Mathematics: A Human Endeavor

by Jacobs, Harold R.

• ISBN13: 9780716724261
• ISBN10: 071672426X
• Edition: 3rd
• Format: Hardcover
• Copyright: 1994-01-15
• Publisher: W. H. Freeman

Summary

For instructors of liberal arts mathematics classes who focus on problem-solving, Harold Jacobs's remarkable textbook has long been the answer, helping teachers connect with of math-anxious students. Drawing on over thirty years of classroom experience, Jacobs shows students how to make observations, discover relationships, and solve problems in the context of ordinary experience.

Table of Contents

Foreward	ix
Martin Gardner
A Letter to the Student	xi
Acknowledgments	xiii
Introduction: Mathematics---A Universal Language	1	(4)
Mathematical Ways of Thinking	5	(54)
The Path of a Billiard Ball	6	(6)
More Billiard-Ball Mathematics	12	(7)
Inductive Reasoning: Finding and Extending Patterns	19	(6)
The Limitations of Inductive Reasoning	25	(6)
Deductive Reasoning: Mathematical Proof	31	(8)
Number Tricks and Deductive Reasoning	39	(20)
Summary and Review	45	(5)
Further Exploration	50	(9)
Number Sequences	59	(62)
Arithmetic Sequences	60	(7)
Geometric Sequences	67	(8)
The Binary Sequence	75	(8)
The Sequence of Squares	83	(9)
The Sequence of Cubes	92	(7)
The Fibonacci Sequence	99	(22)
Summary and Review	107	(6)
Further Exploration	113	(8)
Functions and Their Graphs	121	(62)
The Idea of a Function	122	(7)
Descartes and the Coordinate Graph	129	(7)
Functions with Line Graphs	136	(9)
Functions with Parabolic Graphs	145	(8)
More Functions with Curved Graphs	153	(8)
Interpolation and Extrapolation: Guessing Between and Beyond	161	(22)
Summary and Review	168	(6)
Further Exploration	174	(9)
Large Numbers and Logarithms	183	(62)
Large Numbers	184	(8)
Scientific Notation	192	(7)
An Introduction to Logarithms	199	(10)
Decimal Logarithms	209	(7)
Logarithms and Scientific Notation	216	(8)
Exponential Functions	224	(21)
Summary and Review	230	(5)
Further Exploration	235	(10)
Symmetry and Regular Figures	245	(82)
Symmetry	246	(9)
Regular Polygons	255	(11)
Mathematical Mosaics	266	(10)
Regular Polyhedra: The Platonic Solids	276	(13)
Semiregular Polyhedra	289	(9)
Pyramids and Prisms	298	(29)
Summary and Review	309	(9)
Further Exploration	318	(9)
Mathematical Curves	327	(74)
The Circle and the Ellipse	328	(10)
The Parabola	338	(9)
The Hyperbola	347	(8)
The Sine Curve	355	(10)
Spirals	365	(9)
The Cycloid	374	(27)
Summary and Review	384	(9)
Further Exploration	393	(8)
Methods of Counting	401	(46)
The Fundamental Counting Principle	402	(11)
Permutations	413	(7)
More on Permutations	420	(8)
Combinations	428	(19)
Summary and Review	435	(6)
Further Exploration	441	(6)
The Mathematics of Chance	447	(78)
Probability: The Measure of Chance	448	(9)
Dice Games and Probability	457	(10)
Probabilities of Successive Events	467	(9)
Binomial Probability	476	(10)
Pascal's Triangle	486	(9)
The Birthday Problem: Complementary Events	495	(30)
Summary and Review	504	(7)
Further Exploration	511	(14)
An Introduction to Statistics	525	(76)
Organizing Data: Frequency Distributions	526	(11)
The Breaking of Ciphers and Codes: An Application of Statistics	537	(9)
Measures of Central Tendency	546	(8)
Measures of Variability	554	(10)
Displaying Data: Statistical Graphs	564	(10)
Collecting Data: Sampling	574	(27)
Summary and Review	582	(9)
Further Exploration	591	(10)
Topics in Topology	601	(54)
The Mathematics of Distortion	602	(8)
The Seven Bridges of Konigsberg: An Introduction to Networks	610	(7)
Euler Paths	617	(8)
Trees	625	(9)
The Moebius Strip and Other Surfaces	634	(21)
Summary and Review	641	(6)
Further Exploration	647	(8)
Appendix: Basic Ideas and Operations	655	(8)
1. Angles and Their Measurement	656	(2)
2. The Distributive Rule	658	(1)
3. Signed Numbers	659	(2)
4. Percent	661	(2)
Answers to Selected Exercises	663	(10)
Index	673