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Mathematical Ideas

ISBN: 9780673998934 | 0673998932
Edition: 8th
Format: Hardcover
Publisher: ADDISON-WESLEY EDUCATIONAL PUBLISHERS
Pub. Date: 10/1/1996

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Table of Contents
Approach to Problem Solving
1(50)
Introduction to Inductive Reasoning
2(8)
Investigating Number Patterns
... MORE		10(10)
Problem-Solving Strategies
20(11)
Calculating, Estimating, and Reading Graphs
31(20)
Extension: Using Writing to Learn About Mathematics
40(8)
Collaborative Investigation: Discovering Pascal's Triangle
48(1)
Test
49(2)
Sets
51(47)
Basic Concepts
52(7)
Venn Diagrams and Subsets
59(7)
Operations with Sets
66(14)
Surveys and Cardinal Numbers
80(7)
Cardinal Numbers of Infinite Sets
87(11)
Collaborative Investigation: A Survey of Your Class
95(1)
Test
96(2)
Logic
98(54)
Statements and Quantifiers
99(6)
Truth Tables
105(12)
The Conditional
117(10)
Extension: Circuits
124(3)
More on the Conditional
127(6)
Using Euler Diagrams to Analyze Arguments
133(5)
Using Truth Tables to Analyze Arguments
138(14)
Collaborative Investigation: The Logic of a Rental Contract
149(1)
Test
150(2)
Numeration and Mathematical Systems
152(62)
Historical Numeration Systems
153(9)
Arithmetic in the Hindu-Arabic System
162(9)
Converting Between Number Bases
171(11)
Clock Arithmetic and Modular Systems
182(14)
Other Finite Mathematical Systems
196(8)
Groups
204(10)
Collaborative Investigation: A Perpetual Calendar Algorithm
212(1)
Test
213(1)
Number Theory
214(40)
Prime and Composite Numbers
215(7)
Selected Topics from Number Theory
222(9)
Greatest Common Factor and Least Common Multiple
231(7)
The Fibonacci Sequence and the Golden Ratio
238(16)
Extension: Magic Squares
246(5)
Collaborative Investigation: Investigating an Interesting Property of Number Squares
251(1)
Test
252(2)
The Real Number System
254(64)
Introduction to Sets of Real Numbers
255(7)
Operations, Properties, and Applications of Real Numbers
262(13)
Rational Numbers and Decimals
275(14)
Irrational Numbers and Decimals
289(9)
Applications of Decimals and Percents
298(20)
Extension: Complex Numbers
311(4)
Collaborative Investigation: Babylonian Square Roots
315(1)
Test
315(3)
The Basic Concepts of Algebra
318(82)
Linear Equations
319(10)
Applications of Linear Equations
329(15)
Ratio, Proportion, and Variation
344(13)
Linear Inequalities
357(8)
Properties of Exponents and Scientific Notation
365(13)
Polynomials and Factoring
378(9)
Quadratic Equations and Applications
387(13)
Collaborative Investigation: Calculating the Magic Number in Sports
397(1)
Test
398(2)
Functions, Graphs, and Systems of Equations and Inequalities
400(87)
The Rectangular Coordinate System and Circles
401(8)
Lines and Their Slopes
409(9)
Equations of Lines
418(8)
An Introduction to Functions: Linear Functions and Applications
426(10)
Quadratic Functions and Applications
436(9)
Exponential and Logarithmic Functions and Applications
445(13)
Systems of Equations and Applications
458(18)
Linear Inequalities and Systems of Inequalities
476(11)
Extension: Linear Programming
479(4)
Collaborative Investigation: Modeling Data Using a Linear Function
483(1)
Test
484(3)
Geometry
487(88)
Points, Lines, Planes, and Angles
489(10)
Curves, Polygons, and Circles
499(9)
Perimeter, Area, and Circumference
508(14)
The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem
522(20)
Extension: Right Triangle Trigonometry
536(6)
Space Figures, Volume, and Surface Area
542(10)
Non-Euclidean Geometry, Topology, and Networks
552(12)
Chaos and Fractal Geometry
564(11)
Collaborative Investigation: Generalizing the Angle Sum Concept
571(1)
Test
572(3)
Counting Methods
575(44)
Counting by Systematic Listing
576(9)
The Fundamental Counting Principle
585(9)
Permutations and Combinations
594(10)
Pascal's Triangle and the Binomial Theorem
604(6)
Counting Problems Involving ``Not'' and ``Or''
610(9)
Collaborative Investigation: Approximating Factorials Using a Different Technique
617(1)
Test
618(1)
Probability
619(50)
Probability and Odds
621(9)
Events Involving ``Not'' and ``Or''
630(8)
Events Involving ``And''
638(11)
Binomial Probability
649(5)
Expected Value
654(9)
Simulation
663(6)
Collaborative Investigation: Approximating π Using Probability
667(1)
Test
667(2)
Statistics
669(77)
Frequency Distributions and Graphs
672(12)
Measures of Central Tendency
684(16)
Measures of Dispersion
700(9)
Measures of Position
709(9)
The Normal Distribution
718(16)
Extension: How to Lie with Statistics
727(7)
Regression and Correlation
734(12)
Collaborative Investigation: Combining Sets of Data
742(1)
Test
743(3)
Consumer Mathematics
746(59)
Interest and Inflation
747(17)
Extension: Annuities
761(3)
Consumer Credit
764(9)
Truth in Lending
773(9)
Buying a House
782(12)
Investing in the Stock Market
794(11)
Collaborative Investigation: To Buy or to Rent?
803(1)
Test
804(1)
Matrices and Their Applications
805(55)
Basic Operations on Matrices
807(8)
Multiplication of Matrices
815(12)
Matrix Row Operations and Systems of Equations
827(8)
Matrix Inverses; Input-Output Models
835(14)
Extension: Cryptography
846(3)
Matrices and Game Theory
849(11)
Collaborative Investigation: Algebraic Structure of the System of 2 x 2 Matrices
857(1)
Test
858(2)
Appendix The Metric System860(7)
Answers to Selected Exercises867(42)
Acknowledgments909(4)
Index913

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