns from mathematics, art, and the physical world. Topics may include the nature of number, infinity, dimension, symmetries, alternate geometries, topology, chaos, fractals, probability and social choice. While techniques and concepts have much in common with advanced theoretical mathematics, little background is assumed and the course is not practical preparation for later courses in mathematics. The course title is occasionally changed to reflect a special emphasis.
Students entering 2012 and after: satisfies the Mathematical and Quantitative Thought distribution requirement.
Students entering before 2012: satisfies the Natural Science and Mathematics distribution requirement. |
Enrol online now!
Overview
Based on Marcus du Sautoy's book The Number Mysteries, this course explores the question, how natural is mathematics? Through numerous online activities and 'at home' experiments, you will interact with mathematics as you have never done before.
For information on how the courses work, and a link to our course demonstration site, please click here.
Description
Today, we inhabit a world that is full of technological advances which are only possible due to the huge leaps that science has made over the last few decades; the structure of DNA, the microchip, splitting the atom. Yet, as diverse as these major discoveries may seem, they are all understood through the language of mathematics.
Mathematics has come a long way from its humble origins of notches on a stick and through this ten week course we will take you all the way from the beginning of the number system to the very edges of the universe.
Packed full of diverse activities to suit a wide range of learning styles, The Number Mysteries maths course is for anyone who wants to go on a mathematical odyssey which may change the way they think forever.
Staff
Dr Thomas Woolley
Course aims
This course aims to
give students a deeper knowledge and understanding of the concepts of number, shape, the role of logic and probability in game play, the role of mathematics in codes and the power of mathematical equations to predict the future;
provide students with activities that allow the students to interact with mathematics on a level which they may not considered before;
show how mathematics permeates many aspects of our daily lives;
aid the intuition of the participants when dealing with probability;
show the beauty behind the equations that mathematicians use.
This course will enable students to:
have confidence in situations where numerical processes are necessary.
question the statistical data that the media presents as fact.
organise problems logically, stating their assumptions and understanding their conclusions.
Certification
This course is accredited and you are expected to take the course for credit. To be awarded credit you must complete written contributions satisfactorily. Successful students will receive credit, awarded by the Board of Studies of Oxford University Department for Continuing Education. The award will take the form of 10 units of transferable credit at FHEQ level 4 of the Credit Accumulation and Transfer Scheme (CATS). A transcript detailing the credit will be issued to successful students. Assignments are not graded but are marked either pass or fail.
Assessment methods
Assessment for this course is based on two assignments, placed midway through the course and completed in the 10 weeks of the course (the second assignment due at the end of week 10). Students will have two weeks to complete each assignment. The first piece will be a short exercise designed to demonstrate their understanding of a concept or concepts. Feedback from this will be designed to give them an idea of the progress they have made and of those areas of their work that might need more attention. The later piece of work allows students to demonstrate their learning on the course as a whole.
IT requirements
This course is delivered online; to participate you must to be familiar with using a computer for purposes such as sending email and searching the Internet. You will also need regular access to the Internet and a computer meeting our recommended minimum computer specification. |
Mathematics
MATH 131. College Algebra and Trigonometry. (4) The system of real numbers, functions, trigonometric, exponential and logarithmic functions, equations, systems of equations, permutations, combinations, the binomial theorem, and probability. Prerequisite: one and one-half years of high school algebra and one year of high school plane geometry.
Physical Science
Physics
PHYS 201, 202. General Physics. (4, 4) For biology and related majors. A noncalculus survey of classical and modern physics. First semester: mechanics, heat, and sound. Second semester: electricity, magnetism, light, and a brief summary of modern physics. Laboratory course. Prerequisite: Mathematics 131 or the equivalent. 201 is a prerequisite for 202 or permission of the instructor. |
Stock Options - The Animated Tutorial - Jerry Marlow
A fast and easy way to teach and to learn about stock options, option prices, stock-market volatility, and Black-Scholes options pricing theory. CD and Book $39.95. The theory provides a sophisticated way of analyzing and understanding the relations among
...more>>
Study Economics
Online copies of N. Gregory Mankiw's books Principles of Macroeconomics and Principles of Microeconomics and a tutorial by Daniel Christiansen on calculus and economics.
...more>>
StudyJams! - Scholastic Inc.
An online service that complements the school math and science curriculum for grades 3 - 6. Aligned with state curriculum standards, StudyJams! takes math and science problems and presents them using relevant, real-world examples students can easily understand.
...more>>
TeAch-nology - Teachnology, Inc.
A portal for information about current and past practice in the field of education. Read math teaching "Ideas That Worked"; and tutorials ranging from teacher retirement planning and "What to Consider When Writing a Lesson Plan" to "How to Deal With DisruptiveTopics in Calculus - E. Lee Lady; University of Hawaii
Files in PDF, DVI, and Postscript formats, to help students learn to use calculus in applications and to have confidence in setting up formulas using derivatives and integrals. Contents include: a conceptual approach to applications of integration, max-min
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Trigonometry - Technical Tutoring
Site provides an introduction to trigonometry, includes illustrative examples and exercises in basic trigonometry as well as a summary of the important basic trig identities and formulae.
...more>>
Tutor Amigos - Tutor Amigos, LLC
Also in Spanish. Live, online tutoring and homework help in Math and Science for Spanish-speaking students. Our goals are to provide Latinos and Hispanics with affordable, personalized instruction in Math and Science and to support those English Language
...more>>
tutOR - Moshe Sniedovich and Angie Byrne
An online Operations Research (OR) tutorial system developing tutorial modules for specific OR topics, generic web tools to facilitate the construction of the OR modules, and research of the WWW technologies pertaining to this project. Modules for investigating
...more>>
TutorNEXT - tutorNEXT, Inc.
One-on-one, individualized tutoring sessions in math and English. An enrichment program in math, and free printable math worksheets, are also available. Full listing of services on the site.
...more>>
TutorTeddy.com
Online tutoring sessions across grades in arithmetic, algebra, statistics, probability, calculus, geometry, and trigonometry. The TutorTeddy.com site also freely offers more than a hundred chalkboard video lectures and worked problems.
...more>>
Tutor World Online
This online tutoring service sells homework help and SAT preparation packages. The Tutor World Online journal posts free primers in math.
...more>> |
On this online calculator calculate mathematical expressions and complex numbers. You can do matrix algebra and solve linear systems of equations and graph all 2D graph types. You can also calculate z... More: lessons, discussions, ratings, reviews,...
Plomplex is a complex function plotter using domain coloring. You can compose a function with a complex variable z, and generate a domain coloring plot of it. You can choose the plot range as well as ... More: lessons, discussions, ratings, reviews,...
Simplesim is suited for modelling of non-analytic relations in systems which are causal in the sense that different courses of events interact in a way that is difficult to see and understand. Exam... More: lessons, discussions, ratings, reviews,...
As students drag the ball along the perimeter of the circle a line is drawn between the point on the circle and the corresponding point on the sine curve. The range is from 0 to 360 degrees on the cirThis packet contains a copy of the original problem used to create the activity, rationale and explanation behind the "Change the Representation" focal activity, and some thoughts on why this activity... More: lessons, discussions, ratings, reviews,...
What's the reliability of cancer tests, diabetes tests, and pregnancy tests? This brief discussion shows some functions to be used on your graphing calculator to visualize a graph of the accuracy of |
The Algebra 1: The Complete Course DVD Series will help students build confidence in their ability to understand and solve algebraic problems.
In this episode, students will learn if (a) is positive, the parabola opens upward; if the (a) is negative, the parabola opens downward; and that the function has an absolute minimum/maximum. Grades 5-9. 30 minutes on DVD. |
Geometry For Dummies Education Bundle
Book Description: Learning geometry doesn't have to hurt. With a little bit of friendly guidance, it can even be fun! Geometry For Dummies, 2nd Edition, helps you make friends with lines, angles, theorems, and postulates. It eases you into all the principles and formulas you need to analyze two- and three-dimensional shapes, and it gives you the skills and strategies you need to write geometry proofs.Before you know it, you'll be understanding proofs like an expert. You'll find out how a proof's chain of logic works and discover some basic secrets for getting past rough spots. Soon, you'll be proving triangles congruent, calculating circumferences, using formulas, and serving up pi. The non-proof parts of the book contain helpful formulas and tips that you can use anytime you need to shape up your knowledge of shapes. You'll even get a feel for why geometry continues to draw people to careers in art, engineering, carpentry, robotics, physics, and computer animation, among others. You'll discover how to:Identify lines, angles, and planesMeasure segments and anglesCalculate the area of a triangleUse tips and strategies to make proofs easierFigure the volume and surface area of a pyramidBisect angles and construct perpendicular linesWork with 3-D shapesWork with figures in the x-y coordinate systemSo quit scratching your head. Geometry For Dummies, 2nd Edition, gets you un-stumped in a hurry. When you need to shape up, open up the included Geometry Workbook For Dummies, which contains over 290 pages with hundreds of practice problems featuring ample workspace to work out the problems. Each problem includes a step-by-step answer set to identify where you went wrong (or right). You'll be proving yourself proof-worthy in no time! AUTHOR BIO: Mark Ryan owns and operates The Math Center in Chicago, a teaching and tutoring service for all math subjects as well as test preparation. He also wrote Geometry Workbook For Dummies |
Build your confidence and ability in algebraic methods of problem solving. Learn how algebra can be applied in ways that are both contemporary and representative of a wide range of disciplines. Explore expressions, equations, fractions, exponents, radicals, matrices, trigonometric functions, geometry, graphing and more. Also see our online course.
Note(s):
A final grade of C (63%) or better in this course meets the mathematics admission requirement of most full-time programs at George Brown.
Equivalent:
MATH 1034, MATH 1112
Prerequisites:
You must have completed grade 10 math or MATH 1080 (Math Essentials) . If you do not meet this requirement, you must complete the General Math Assessment and score high enough to be assigned to Mathematics. You must present proof at the first class. |
Euclidean geometry
Bibliography
Benno Artmann, Euclid: The Creation of Mathematics (1999), presents the contents of the Elements in modern terms accessible to a general reader and shows how many aspects of modern mathematics are prefigured by Euclid.
H.S.M. Coxeter, Introduction to Geometry, 2nd ed. (1969, reissued 1989), is a very readable scientific work starting from elementary Euclidean geometry and going on to more advanced topics.
