Mathematical Ideas

by Miller, Charles David; Heeren, Vern E.; Hornsby, E. John

• ISBN13: 9780673998934
• ISBN10: 0673998932
• Edition: 8th
• Format: Hardcover
• Copyright: 1996-10-01
• Publisher: ADDISON-WESLEY EDUCATIONAL PUBLISHERS

Table of Contents

Approach to Problem Solving	1	(50)
Introduction to Inductive Reasoning	2	(8)
Investigating Number Patterns	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 System	860	(7)
Answers to Selected Exercises	867	(42)
Acknowledgments	909	(4)
Index	913