Robin Hartshorne, Geometry: Euclid and Beyond (2000), is an exhaustive modern presentation for mathematics students; it includes an extensive bibliography. |
Geometry Lessons in the Waldorf School – Volume 2
Freehand Form Drawing and Basic Geometric Construction in Grades 4 and 5
Ernst Schuberth
Softbound
Includes CD-ROM with additional exercises and color plates
$18.00
This book is the second volume* of mathematician and Waldorf teacher Ernst Schuberth's Geometry Lessons in the Waldorf School. With an abundance of black and white drawings and a clear, descriptive text, Schubreth covers the free form drawing and basic constructions taught in the Waldorf school fourth and fifth grades.
A real bonus is the accompanying CD Rom that has offers additional exercises and color plates for the teacher to study. |
Explorations in Signals and Systems Using MATLAB
A comprehensive set of computer exercises of varying levels of difficulty covering the fundamentals of signals and systems. The exercises require the ...Show synopsisA comprehensive set of computer exercises of varying levels of difficulty covering the fundamentals of signals and systems. The exercises require the reader to compare answers they compute in MATLAB (R) with results and predictions made based on their understanding of material. Chapter covered include Signals and Systems; Linear Time-Invariant Systems; Fourier Series Representation of Periodic Signals; The Continuous-Time Fourier Transform; The Discrete-Time Fourier Transform; Time and Frequency Analysis of Signals and Systems; Sampling; Communications Systems; The Laplace Transform; The z-Transform; Feedback Systems. For readers interested in signals and linear systems30421555421555.
Description:Fair. 0130421553 Student Edition. No apparent missing pages....Fair. 0130421553 |
& You: The Power & Use of Mathematics
As the world around us changes and information comes at warp speed, it is more important than ever to be quantitatively literate. Yet most U.S. ...Show synopsisAs the world around us changes and information comes at warp speed, it is more important than ever to be quantitatively literate. Yet most U.S. students leave high school with quantitative skills far below what they need and what employers are seeking, and virtually every college finds that many students need remedial mathematics. Based on the latest educational research, "Math & YOU" helps students develop the quantitative skills needed to be successful in school and the workplace, using real data, problems based on everyday situations, and activities built around topics that are recognizable and relevant. With this approach, students become comfortable with quantitative ideas and proficient in applying them. In addition, to support the printed text, "Math & YOU" provides an online eBook accompanied by additional teaching aids, all part of a robust companion Web site. Hardcover edition available upon request. Ask your local W.H. Freeman representative. Math & YOU HallmarksConfidence with Mathematics. One of the goals of the ""Math & YOU"" program is to help students become comfortable with quantitative ideas and proficient in applying them. Students routinely quantify, interpret, and check information such as comparing the total compensation of two job offers, or comparing and analyzing a budget Cultural Appreciation. "Math & YOU" provides examples and exercises that help student to understand the nature of mathematics and its importance for comprehending issues in the public realm. Logical Thinking. "The Math & YOU" program develops habits of inquiry, prepares students to look for appropriate information, and exposes them to arguments so that they can analyze and reason to get at the real issues. Making Decisions. One of the main threads of the "Math & YOU" program is to help students develop the habit of using mathematics to make decisions in everyday life. One of the goals of the text is for students to see that mathematics is a powerful tool for living. Mathematics in Context. The "Math & YOU" program helps students to learn to use mathematical tools in specific settings where the context provides meaning. Number Sense. "The Math & YOU" program begins with a chapter that reviews the meaning of numbers, estimation and measuring. Throughout the rest of the program students develop intuition, confidence, and common sense for employing numbers. Practice Skills. Throughout the "Math & YOU" program students encounter quantitative problems that they are likely to encounter at home or work. This helps students become adept at using elementary mathematics in a wide variety of common situations 1608406024 Purchased like new but not a guarantee that...Fine.
Description:New. 1608406024 Purchased like new but not a guarantee that...New |
It's essential that you try to do as many problems as possible, because
Math is not a "spectator sport", and you can't learn calculus just by watching
your instructor or TA solve problems.
Doing problems is the best way to test whether you understand the material
and to find areas where you need more work.
Some (not all) quiz questions and exam questions will be very similar to
assigned homework problems and textbook examples. Not understanding
these problems simply guarantees that you'll throw away quiz and exam points.
Some of the problems assigned each day are routine "drill" exercises.
There are certain basic techniques in calcuus that should become complely
mechanical procedures for you: procedures you can do "with your spine"
rather than your brain. Other problems require more thought. Sometimes
you'll think that you can do a problem but get stuck if you actually try
to write down the details. It's important to write out neat careful
solutions for yourself, even in sections where homework is not
collected. It's good to organize these in a separate notebook or file folder.
You'll appreciate having them in one place when you want to review, especially
if you can read them easily and don't have to work to decipher later what
you did a few weeks earlier.
After you finish and write up a solution, go back and talk to yourself
(or others) about the problem. For example, ask "What are
the main ideas involved?", "What's involved with this problem that
puts it in this section of the book?", "Why couldn't I have done this problem
last week?", "Is there some other way to solve the same problem?"
You can learn much more by solving the same problem in a different way,
if possible, than by solving several problems all in more or less the same
way.
In the same vein: if a problem seems hard, don't give up and turn
immediately to the solutions manual. You can often learn a lot
more by spending hours (perhaps not all at once!) grappling with a hard
problem than by working many simpler problems in the same amount of time.
The "Principles for Problem Solving" in the text (pp. 87 ff.)
may be helpful. They're not magic, but they can help you organize
your thoughts. At the end of each chapter, the section "Focus on
Problem Solving" illustrates how to apply these principles to some harder
problems.
The answers to odd-numbered problems are in the back of the textbook.
The Student Solutions Manual, containing more complete solutions to odd-numbered
problems, is available in the bookstore. If you're interested, consider
sharing a manual with one or more friends to save money. We actually
recommend against more than a casual use of the Solutions Manual: students
become too dependent on it and don't develop confidence in their own work.
You and your friends should usually be able to confirm solutions by comparing
your work. Moreover, convincing friends that your solution is correct,
or becoming convinced by their alternative solution, helps teach the skills
of communicating mathematical arguments.
A schedule of Daily
Reading and Homework Problems is part of the syllabus. We will try
to follow it fairly closely. You will probably find the lectures
more valuable if you read the assigned material and attempt some of the
problems before coming to class. There may be modifications to the assignment
list as the course moves along, so you might want to print out a new copy
of it immediately after each exam. |
Instructor Help
Evaluation Modes for Math Questions
For many question types in WebAssign®, such as Multiple-Choice or pencilPad, the question
mode you select has immediately visible effects on the question you are creating. When you create
questions that evaluate mathematical expressions, however, the question mode you select affects
what kind of responses your students can enter and how your students' responses are evaluated, but
has no corresponding visual effect.
Before creating a question that asks your students to enter a mathematical expression or
equation, determine how that expression should be evaluated.
Symbolic Mode
Symbolic questions evaluate your students' responses symbolically by substituting a series of
values for the variables in the response and in the key. If the response and the key are equal
for all tested values, then the response is accepted as correct.
This evaluation behavior provides reliable scoring of responses and can accept any form of a
mathematical expression that is equivalent to the key. However, it cannot evaluate responses
that are equations, and it cannot evaluate whether responses are in a particular form, such as a
completely factored expression.
Algebraic Mode using Mathematica®
Algebraic questions evaluate your students' responses algebraically using Mathematica, in much
the same way you would solve an equation.
Older questions created using Algebraic mode do not necessarily use Mathematica; however,
the general principles still apply, and these questions will continue to function.
Algebraic mode is a much more powerful method for evaluating your students' responses, but
specifying your key in Algebraic mode can sometimes be more complicated than with Symbolic mode.
Additionally, you cannot by default accept any mathematically equivalent response using
Algebraic mode; you must therefore make sure that your students understand what form of response
is needed.
Choosing a Mode to use Based on Selected Criteria
Refer to the following table to help you decide which mode to use.
Best Practice: If you can use either Symbolic mode or Algebraic mode, use Symbolic
mode.
Criterion / Example
Symbolic Mode
Algebraic Mode using Mathematica
Accept any response that is equivalent to the key
Allow your students to type commas in large numbers
The answer is a single mathematical expression that is not an equation.
Solve for x:
2x+y2-6=0
x=___
The answer is a finite list of set members.
List the first three natural numbers.
The answer is any member of a set.
List any multiple of both 2 and 3.
The answer is a single ordered pair.
What are the coordinates of the center of the circle defined by the following equation:
(x+3)2+(y-4)2=25
The answer is two or more ordered pairs.
List the coordinates of the first five data points shown on the graph.
The answer is a vector.
Find a vector perpendicular to ‹1,2›.
The answer is an equation.
What is the equation for a circle with center (x,y)
and radius r?
Only a particular form of the answer is correct.
Factor the expression: x2-x-12
Key can specify multiple correct answers.
Key can perform complex evaluation functions for you, such as factoring polynomials or
computing derivatives. |
Synopses & Reviews
Publisher Comments:
Providing solid tips for every stage of study, Mastering Mathematics stresses the importance of a positive attitude and gives students the tools to succeed in their math course. This practical guide will help students: avoid mental blocks during math exams, identify and improve areas of weakness, get the most out of class time, study more effectively, overcome a perceived "low math ability," be successful on math tests, get back on track when feeling "lost," and much more!
Synopsis:
Provides solid tips for every stage of study, stressing the importance of a positive attitude.
Table of Contents
Preface to the Instructor / Introduction to the Student / How to Evaluate How Well You Study in Math Courses PART I: MAKE A FRESH START 1. How to Have the Right Attitude in Math Courses PART II: MAKE SUCCESSFUL COURSE PREPARATION YOUR CONSISTENT ROUTINE 2. How to Begin Before Your Math Course Starts 3. How to Master the Course Using Four Major Steps 4. How to Use Class Time Effectively 5. How to Use Your Time Between Classes--Notes and Textbook 6. How to Use Your Time Between Classes--Homework and Beyond PART III: MAKE PREPARING FOR TESTS A SURE THING 7. How to Aim for Perfection in Your Test Preparation 8. How to Make a List of Topics That Might Be Covered on the Test 9. How to Master Each Topic 10. How to Be a Perfectionist When Preparing for a Test 11. How to Take a Math Test PART IV: MAKE USE OF THESE ADDITIONAL STUDY TIPS TO IMPROVE YOUR GRADE 12. How to Cope with a "Difficult" Teacher 13. How to Go the Extra Mile In Your Course Preparation Conclusion / Appendix A: Study Habits Improvement Check /Appendix B: Recommended Books for Students |
047166 Elementary Teachers: A Contemporary Approach
This leading mathematics text for elementary and middle school educators helps you quickly develop a true understanding of mathematical concepts. It integrates rich problem-solving strategies with relevant topics and extensive opportunities for hands-on experience. By progressing from the concrete to the pictorial to the abstract, Musser captures the way math is generally taught in elementary schools.
This title will give you all the essentials mathematics teachers need for teaching at the elementary and middle school levels:
Highlights algebraic concepts throughout the text and includes additional supporting information.
Provides enhanced coverage of order of operations, Z-scores, union of two events, Least Common Multiple, and Greatest Common Factor.
Focuses on solid mathematical content in an accessible and appealing way.
Offers the largest collection of problems (over 3,000!), worked examples, and problem-solving strategies in any text of its kind.
Includes a comprehensive, five-chapter treatment of geometry based on the van Hiele model |
Translator
The Google translation of this page's content may not be completely accurate. Please contact the school directly for clarification of official information.
Math 8
Doug Ingamells, Periods 2 & 5
Unlike years past these classes are entirely populated with 8th graders. The two classes are usually on
the same page and assignment, except that they have different "block"
days so assignment and due dates can differ. There are two other
sections of Math 8, both taught by Kerry Bayne.
PPS has decided that the first six (of twelve total) chapters in the
algebra text will be part of the Math 8 curriculum. This means that
Algebra 1-2 next year will start at Chapter 7, and students must complete the
first six chapters before enrolling in Algebra 1-2. The district
calendar has us working with a few
pre-algebra topics in addition. All students in Math 8 should
be in Algebra 1-2 the following year.
PPS uses standard A-F grades. In this class grades are weighted so
that tests count 60% and homework/classwork counts 40%. We use the
standard 90%(A), 80%(B), 70%(C), 60%(D) breakpoints.
A copy of the general information letter for this class can be found here: |
Naples and Pompeii"
Rick finds Naples is Italy in the extreme. He prowls backstreet fish markets, dodges fast-moving Vespas, and dines on pizza where it was invented. He climbs to the top of nearby Mount Vesuvius, then wanders through the ruins of Pompeii.G
11:00 pm
Learning Math: Patterns, Functions & Algebra"Non-Linear Functions"
Continue exploring functions and relationships with two types of non-linear functions: exponential and quadratic functions. This session reveals that exponential functions are expressed in constant ratios between successive outputs and that quadratic functions have constant second differences. Work with graphs of exponential and quadratic functions and explore exponential and quadratic functions in real-life situations.G
11:30 pm
Learning Math: Patterns, Functions & Algebra"More Non-Linear Functions"
Investigate more non-linear functions, focusing on cyclic and reciprocal functions. Become familiar with inverse proportions and cyclic functions, develop an understanding of cyclic functions as repeating outputs, work with graphs, and explore contexts where inverse proportions and cyclic functions arise. Explore situations in which more than one function may fit a particular set of data.G |
Essential Arithmetic
9780534944827
ISBN:
0534944825
Edition: 7 Pub Date: 1994 Publisher: Thomson Learning
Summary: This new ADVANTAGE SERIES of C. L. Johnston, Alden T. Willis, and Jeanne Lazaris' ESSENTIAL ARITHMETIC is a traditional, straight-forward, extremely popular book which is noted for its one-step, one-concept-at-a-time approach. All major topics are divided into small sections, each with its own examples and often with its own exercises--an approach that helps students master each section before proceeding to the next ...one. As part of the ADVANTAGE SERIES, this version will offer all the quality content you've come to expect from Johnston, Willis, and Hughes sold to your students at a significantly lower price.
Johnston, Carol L. is the author of Essential Arithmetic, published 1994 under ISBN 9780534944827 and 0534944825. Five hundred fifty two Essential Arithmetic textbooks are available for sale on ValoreBooks.com, one hundred eleven used from the cheapest price of $7.90, or buy new starting at $71 traditional, straight-forward, extremely popular book is noted for its one-step, one-concept-at-a-time approach. In the new edition, the authors have brought in new cove [more]
This traditional, straight-forward, extremely popular book is noted for its one-step, one-concept-at-a-time approach. In the new edition, the authors have brought in new coverage to meet NCTM standards where appropriate.[less] |
Offering
10+ subjects
including logic logic logic |
Bob Miller's Basic Math and Pre-Algebra for the Clueless
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 the author's acclaimed and patented fail-safe methodology for making mathematics easy to understand, Bob Miller's Basic Math and Pre-Algebra for the Clueless enhances students' facility in these techniques and in understanding the basics. This valuable new addition to Bob Miller's Clueless series provides students with the reassuring help they need to master these fundamental techniques, gives them a solid understanding of how basic mathematics works, and prepares them to perform well in any further mathematics courses they take.
Tcl/Tk is enjoying a resurgence of popularity and interest in the computing community due to the fact that it is relatively easy to learn, powerful, fast, permits rapid development, and runs on all ... |
Ok guys I got my degree in mathematics and a few things I can tell you about are the following:
First of all lets anwser the question on what CALCULUS means.. Calculus comes from the Latin word "calculus", which means a counting stone..
More over, calculus two main branches are: INTEGRAL Calculus, which has to do with finding the area under a curve for example and the second is differential calculus, which deals with finding the rate of change, and slopes on curves.
In addition, integral, and differential calculus used the fundamental infinite sequences and series, which is both theorems based on ALGEBRA, under defined limits. And we do that in order to measure the differences with more absolute results. Furthermore, this brunches have been subdivided to other categories of calculus, the plural form in Latin for this is "calculi", such us lambda calculus, proportional calculus,calculus of variations etc.. And of course you have the differential equations, which is also calculus, which is the study of properties and applications of the derivative of a function.
Calculus is used in physics, chemistry and even biology, because a very important question in these fields is always, what is the rate of which things are changing my friend. |
Product Details
See What's Inside
Product Description
By Frances Curcio, Theresa Gurl, Alice Artzt, Alan Sultan
Connect the Process of Problem Solving with the Content of the Common Core
Mathematics educators have long recognized the importance of helping students to develop problem-solving skills. More recently, they have searched for the best ways to provide their students with the knowledge encompassed in the Common Core State Standards (CCSS). This volume is one in a series from NCTM that equips classroom teachers with targeted, highly effective problems for achieving both goals at once.
The 44 problems and tasks for students in this book are organized into the major areas of the high school Common Core: algebra, functions, geometry, statistics and probability, and number and quantity. Examples of modeling, the other main CCSS area, are incorporated throughout. Every domain that is required of all mathematics students is represented.
For each task, teachers will find a rich, engaging problem or set of problems to use as a lesson starting point. An accompanying discussion ties these tasks to the specific Common Core domains and clusters they help to explore. Follow-up sections highlight the relevant CCSS Standards for Mathematical Practice that students will engage in as they work on these problems.
This book provides high school mathematics teachers with dozens of problems they can use as is, adapt for their classrooms, or be inspired by while creating related problems on other topics. For every mathematics educator, the books in this series will help to illuminate a crucial link between problem solving and the Common Core State Standards$36.95
Customers Who Bought This Also Bought...
This book focuses on essential knowledge for teachers about proof and the process of proving. It is organized around five big ideas, supported by multiple smaller, interconnected ideas—essential understandings.
By connecting the CCSSM to previous standards and practices, the book serves as a valuable guide for teachers and administrators in implementing the CCSSM to make mathematics education the best and most effective for all students.
This practical, useful book introduces tested tools and concepts for creating equitable collaborative learning environments that supports all students and develops confidence in their mathematical abilityA valuable resource to any mathematics teacher, this rich collection of mathematical tasks will enliven students' engagement in mathematical thinking and reasoning and help them succeed in the classroom.
The Center for the Study of Mathematics Curriculum (CSMC) leaders developed this volume to further the goal of teachers having opportunities to interact across grades in ways that help both teachers and their students see connections in schooling as they progress through the grades. Each section of this volume contains three companion chapters appropriate to the three grade bands—K–5, 6–8, and 9–12—focusing on important curriculum issues related to understanding and implementing the CCSSM.
The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research. |
Guide students through the Further Maths certificate with this handy practice book, featuring short topic explanations, worked examples and loads of graded practice exercises that will stretch and challenge. |
CONTEMPORARY ABSTRACT ALGEBRA solutions fifth edition
6. High school math teachers should be adept at looking at data and making plausible conjectures and generalizations. They should also teach their students to do this. This is a skill that can be learned with practice. Groups and rings provide abundant opportunities for developing this skill.
This entry was posted on Saturday, June 30th, 2012 at 10:37 pm and is filed under Grad School. You can follow any responses to this entry through the RSS 2.0 feed.
Both comments and pings are currently closed. |
Major Requirements
Coursework Requirements
Students majoring in mathematics must complete MATH 115 and one of 116/120 (or the equivalent) and at least eight units of 200-level and 300-level courses. These eight units must include 205, 206, 302, 305, and two additional 300-level courses. (Thus a student who places out of 115/116 and starts in 205 requires only eight courses.) At most two of 206, 210 and 215 may be counted towards the major. These courses must be completed for the mathematics major:
Math 115: Calculus I and Math 116: Calculus II, or the equivalent
Math 205: Multivariable Calculus
Math 206: Linear Algebra
Math 302: Elements of Analysis I
Math 305: Abstract Algebra
At least two elective 300-level courses not counting any of 350, 360, 370.
A student may count Math 215/Phys 215 towards her mathematics major. However, she may count at most two of the course 206, 210, and 215 toward the major. Credit for Math 216/Phys 216 satisfies the requirement that a math major take 205, but cannot be counted as one of the 200- or 300-level units required for the major.
Major Presentation Requirement
Majors are also required to present one classroom talk in either their junior or senior year. This requirement can be satisfied with a presentation in the student seminar, but it can also be fulfilled by giving a talk in one of the courses whose catalog description says"Majors can fulfill the major presentation requirement in this course." In addition, a limited number of students may be able to fulfill the presentation requirement in other courses, with permission of the instructor |
t... read more
Famous Problems of Geometry and How to Solve Them by Benjamin Bold Delve into the development of modern mathematics and match wits with Euclid, Newton, Descartes, and others. Each chapter explores an individual type of challenge, with commentary and practice problems. Solutions.
Proof in Geometry: With "Mistakes in Geometric Proofs" by A. I. Fetisov, Ya. S. Dubnov This single-volume compilation of 2 books explores the construction of geometric proofs. It offers useful criteria for determining correctness and presents examples of faulty proofs that illustrate common errors. 1963 editionsAdvanced Euclidean Geometry by Roger A. Johnson This classic text explores the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and examining in detail many relatively recent theorems. 1929 editionFoundations of Geometry by C. R. Wylie, Jr. Geared toward students preparing to teach high school mathematics, this text explores the principles of Euclidean and non-Euclidean geometry and covers both generalities and specifics of the axiomatic method. 1964 edition., Relativity and the Fourth Dimension by Rudolf Rucker Exposition of fourth dimension, concepts of relativity as Flatland characters continue adventures. Topics include curved space time as a higher dimension, special relativity, and shape of space-time. Includes 141 illustrations.
Taxicab Geometry: An Adventure in Non-Euclidean Geometry by Eugene F. Krause Fascinating, accessible introduction to unusual mathematical system in which distance is not measured by straight lines. Illustrated topics include applications to urban geography and comparisons to Euclidean geometry. Selected answers to problemsProduct Description:
the most effective methods from discussions with students. Topics include lines and planes, determinants and linear equations, matrices, groups and linear transformations, and vectors and vector spaces. Additional subjects range from conics and quadrics to homogeneous coordinates and projective geometry, geometry on the sphere, and reduction of real matrices to diagonal form. Exercises appear throughout the text, with complete answers at the end |
Precalculus - 3rd edition
Summary: These authors have created a book to really help students visualize mathematics for better comprehension. By creating algebraic visual side-by-sides to solve various problems in the examples, the authors show students the relationship of the algebraic solution with the visual, often graphical, solution. In addition, the authors have added a variety of new tools to help students better use the book for maximum effectiveness to not only pass the course, but truly understa...show morend the material.
Features
Functions Early and Integrated: Functions are introduced right away in Chapter 1 to get students interested in a new topic. Equations and expressions are reviewed in the second chapter showing their connection to functions. This approach engages students from the start and gives them a taste of what they will learn in this course, instead of starting out with a review of concepts learned in previous courses.
Algebraic Visual Side-by-Sides: Examples are worked out both algebraically and visually to increase student understanding of the concepts. Additionally, seeing these solutions side-by-side helps students make the connection between algebraic manipulation and the graphical interpretation.
Zeros, Solutions, and x-Intercepts Theme: This theme allows students to reach a new level of mathematical comprehension through connecting the concepts of the real zeros of the function, the solutions of the associated equation, and the x-coordinates of the x-intercept of the graph of the function.
Technology Connection: In each chapter, optional Technology Connections guide students in the use of the graphing calculator as another way to check problems.
Review Icon: These notes reference an earlier, related section where a student can go to review a concept being used in the current section.
Study Tips: These occasional, brief reminders appear in the margin and promote effective study habits such as good note taking and exam preparation.
Connecting the Concepts: Comprehension is streamlined and retention is maximized when the student views a concept in a visual form, rather than a paragraph. Combining design and art, this feature highlights the importance of connecting concepts. Its visual aspect invites the student to stop and check that he or she has understood how the concepts within a section or several sections work together.
Visualizing the Graph: This feature asks students to match an equation with its graph. This focus on visualization and conceptual understanding appears in every chapter to help students see ''the big picture.''
Vocabulary Review: Appearing once per chapter in the Skill Maintenance portion of an exercise set, this feature checks and reviews students' understanding of the language of mathematics.
Classify the Function: With a focus on conceptual understanding, students are asked to identify a number of functions by their type (i. e., linear, quadratic, rational, and so forth). As students progress through the text, the variety of functions they know increases and these exercises become more challenging. These exercises appear with the review exercises in the Skill Maintenance portion of an exercise set894.8990 +$3.99 s/h
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BOOKLORD El Cerrito, CA
Third Edition, Second Printing. Spine is cocked, bumping/chipping/creasing, rubbing and soiling on covers. "Used" sticker and length of tape along spine, rippling present throughout book. Fair conditi...show moreon. Moderate to heavy shelf wear or edge wear on covers and spine. Books in Fair condition most likely will have markings or highlights on pages or binding defects. (GG87 |
Navigating mathematics.
Problem: In 2004,at Lake Highlands Junior High
School (LHJH) in the(RISD RISD Rhode Island School of Design RISD Rockwall Independent School District (Texas) RISD Richardson Independent School District (Texas) RISD Roswell Independent School District ),
Texas, were falling behind mathematically, with none passing the Texas
Assessment of Knowledge and Skills (TAKS TAKS Texas Assessment of Knowledge and Skills (statewide student assessment as of Spring 2003)). Performance by seventh-and
eighth-graders on the TAKS needed improvement.
Additionally, a large district teacher turnover had increased the
number of new teachers who lacked math-teaching experience.
Solution: In August 2005, a new mathnew math n. Mathematics taught in elementary and secondary schools that constructs mathematical relationships from set theory. Also called new mathematics. intervention was piloted at
Lake Highlands Junior High for 125 students who had failing math scores
on the 2005 TAKS. Of the eight teachers in the pilot program, four had
an average of three years' experience, and four were new teachers
who had taken an alternate teaching certification route.
A TI engineer, Jack Kilby invented the integrated circuit in 1958. Three TI employees left the company in 1982 to start Compaq. provided the technology, including the
TI-Navigator Classroom Learning System and the TI-73 Explorer graphing
calculators, training instructors and a program manager to oversee the
project. LHJH instituted common weekly planning periods for teachers and
IT staff and set assessment benchmarks.
Two very important needs were suggested, and both played a crucial
role in the intervention process. Students were asked what they wanted
out of a math class, and they said more time. Teachers were asked what
they needed to be successful, and their answer was more math training.
Based on those suggestions-plus district needs and data-LHJH and
Texas Instruments developed key points to positively impact math
performance. They doubled instruction time from 50 to 100 minutes on a
daily basis, integrated Texas Instrument's technology, used common
aligned assessment, accelerated the curriculum, and set high student
expectations.
Math Class
Teachers learned how to integrate the TI-Navigator system's
real-time feedback into their teaching and to instantly assess student
understanding. Because they could quickly see whether students
understood a concept, they knew when they could move forward, or if
additional teaching was needed. Participation increased, which led to
in-depth student explanations, where students planned how to solve
problems. "I've actually seen the achievement gap
closing," says Kristen , the Texas Instrument's math
block program specialist, "and this has taught me that every
student is capable of lemminglemming, name for several species of mouselike rodents related to the voles. All live in arctic or northern regions, inhabiting tundra or open meadows. They frequently nest in underground burrows, particularly in winter, although they do not hibernate. ."
Benchmarks
Based on initial benchmarks, the mid-year review showed LHJH
students were enjoying math more than in previous years and that
students were more motivated.
Over 30 percent of the students who participated in the
intervention passed the 2006 TAKS after failing the previous year.
At the end of 2006, LHJH increased its district rankings from
seventh to second for seventh-graders and from seventh to fifth for
eighth-graders.
According toaccording to prep. 1. As stated or indicated by; on the authority of: according to historians.
2. In keeping with: according to instructions.
3. RISD Deputy Superintendent Patti Keiker, Texas
Instruments and RISD have teamed up and implemented a successful math
program. The pilot program's success has expanded this year to
include a more heterogeneous, mixed-ability group of over 700 students
and more than 20 teachers at five other district junior high schools.
RISD has purchased over $60,000 worth of technology for the
implementation, and Texas Instruments will continue to deliver
professional development. RISD is hoping that the project will continue
to show positive results, allowing the district to complete its plan to
include all eight junior high schools in the district. DA
RESOURCES
Lake Highlands
Junior High School
Richardson Independent
School District
Ken Royal is associate editor.
COPYRIGHT 2007 Professional Media Group LLC
No portion of this article can be reproduced without the express written permission from the copyright holder. |
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Description
Symbols and Meanings in School Mathematics explores the various uses and aspects of symbols in school mathematics and also examines the notion of mathematical meaning. It is concerned with the power of language which enables us to do mathematics, giving us the ability to name and rename, to transform names and to use names and descriptions to conjure, communicate and control our images. It is in the interplay between language, image and object that mathematics is created and can be communicated to others.
The book also addresses a set of questions of particular relevance to the last decade of the twentieth century, which arise due to the proliferation of machines offering mathematical functioning.
Related Subjects
Name: Symbols and Meanings in School Mathematics (Paperback) – Routledge
Description: By David Pimm. Symbols and Meanings in School Mathematics explores the various uses and aspects of symbols in school mathematics and also examines the notion of mathematical meaning. It is concerned with the power of language which enables us to do mathematics, giving...
Categories: Education, Curriculum Studies |
Hello guys I am about one week through the semester, and getting a bit worried about my course work. I just don't seem to comprehend the stuff I am learning, especially things to do with math powerpoints on ratios. Could somebody out there please help me with function domain, interval notation and quadratic formula. I can't afford to get a tutor, but if anyone knows about other ways of improving topics like quadratic formula or percentages without fuss, please drop me a line Thanks heaps
I know how hard it can be if you are having problems with math powerpoints on ratios. It's a bit hard to help without more information of your situation. But if you can't afford a tutor, then why not just use some software and see how it goes. There are so many programs out there, but one you should test out would be Algebrator. It is pretty handy plus it is pretty cheap.
Hi there. Algebrator is really fantastic! It's been months since I used this program and it worked like magic! Algebra problems that I used to spend answering for hours just take me 4-5 minutes to answer now. Just enter the problem in the software and it will take care of the solving and the best part is that it shows the whole solution so you don't have to figure out how did it come to that answer. |
grid Service Platform - grid WebOS -
Utilities/Other Utilities ... In this project, we combine the WebOS platform with the computing resources to offer users a friendlier grid environment. We have come up with a new and extremely lightweight approach to acquiring grid services via grid Widgets. ...
algebra - One On One -
Educational/Mathematics ... algebra One on One is an educational game for those wanting a fun way to learn and practice algebra. This program covers 21 functions which includes maximums, minimums, absolute values, averages, x/y, ax + b, axy + b, ax + by + c, squares, cubes, and so on. It has a practice and a game area. It has a great help system that makes it easy for the beginner to do and understand algebra. It also has a "Einstein" level that even algebra experts will find fun and challenging. You can choose from a ten ...
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algebra Vision -
Educational/Mathematics ... algebra Vision is a unique educational software tool to help students develop algebraic problem solving strategies. It provides an environment to play and see algebra in a more tangible light. You can literally move expressions around! Draw lines connecting distributive elements! ...
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Infinite algebra 2 -
Educational/Other ... Stop searching through textbooks, old worksheets, and question databases. Infinite Pre-algebra helps you create questions with the characteristics you want them to have. It enables you to automatically space the questions on the page and print professional-looking assignments. Give Infinite algebra 2 a try to fully assess its capabilities! FEATURES: TE Change All Questions to Free-Response TE Change All Questions to Multiple-Choice TE Change the Heading TE Change the Starting Number TE ...
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MathAid algebra II -
Educational/Mathematics ... Highly interactive tutorials and self-test system for individual e-learning, home schooling, college and high school rectangular ...
Algebra Grid Work
From Short Description
1.
MathProf -
Educational/Education ... MathProf can display mathematical correlations in a very clear and simple way. The program covers the areas Analysis, Geometry, algebra, Stochastics, Vector algebra. It helps Junior High School students with problems in Geometry and algebra. High School and College students, seeking to expand their knowledge into further reaching mathematical concepts find this program very useful as well. ...
Xceed grid for .NET -
Internet/Tools & Utilities ... Introdu grid-enabled apps. ...
6.
Linear algebra Class Library -
Utilities/Other Utilities ... The Linear algebra class library for Java provides a full set of tools to programmers who need linear algebra operations to use in their own projects.Currently the library supports elementary matrix operations. ...
7.
Basic algebra Shape-Up -
Educational/Mathematics ... Basic algebra Shape-Up helps students master specific basic algebra skills, while providing teachers with measurable results. Concepts covered include creating formulas; using ratios, proportions, and scale; working with integers, simple and multi-step equations, and variables. Students start with an assessment and receive immediate instructional feedback throughout. Step-by-step tutorials, which introduce each level, can be referred to during practice. Problems are broken down into small, ...
EMSolution algebra Equations short -
Educational/Mathematics ... This bilingual problem-solving mathematics software allows you to work through 5018 algebra equations with guided solutions, and encourages to learn through in-depth understanding of each solution step and repetition rather than through rote memorization. The software includes linear, quadratic, biquadratic, reciprocal, cubic and fractional algebraic equations. Each solution step is provided with its objective, related definition, rule and underlying math formula or theorem. A translation option ...
10.
EMSolution Arithmetic -
Educational/Mathematics ... This bilingual problem-solving mathematics software allows you to work through 36319 arithmetic and pre-algebra problems with guided solutions, and encourages to learn through in-depth understanding of each solution step and repetition rather than through rote memorization. Each solution step is provided with its objective, related definition, rule and underlying math formula or theorem. A translation option offers a way to learn math lexicon in a foreign language. Test preparation options ...
Algebra Grid Work
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Innoexe Visual algebra -
Educational/Mathematics ... Innoexe Visual algebra works in three modes. work with others over the internet, network, or alone. Chat with others and solve problems at the same time. IVA is perfect for tutors teaching students over the internet or a network connection. Innoexe Visual algebra will solve your problems step by step and explain as it goes. Innoexe Visual algebra will change the way you look at algebra problems. All registered users will receive free up grades. ...
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Gaigen -
Utilities/Other Utilities ... Gaigen is a Geometric algebra Implementation Generator. You specify the geometric algebra you want to use in your (C++) project, and then Gaigen generates C++ code that implemenents this algebra. Requires FLTK library for the user interface. ...
3.
Equator for Mac OS -
Educational/Mathematics ... A word-processor-like editor specifically designed for use in high school and college-level algebra-based physics courses. Equator helps high school and college physics students to easily navigate the algebra. The program integrates a math editor, drawing palette, formula reference library, drag-and-drop algebra generator, and calculator. It records each work step, accepts figures and comments, collects all of an assignment into a single file, and in one click prints homework-quality documents. ...
Math.NET -
Utilities/Mac Utilities ... Math.NET aims to provide a self contained clean framework for symbolic mathematical (Computer algebra System) and numerical/scientific computations, including a parser and support for linear algebra, complex differential analysis, system solving and more ...
7.
The grid Framework -
Utilities/Mac Utilities ... grid Framework allows you to use the power of grid computing in a natural way. Just devlop your application and let the framework do all the dirty work for you. ...
MiJAL (Minor Java algebra Library) -
Utilities/Mac Utilities ... The Minor Java algebra Library aims to become an open, standard Java library for common problems in the domain of algebra and selected optimisation problems such as TSP and others. MiJAL is aimed to be used in educational envirements but not limited to. ...
10.
Edit Grids for Mac OS -
Multimedia & Design/Other Related Tools ... A unique grid Warping with the help of a mesh lets you move points of the overlay grid in any direction to expand, pinch and distort like a rubber desktop.- You may decide to turn your grid as a set of Bezier curves.- Save any distortion effect and reapply it on another picture!- You can adjust the number of steps independently in X and Y direction on your grid. - compatibility update for Aperture 3.1 they are released! Always visit Shareme for your software needs. |
Arithmetic - This is the workshop for you if you need to brush up on your basic number skills including fractions, decimals, and percentages. Variables (like x and y) will not be covered.
Date
Time
Location
Presenter
Monday, December 2
6:00 - 8:00 pm
CentreTech Campus, Classroom Rm 207A
LaVelle Knight
Friday, December 6
2:00 - 4:00 pm
CentreTech Campus, Classroom Rm 106
Mike Pfaff
Wednesday, January 8
6:00 - 8:00 pm
CentreTech Campus, Classroom Rm 207A
LaVelle Knight
Saturday, January 11
9:00 - 11:00 am
CentreTech Campus, Classroom Rm 207A
LaVelle Knight
Elementary Algebra - This workshop is for you if, at some point, you've taken algebra and if your basic arithmetic is solid. This workshop will cover working with variables (like x and y), simplifying expressions, and solving equations. (Please attend the Arithmetic workshop if you want to brush up on your numbers.)
We've prepared an online mathematics pre-assessment workshop video you can watch at the convenience of your own computer. The files are sizeable, so users on slower connections may prefer to download the entire workshop in one zip file (100 megabytes; 4-7 hrs on a dial-up connection, 2-24 mins on broadband) instead of viewing them here.
If you are deaf or hard of hearing and would like to have this information interpreted for you, please contact the Accessibility Services Office at Reniece.Jones@CCAurora.edu or 303.361.7395 V/TDD/VP to schedule an interpreter. |
Math Mammoth Fractions & Decimals 3 continues the study of fraction and decimal topics, on the 6th grade level. The goal of the book is to go through all of the fraction and decimal arithmetic,... More > using up to six decimal digits and larger denominators in fractions than what is commonly encountered in 4th and 5th grade materials. It starts out with the study of decimals, the metric system, and using decimals in measuring units. Scientific notation is a new topic.<Yikes! Chemistry is coming up! This book is designed for beginning chemistry students who would like to master the math skills they will need to be successful in chemistry (and may have missed along... More > the way).
The topics covered include: using units, algebra for chemistry, scientific notation, scientific calculators, significant figures, making conversions, graphing with calculators and Excel, direct and inverse proportions, the mole concept and geometry for chemistry.
If a student completes this book before taking a chemistry course, they will get better grades, enjoy chemistry more and find themselves helping their friends with the concepts they learned here.< Less |
Description
This package contains the Access Kit for the Trigsted/Bodden/Gallaher MyMathLab eCourse plus the Guided Notebook.
Developmental Mathematics by Trigsted, Bodden, and Gallaher is the first online, completely "clickable" combined Prealgebra, Beginning Algebra, and Intermediate Algebra text to take full advantage of MyMathLab's features and benefits. Kirk Trigsted saw marked improvements in student learning when he started teaching with MyMathLab, but he noticed that most students started their assignments by going directly to the MyMathLab homework exercises without consulting their textbook. This inspired Kirk to write a true eText, built within MyMathLab, to create a dynamic, seamless learning experience that would better meet the needs and expectations of his students. Completely clickable and fully integrated—the Trigsted eText is designed for today's learners.
Developmental Mathematics is also available to be packaged with two printed resources to provide additional support for you:
The eText Reference is a spiral-bound, printed version of the eText that provides a place for you to do practice work and summarize key concepts from the online videos and animations. In addition to the benefits it provides you, the eText Reference is also a nice resource for those instructors that prefer a printed text for class preparation.
The Guided Notebook is an interactive workbook that guides you through the course by asking you to write down key definitions and work through important examples for each section of the eText. This resource is available in a three-hole-punched, unbound format to provide the foundation for a personalized course notebook. You can integrate your class notes and homework notes within the appropriate section of the Guided Notebook. Instructors can customize the Guided Notebook files found within MyMathLab.
Table of Contents
Module 1. Whole Numbers
1.1 Study Tips for This Course
1.2 Introduction to Whole Numbers
1.3 Adding and Subtracting Whole Numbers; Perimeter
1.4 Multiplying Whole Numbers; Area
1.5 Dividing Whole Numbers
1.6 Exponents and Order of Operations
1.7 Introduction to Variables, Algebraic Expressions, and Equations
Module 2. Integers and Introduction to Solving Equations
2.1 Introduction to Integers
2.2 Adding Integers
2.3 Subtracting Integers
2.4 Multiplying and Dividing Integers
2.5 Order of Operations
2.6 Solving Equations: The Addition and Multiplication Properties
Module 3. Solving Equations and Problem Solving
3.1 Simplifying Algebraic Expressions
3.2 Revisiting the Properties of Equality
3.3 Solving Linear Equations in One Variable
3.4 Using Linear Equations to Solve Problems
Module 4. Fractions and Mixed Numbers
4.1 Introduction to Fractions and Mixed Numbers
4.2 Factors and Simplest Form
4.3 Multiplying and Dividing Fractions
4.4 Adding and Subtracting Fractions
4.5 Complex Fractions and Review of Order of Operations
4.6 Operations on Mixed Numbers
4.7 Solving Equations Containing Fractions
Module 5. Decimals
5.1 Introduction to Decimals
5.2 Adding and Subtracting Decimals
5.3 Multiplying Decimals; Circumference
5.4 Dividing Decimals
5.5 Fractions, Decimals and Order of Operations
5.6 Solving Equations Containing Decimals
Module 6. Ratios and Proportions
6.1 Ratios, Rates, and Unit Prices
6.2 Proportions
6.3 Proportions and Problem Solving
6.4 Congruent and Similar Triangles
6.5 Square Roots and the Pythagorean Theorem
Module 7. Percent
7.1 Percents, Decimals, and Fractions
7.2 Solving Percent Problems with Equations
7.3 Solving Percent Problems with Proportions
7.4 Applications of Percent
7.5 Percent and Problem Solving: Sales Tax, Commission, and Discount
7.6 Percent and Problem Solving: Interest
Module 8. Geometry and Measurement
8.1 Lines and Angles
8.2 Perimeter, Circumference, and Area
8.3 Volume and Surface Area
8.4 Linear Measurement
8.5 Weight and Mass
8.6 Capacity
8.7 Time and Temperature
Module 9. Statistics
9.1 Mean, Median, and Mode
9.2 Histograms
9.3 Counting
9.4 Probability
Module 10. Real Numbers and Algebraic Expressions
10.1 The Real Number System
10.2 Adding and Subtracting Real Numbers
10.3 Multiplying and Dividing Real Numbers
10.4 Exponents and Order of Operations
10.5 Variables and Properties of Real Numbers
10.6 Simplifying Algebraic Expressions
Module 11. Linear Equations and Inequalities in One Variable
11.1 The Addition and Multiplication Properties of Equality
11.2 Solving Linear Equations in One Variable
11.3 Introduction to Problem Solving
11.4 Formulas
11.5 Geometry and Uniform Motion Problem Solving
11.6 Percent and Mixture Problem Solving
11.7 Linear Inequalities in One Variable
11.8 Compound Inequalities; Absolute Value Equations and Inequalities
Module 12. Graphs of Linear Equations and Inequalities in Two Variables
12.1 The Rectangular Coordinate System
12.2 Graphing Linear Equations in Two Variables
12.3 Slope
12.4 Equations of Lines
12.5 Linear Inequalities in Two Variables
Module 13. Systems of Linear Equations and Inequalities
13.1 Solving Systems of Linear Equations by Graphing
13.2 Solving Systems of Linear Equations by Substitution
13.3 Solving Systems of Linear Equations by Elimination
13.4 Applications of Linear Systems
13.5 Systems of Linear Inequalities
13.6 Systems of Linear Equations in Three Variables
Module 14. Exponents and Polynomials
14.1 Exponents
14.2 Introduction to Polynomials
14.3 Adding and Subtracting Polynomials
14.4 Multiplying Polynomials
14.5 Special Products
14.6 Negative Exponents and Scientific Notation
14.7 Dividing Polynomials
14.8 Polynomials in Several Variables
Module 15. Factoring Polynomials
15.1 Greatest Common Factor and Factoring by Grouping
15.2 Factoring Trinomials of the Form x2 + bx + c
15.3 Factoring Trinomials of the Form ax2 + bx + c Using Trial and Error
15.4 Factoring Trinomials of the Form ax2 + bx + c Using the ac Method |
Numbers
This unit will help you understand more about real numbers and their properties. It...
This
By the end of this unit you should be able to:
explain the relationship between rational numbers and recurring decimals;
explain the term irrational number and describe how such a number can be represented on a number line;
find a rational and an irrational number between any two distinct real numbers;
solve inequalities by rearranging them into simpler equivalent forms;
solve inequalities involving modulus signs;
state and use the Triangle Inequality;
use the Binomial Theorem and mathematical induction to prove inequalities which involve an integer n;
explain the terms bounded above, bounded below and bounded;
use the strategies for determining least upper bounds and greatest lower bounds;
state the Least Upper Bound Property and the Greatest Lower Bound Property;
explain how the Least Upper Bound Property is used to define arithmetical operations with real numbers;
Hi,
I've spoken to the course team and this unit, along with several others in Maths, is currently being looked at. Due to a system change some of the file formats are not compatible and so the course teams are deciding how to deal with the problem.
I have asked to be informed as soon as they have made their decision and I will get back to you when I hear from them.
Many apologies for the problems on this unit.
Best wishes
OpenLearn Moderator
Copyright & revisions
Publication details
Originally published: Wednesday, 29 |
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 condition. Interior is tight and bright. Paperback cover has moderate scuffing and corner bumps from shelf and reader wear. FREE shipping upgrade - If you live in the USA this book will arrive in...show more 4 to 6 business days when you choose the lowest cost shipping method when checking out. 100% Satisfaction Guaranteed. We ship promptly and worldwide |
Outlines and Highlights for Excursions in Modern Mathematics by Peter Tannenbaum, Isbn : 9780321568038
Student Resource Guide To Accompany Excursions In Modern Math
Videos on DVD with Optional Subtitles for Excursions in Modern Mathematics
Summary
For undergraduate courses in Liberal Arts Mathematics, Quantitative Literacy, and General Education. This very successful liberal arts mathematics textbook is a collection of "excursions"
Table of Contents
Preface
xv
part 1 The Mathematics of Social Choice
The Mathematics of Voting
2
(46)
The Paradoxes of Democracy
Preference Ballots and Preference Schedules
4
(2)
The Plurality Method
6
(4)
The Borda Count Method
10
(2)
The Plurality-with-Elimination Method (Instant Runoff Voting)
12
(5)
The Method of Pairwise Comparisons (Copeland's Method)
17
(6)
Rankings
23
(25)
Conclusion: Elections, Fairness, and Arrow's Impossibility Theorem
28
(1)
Profile: Kenneth J. Arrow
29
(1)
Key Concepts
30
(1)
Exercises
30
(11)
Projects and Papers
41
(1)
Appendix 1: Breaking Ties
42
(1)
Appendix 2: A Sampler of Elections in the Real World
43
(3)
References and Further Readings
46
(2)
Weighted Voting Systems
48
(36)
The Power Game
Weighted Voting Systems
50
(3)
The Banzhaf Power Index
53
(8)
Applications of Banzhaf Power
61
(2)
The Shapley-Shubik Power Index
63
(5)
Applications of Shapley-Shubik Power
68
(16)
Conclusion
70
(1)
Profile: Lloyd S. Shapley
71
(1)
Key Concepts
72
(1)
Exercises
72
(7)
Projects and Papers
79
(1)
Appendix: Power in the Electoral College
80
(2)
References and Further Readings
82
(2)
Fair Division
84
(44)
The Mathematics of Sharing
Fair-Division Games
86
(2)
Two Players: The Divider-Chooser Method
88
(1)
The Lone-Divider Method
89
(6)
The Lone-Chooser Method
95
(3)
The Last-Diminisher Method
98
(5)
The Method of Sealed Bids
103
(3)
The Method of Markers
106
(22)
Conclusion
109
(1)
Profile: Hugo Steinhaus
110
(1)
Key Concepts
111
(1)
Exercises
111
(15)
Projects and Papers
126
(1)
References and Further Readings
127
(1)
The Mathematics of Apportionment
128
(32)
Making the Rounds
Apportionment Problems
129
(5)
Hamilton's Method and the Quota Rule
134
(2)
The Alabama and Other Paradoxes
136
(5)
Jefferson's Method
141
(3)
Adams's Method
144
(1)
Webster's Method
145
(15)
Conclusion
147
(2)
Historical Note: A Brief History of Apportionment in the United States |
Deep Dive into Mathematica's Numerics: Applications and Tips
Andrew Moylan
In this course from the Wolfram Mathematica Virtual Conference 2011, you'll learn how to best use Mathematica's numerics functions in advanced settings. Topics include techniques and best practices for using multiple numerics functions together, advanced numeric features, and understanding precision and accuracy. |
7.7 The Distance Formula, the Midpoint Formula, and Other Applications
7.8 The Complex Numbers
8. Quadratic Functions and Equations
8.1 Quadratic Equations
8.2 The Quadratic Formula
8.3 Studying Solutions of Quadratic Equations
8.4 Applications Involving Quadratic Equations
8.5 Equations Reducible to Quadratic
8.6 Quadratic Functions and Their Graphs
8.7 More About Graphing Quadratic Functions
8.8 Problem Solving and Quadratic Functions
8.9 Polynomial Inequalities and Rational Inequalities
9. Exponential Functions and Logarithmic Functions
9.1 Composite Functions and Inverse Functions
9.2 Exponential Functions
9.3 Logarithmic Functions
9.4 Properties of Logarithmic Functions
9.5 Common Logarithms and Natural Logarithms
9.6 Solving Exponential Equations and Logarithmic Equations
9.7 Applications of Exponential Functions and Logarithmic Functions
10. Conic Sections
10.1 Conic Sections: Parabolas and Circles
10.2 Conic Sections: Ellipses
10.3 Conic Sections: Hyperbolas
10.4 Nonlinear Systems of Equations
11. Sequences, Series, and the Binomial Theorem
11.1 Sequences and Series
11.2 Arithmetic Sequences and Series
11.3 Geometric Sequences and Series
11.4 The Binomial Theorem
Marvin Bittinger has been teaching math at the university level for more than thirty-eight years. Since 1968, he has been employed at Indiana University Purdue University Indianapolis, Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled "Baseball and Mathematics." His hobbies include hiking in Utah, baseball, golf, and bowling. In addition, he also has an interest in philosophy and theology, in particular, apologetics. Professor Bittinger currently lives in Carmel, Indiana, with his wife Elaine. He has two grown and married sons, Lowell and Chris, and four granddaughters.
David Ellenbogen has taught math at the college level for nearly 30 years, spending most of that time in the Massachusetts and Vermont community college systems, where he has served on both curriculum and developmental math committees. He has taught at St. Michael's College and The University of Vermont. Professor Ellenbogen has been active in the American Mathematical Association of Two Year Colleges (AMATYC) since 1985, having served on its Developmental Mathematics Committee and as a delegate. He has been a member of the Mathematical Association of America (MAA) since 1979. He has authored dozens of texts on topics ranging from prealgebra to calculus and has delivered lectures on the use of language in mathematics. Professor Ellenbogen received his bachelor's degree in mathematics from Bates College and his master's degree in community college mathematics education from The University of Massachusetts–Amherst. In his spare time, he enjoys playing piano, biking, hiking, skiing and volunteer work. He currently serves on the boards of the Vermont Sierra Club and the Vermont Bicycle Pedestrian Coalition. He has two sons, Monroe and Zachary.
Barbara Johnson has a BS in mathematics from Bob Jones University and a MS in math from Clemson University. She has taught high school and college math for 25 years, and enjoys the challenge of helping each student grow in appreciation for and understanding of mathematics. As a Purdue Master Gardener, she also enjoys helping others learn gardening skills. Believing that the best teacher is always learning, she recently earned a black belt in karate. |
Linear Algebra
A college level study of linear algebra which includes systems of equations, matrices, vector spaces, linear transformations, bases, dimension, eigenvalues, eigenvectors, and orthogonality. This course emphasizes computational techniques, geometry and theoretical structure, creative problem solving, and proofs. Upon successful completion of the course, the student will receive 3 credit hours from the Central Virginia Community College.
Course Materials:
Textbook: David C. Lay, Linear Algebra and its Applications, 2nd edition. We will also use graphing calculators.
Typical Hours for Students Session I (7:30-10:10)Session II (8:25-11:05)
Period 1: 7:30-8:20 Period 2: 8:25-9:15
Period 2: 8:25-9:15 Period 3: 9:20-10:10
Period 3: 9:20-10:10 Period 4: 10:15-11:05 |
same thing. I remembered too late that you can just subtract the relevant exponents from each other when dividing identical expressions with different exponential values. Been a while since Algebra.
I have a harder time with trig identities and certain relations to them, like the unit circle. I can use it, I just have a hard times having it click it my head. I also often mix up the "direction" I'm going with derivatives and integrals. "Was the integral of 1/x = lnx, or was that the derivative?"
The thing I never grasped very well was proofs. I've only had to do them in a geometry class years ago, but I remember doing terrible on that exam. I never understood what my teacher wanted for proofs, as far as work goes.
Well, not exactly. Just about every single algebraic formula was derived through calculus. So, in reality, algebra requires a solid understanding of calculus, but it can be taught as if calculus doesn't exist.
You are correct, but i must say fuck abstract algebra. Give me a PDE any day over that shit.
As an edit - Calculus also does not really need a high understanding of algebra either. Take any analysis course and its main purpose is to prove the shit you learn in calculus. Just starting from definitions and shit. However most people do not get that far to really understand either field.
I've seen people with calculators that can solve differential equations, so that's not entirely true. Of course, the important part of higher level math is actually knowing how to do the work, not just how to type an equation into a calculator.
Ah, I guess that depends on the professor then. For most of my classes we're allowed to use calculators if we want, but we have to show all of our work anyway. So the calculator would really only be useful for checking your answer.
That's the way my teacher is. My last teacher though was a horrible teacher and a lot of people were failing his class. He just did the problems without explaining all the steps, then gave out an hour of work. He only looked at the final answer on tests though so I was able to pass using the calculator. Now that I've switched teachers, I'm finally learning again how to do the problems. One thing to note is that I know how to do most of the problems; just over time, I forget small things. Once a teacher goes over the problem again I catch on quickly and end up getting A's on tests.
I think it's more worthless in a physics class than a math class. The thing making physics hard is figuring out what equations you actually NEED to throw into a calculator. The actual computation is the easy part. |
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.
Allen R. Angel is the author of Survey of Mathematics with Applications, A (9th Edition), published 2012 under ISBN 9780321759665 and 0321759664. Seven hundred ninety three Survey of Mathematics with Applications, A (9th Edition) textbooks are available for sale on ValoreBooks.com, one hundred ninety nine used from the cheapest price of $58.57, or buy new starting at $74.00.[read more]
Ships From:Multiple LocationsShipping:Standard, ExpeditedComments:RENTAL: Supplemental materials are not guaranteed (access codes, DVDs, workbooks). Book is in great shape. No highlighting or writing. May not contain CDs or access codes. Awesome ... [more]RENTAL: Supplemental materials are not guaranteed (access codes, DVDs, workbooks). Book is in great shape. No highlighting or writing. May not contain CDs or access codes. Awesome customer service! We ship to APO/FPO. We ship every business day! AD [less]
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Ships From:Raleigh, NCShipping:Standard, ExpeditedComments:NEW, might have cosmetic shelf wears, BOOK ONLY shipped the SAME or next day. Perfect absolutelly... [more]NEW, might have cosmetic shelf wears, BOOK ONLY shipped the SAME or next day. Perfect absolutelly new. BUY WITH CONFIDENCE. FREE TRACKING, EXPEDITED SHIPPING AVAILABLE |
ugopolski's Precalculus: Functions and Graphs, Fourth Edition, gives you the essential strategies you need to make the transition to calculus. Throughout this book, you will find carefully placed learning aids and review tools to help them learn the math without getting distracted. The new edition includes over 900 additional exercises that are specifically designed to increase student understanding and retention of the concepts. Along the way, you'll see how the algebra connects to your future calculus course, with tools like Foreshadowing Ca... MORElculus and Concepts of Calculus. Dugopolski's emphasis on problem solving and critical thinking helps you be successful in this course, as well as in future calculus courses.
Concepts of Calculus: Instantaneous Rate of Change of the Power Functions
4. Exponential and Logarithmic Functions
4.1 Exponential Functions and Their Applications
4.2 Logarithmic Functions and Their Applications
4.3 Rules of Logarithms
4.4 More Equations and Applications
Chapter 4 Highlights
Chapter 4 Review Exercises
Chapter 4 Test
Tying it all Together
Concepts of Calculus: The Instantaneous Rate of Change of f(x)= ex
5. The Trigonometric Functions
5.1 Angles and Their Measurements
5.2 The Sine and Cosine Functions
5.3 The Graphs of the Sine and Cosine Functions
5.4 The Other Trigonometric Functions and Their Graphs
5.5 The Inverse Trigonometric Functions
5.6 Right Triangle Trigonometry
Chapter 5 Highlights
Chapter 5 Review Exercises
Chapter 5 Test
Tying it all Together
Concepts of Calculus: Evaluating Transcendental Functions
6. Trigonometric Identities and Conditional Equations
6.1 Basic Identities
6.2 Verifying Identities
6.3 Sum and Difference Identities
6.4 Double-Angle and Half-Angle Identities
6.5 Product and Sum Identities
6.6 Conditional Trigonometric Equations
Chapter 6 Highlights
Chapter 6 Review Exercises
Chapter 6 Test
Tying it all Together
Concepts of Calculus: Area of a Circle and π
7. Applications of Trigonometry
7.1 The Law of Sines
7.2 The Law of Cosines
7.3 Vectors
7.4 Trigonometric Form of Complex Numbers
7.5 Powers and Roots of Complex and Numbers
7.6 Polar Equations
Chapter 7 Highlights
Chapter 7 Review Exercises
Chapter 7 Test
Tying it all Together
Concepts of Calculus: Limits and Asymptotes
8. Systems of Equations and Inequalities
8.1 Systems of Linear Equations in Two Variables
8.2 Systems of Linear Equations in Three Variables
8.3 Nonlinear Systems of Equations
8.4 Partial Fractions
8.5 Inequalities and Systems of Inequalities in Two Variables
8.6 The Linear Programming Model
Chapter 8 Highlights
Chapter 8 Review Exercises
Chapter 8 Test
Tying it all Together
Concepts of Calculus: Instantaneous Rate of Change and Partial Fractions
9. Matrices and Determinants
9.1 Solving Linear Systems Using Matrices
9.2 Operations with Matrices
9.3 Multiplication of Matrices
9.4 Inverses of Matrices
9.5 Solution of Linear Systems in Two Variables Using Determinants
9.6 Solution of Linear Systems in Three Variables Using Determinants
Chapter 9 Highlights
Chapter 9 Review Exercises
Chapter 9 Test
Tying it all Together
10. The Conic Sections
10.1 The Parabola
10.2 The Ellipse and the Circle
10.3 The Hyperbola
10.4 Rotation of Axes
10.5 Polar Equations of the Conics
Chapter 10 Highlights
Chapter 10 Review Exercises
Chapter 10 Test
Tying it all Together
Concepts of Calculus: The Reflection Property of a Parabola
11. Sequences, Series, and Probability
11.1 Sequences
11.2 Series
11.3 Geometric Sequences and Series
11.4 Counting and Permutations
11.5 Combinations, Labeling, and the Binomial Theorem
11.6 Probability
11.7 Mathematical Induction
Chapter 11 Highlights
Chapter 11 Review Exercises
Chapter 11 Test
Concepts of Calculus: Limits of Sequences
A. Appendix: Basic Algebra Review
A.1 Real Numbers and Their Properties
A.2 Exponents and Radicals
A.3 Polynomials
A.4 Factorials Polynomials
A.5 Rational Expressions
B. Appendix: Solutions to Try This Exercises
Credits
Answers to Selected Exercises
Index of Applications
Index
Mark Dugopolski was born in Menominee, Michigan. After receiving a B.S. from Michigan State University, he taught high school for four years, and then went on to receive an M.S. in mathematics from Northern Illinois University. He also received a Ph.D. in the area of topology from the University of Illinois at Champaign-Urbana. Mark has been teaching at Southeastern Louisiana in Hammond, LA, ever since. Mark has been writing textbooks for about fifteen years. He is married and has two daughters, and enjoys playing tennis, jogging, and riding his bicycle in his spare time. |
Advanced Mathematics: An Incremental Development
Advanced Mathematics fully integrates topics from algebra, geometry, trigonometry, discrete mathematics, and mathematical analysis. Word problems are developed throughout the problem sets and become progressively more elaborate. With this practice, high-school level students will be able to solve challenging problems such as rate problems and work problems involving abstract quantities. Conceptually oriented problems that help prepare students for college entrance exams (such as the ACT and SAT) are included in the problem sets.
Customer Reviews:
Saxon does it again!
By "hranda" - December 16, 1999
I used the Saxon books through all of my High school math courses, and think they are *the* best way to learn algebra and higher math. The key to the success is really twofold. 1) New types of problems are introduced with every lesson - but these are not drilled into the student by giving them 20 or more "practice problems" to do. Instead, only about 5 of the "new" problems are given for practice - letting the new ideas "sink in" over a period of days. 2) Constant review. Because the student is not burdened with lots of new ideas every lesson, the remaining homework problems are review of everything the student has done to date. This ensures that the student doesn't forget how to do the math, and makes reviewing for a test almost obsolete. I am now in graduate school, soon to get my PhD in theoretical biophysics. Learning math so well in high school put me far ahead in college. I also tutor out of the Saxon books (and others, depending on... read more
Excellence in Mathematics
By L. Strube - March 4, 2006
I have been using Saxon mathematics for 15 years, first as a 5th-12th grade student and more recently as a tutor. This program is excellent and like one of the other reviewers I can agree that even my "average" Saxon students have significantly better mathematics skills that those students using other programs.
I began using Saxon math in 5th grade. Prior to that I used a typical "learn and drill" method. A new concept was taught and drilled for 20+ problems and then the instruction moved on to another topic. By the time I reached an end of unit exam I had forgotten the early material.
Then in 5th grade we changed curriculums. I didn't become a "math lover" overnight. In fact, although my math skills improved, I adamently hated math all the way through junior high. Then I began algebra. By the end of Saxon's algebra 2 textbook I loved algebra and was making high A's in my homework.
A couple of years after highschool I was invited to begin... read more
Amazing
By Mark A. Felice "chucklehead" - November 13, 2007
I am currently using Saxons book, and it has greatly increased my understanding about Pre Calculus. I have been using Saxon for three years (since i was in 6th grade) and have failed to find a flaw in their work. The one-star review written doesn't understand their teaching method. By having a wide variety of problems in each problem set, Saxon really gets the lesson in your head. I currently teach myself the material and have a 98 average. If you REALLY want to learn Advanced mathematics, get this book! |
More About
This Textbook
Overview
The new 3rd edition of Cynthia Young's Algebra & Trigonometry continues to bridge the gap between in-class work and homework by helping readers overcome common learning barriers and build confidence in their ability to do mathematics. The text features truly unique, strong pedagogy and is written in a clear, single voice that speaks directly to students and mirrors how instructors communicate in lectures. In this revision, Young enables readers to become independent, successful learners by including hundreds of additional exercises, more opportunities to use technology, and a new themed modeling project that empowers them to apply what they have learned in the classroom to the world outside the classroom. The seamlessly integrated digital and print resources to accompany Algebra & Trigonometry 3e offer additional tools to help users experience success.
Meet the Author
Cynthia Young received her BA in Math Education from UNC in 1990, has two masters, one in Mathematical Sciences from UCF in 1993 and a second in Electrical Engineering from the University of Washington in 1997. Finally, she received a PhD in Applied Mathematics from the University of Washington in 1996. She is already a tenured professor at UCF and is very actively involved in the supervision of UCF's graduate and undergraduate research assistants. Before becoming an award-winning Associate Professor at UCF, Cynthia taught High School. Cynthia received numerous grants and was named the principal investigator on six military and academic research projects. She has been an administrator/advisor to the Florida Space Institute at the Kennedy Space Center since 1998. Cynthia is a veteran presenter at conferences and conventions and has published over a dozen journal articles. In addition, she has been a contributor to several texts, including a College Algebra workbook for McGraw-Hill. Lastly, she edited the Marcel Decker's Optical Engineering Encyclopedia |
really nice and helpful even though he uses the textbook, you can learn more if you do the work too. You get used to the accent. His tests are tough, but they're ok. Average tends to be ~55 so anything above that and you're good.
Excellent Calc teacher. Lecture is very organized and is responsive to students. He uses effective methods to help students clear the fog surrounding Calculus. Introduces a lecture with how a topic applies to the real world. Game me a strong foundation for Calc II
He is a nice guy. Moves rather fast in the lectures. Once you get used to the Chinese accent, you'll be alright. I don't go to class much as he confuses me, so I heavily depend on recitation. Guess it depends on the person. Exams aren't too easy - make sure you do everything on the syllabus, even though he doesn't personally assign it for homework.
He's a pretty decent lecturer (once you get past the Engrish, count the times he says "Wector we"), but the fact that he takes attendance for the lecture and other silly things (like seating by name during exams, for example) will drive you up the wall.
You will get used to his accent after a few classes. If you want to understand, go to class, but you could probably just teach yourself. Class is heavily curved (i got a 52% on the final, and 68% on midterm, and stopped handing in homework after the midterm) and still got a C. The class is hard, but with such a big curve it's bearable.
The accent is terrible, but the class is great. He always seems to have the answer to any question one may ask and to every problem in the book. He presents the classes very organize and clearly. The best way of learning Calculus
Very clear, much better than other professors. If you don't understand something, he'll think of another way to present it, and he'll do so until you understand - sign of a true teacher. Accent is thick, but you get used to it.
This class is simple, so are the exams. I see other people in Calc I who have to do all the problems on the syllabus, Rong only makes you do 10 a week, and a workshop. Recessitation is pointless, but u have to go.
Jesus, I can't seem to understand why people have such an issue with these classes. If you're in engineering and you take this guy expect an easy A the exams are painfully easy, you can sleep through all his classes and miss absolutely nothing. Recitation is useless. Easy class. |
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$158.59Elayn Martin-Gay's success as a developmental math author starts with a strong focus on mastering the basics through well-written explanations, innovative pedagogy and a meaningful, integrated program of learning resources. The revisions to this edition provide new pedagogy and resources to build reader confidence and help readers develop basic skills and understand concepts. Martin-Gay's 4-step problem solving process-Understand, Translate, Solve and Interpret-is integrated throughout. Also includes new features such as Study Skills Reminders, "Integrated Reviews", and "Concept Checks." For readers interested in learning or revisiting essential skills in beginning and intermediate algebra through the use of lively and up-to-date applications.
Table of Contents
Preface
p. xiii
Index of Applications
p. xxiv
Review of Real Numbers
p. 2
Tips for Success in Mathematics
p. 4
Symbols and Sets of Numbers
p. 8
Fractions
p. 17
Introduction to Variable Expressions and Equations
p. 25
Adding Real Numbers
p. 34
Subtracting Real Numbers
p. 41
Multiplying and Dividing Real Numbers
p. 48
Properties of Real Numbers
p. 56
Reading Graphs
p. 61
Chapter 1 Project: Creating and Interpreting Graphs
p. 68
Chapter 1 Vocabulary Check
p. 68
Chapter 1 Highlights
p. 69
Chapter 1 Review
p. 73
Chapter 1 Test
p. 76
Equations, Inequalities, and Problem Solving
p. 78
Simplifying Algebraic Expressions
p. 80
The Addition and Multiplication Properties of Equality
p. 86
Solving Linear Equations
p. 96
An Introduction to Problem Solving
p. 104
Formulas and Problem Solving
p. 113
Percent and Problem Solving
p. 121
Solving Linear Inequalities
p. 130
Chapter 2 Project: Developing a Budget
p. 140
Chapter 2 Vocabulary Check
p. 141
Chapter 2 Highlights
p. 142
Chapter 2 Review
p. 146
Chapter 2 Test
p. 148
Chapter 2 Cumulative Review
p. 149
Graphs and Functions
p. 150
The Rectangular Coordinate System
p. 152
Graphing Equations
p. 163
Introduction to Functions
p. 173
Graphing Linear Functions
p. 188
The Slope of a Line
p. 195
Equations of Lines
p. 209
Graphing Linear Inequalities
p. 220
Chapter 3 Project: Modeling Real Data
p. 225
Chapter 3 Vocabulary Check
p. 226
Chapter 3 Highlights
p. 227
Chapter 3 Review
p. 232
Chapter 3 Test
p. 235
Chapter 3 Cumulative Review
p. 236
Solving Systems of Linear Equations
p. 238
Solving Systems of Linear Equations by Graphing
p. 240
Solving Systems of Linear Equations by Substitution
p. 247
Solving Systems of Linear Equations by Addition
p. 253
Systems of Linear Equations and Problem Solving
p. 259
Chapter 4 Project: Analyzing the Courses of Ships
p. 269
Chapter 4 Vocabulary Check
p. 270
Chapter 4 Highlights
p. 271
Chapter 4 Review
p. 274
Chapter 4 Test
p. 275
Chapter 4 Cumulative Review
p. 276
Exponents and Polynomials
p. 278
Exponents
p. 280
Negative Exponents and Scientific Notation
p. 290
Polynomial Functions and Adding and Subtracting Polynomials
p. 298
Multiplying Polynomials
p. 309
Special Products
p. 313
Dividing Polynomials
p. 320
Synthetic Division and the Remainder Theorem
p. 326
Chapter 5 Project: Modeling with Polynomials
p. 330
Chapter 5 Vocabulary Check
p. 331
Chapter 5 Highlights
p. 332
Chapter 5 Review
p. 334
Chapter 5 Test
p. 337
Chapter 5 Cumulative Review
p. 338
Factoring Polynomials
p. 340
The Greatest Common Factor and Factoring by Grouping
p. 342
Factoring Trinomials of the Form x[subscript 2] + bx + c
p. 348
Factoring Trinomials of the Form ax[subscript 2] + bx + c
p. 354
Factoring Binomials
p. 362
Choosing a Factoring Strategy
p. 368
Solving Quadratic Equations by Factoring
p. 373
Quadratic Equations and Problem Solving
p. 380
An Introduction to Graphing Polynomial Functions
p. 391
Chapter 6 Project: Choosing Among Building Options
p. 400
Chapter 6 Vocabulary Check
p. 400
Chapter 6 Highlights
p. 401
Chapter 6 Review
p. 405
Chapter 6 Test
p. 406
Chapter 6 Cumulative Review
p. 407
Rational Expressions
p. 408
Rational Functions and Simplifying Rational Expressions
p. 410
Multiplying and Dividing Rational Expressions
p. 418
Adding and Subtracting Rational Expressions with Common Denominators and Least Common Denominator |
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Chapter 1: Analyzing Functions
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Topics in this chapter include: function minimums and maximums, increasing and decreasing functions, end behavior of functions, function families, transformations of functions, operations and compositions, and mathematical models. |
Mathematics
Mathematics is an expanding and evolving body of knowledge as well as a way of perceiving, formulating and solving problems in many disciplines. The subject is a constant interplay between the worlds of thought and application. The student of mathematics will find worthy challenges and the subsequent reward in meeting them.
The general student will find preparatory courses in precalculus mathematics and traditional mathematics courses such as calculus, linear algebra, geometry, abstract algebra, and analysis. Also, more specialized courses in discrete mathematics, number theory and the history of mathematics are offered. Special needs of Computer Science majors, Elementary Education majors and general education requirements are also met by courses in the Mathematics Department.
For those desiring concentrated work in mathematics, the Mathematics Department offers four programs leading to Bachelor degrees. |
Publisher's Description
Four Variables is a pre-algebra investigation for students in grades five through nine. The program secretly assigns values to four variables (w, x, y, and z) and the student must find these values by requesting the computer to perform operations with the variables. For example: the student might ask the program to divide x by z; the program would respond "x/z = 0.875." The are two different investigation types: one where all four operations are allowed, and one where only division is allowed |
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