The Nature of Problem Solving in Geometry and Probability A Liberal Arts Approach (with InfoTrac)

by Smith, Karl J.

• ISBN13: 9780534421489
• ISBN10: 0534421482
• Edition: 1st
• Format: Hardcover
• Copyright: 2003-09-04
• Publisher: Cengage Learning

Summary

Liberal Arts mathematics books often cover much more material than can be addressed in a one-semester course. Karl Smith has created a solution to this problem with his new book: THE NATURE OF PROBLEM SOLVING IN GEOMETRY AND PROBABILITY. Loyal customers of Karl Smith's books laud his clear writing, coverage of historical topics, selection of topics, and emphasis on problem solving. Based on the successful NATURE OF MATHEMATICS text, this new book is designed to give you only the chapters and information you need, when you need it. Smith takes great care to provide insight into precisely what mathematics is--the nature of mathematics--what it can accomplish, and how it is pursued as a human enterprise. At the same time, Smith emphasizes Polya's problem-solving method throughout the text so students can take from the course an ability to estimate, calculate, and solve problems outside the classroom. Moreover, Smith's writing style gives students the confidence and ability to function mathematically in their everyday lives. This new text emphasizes problem solving and estimation, which, along with numerous in-text study aids, encourage students to understand the concepts as well as mastering techniques.

Table of Contents

Prologue-Why Math? A Historical Overview	P1
1 THE NATURE OF PROBLEM SOLVING
1.1 Problem Solving	2	(14)
1.2 Inductive and Deductive Reasoning	16	(8)
1.3 Scientific Notation and Estimation	24	(15)
1.4 Finite and Infinite	39	(8)
Chapter 1 Summary	47	(6)
2 THE NATURE OF LOGIC	53	(48)
2.1 Deductive Reasoning	54	(7)
2.2 Truth Tables and the Conditional	61	(8)
2.3 Operators and Laws of Logic	69	(6)
2.4 The Nature of Proof	75	(9)
2.5 Problem Solving Using Logic	84	(6)
2.6 Logic Circuits	90	(4)
Chapter 2 Summary	94	(7)
3 THE NATURE OF SET THEORY AND COUNTING	101	(54)
3.1 Sets, Subsets, and Venn Diagrams	102	(7)
3.2 Combined Operations with Sets	109	(8)
3.3 Permutations	117	(8)
3.4 Combinations	125	(5)
3.5 Counting without Counting	130	(10)
3.6 Binomial Theorem	140	(5)
3.7 Rubik's Cube and Instant Insanity	145	(3)
Chapter 3 Summary	148	(7)
4 THE NATURE OF PROBABILITY	155	(56)
4.1 Introduction to Probability	156	(11)
4.2 Mathematical Expectation	167	(9)
4.3 Probability Models	176	(11)
4.4 Calculated Probabilities	187	(8)
GUEST ESSAY: "Extrasensory Perception"	195	(206)
4.5 The Binomial Distribution	198	(7)
Chapter 4 Summary	205	(6)
5 THE NATURE OF STATISTICS	211	(58)
5.1 Frequency Distributions and Graphs	212	(14)
5.2 Descriptive Statistics	226	(11)
5.3 The Normal Curve	237	(10)
5.4 Correlation and Regression	247	(8)
5.5 Sampling	255	(7)
Chapter 5 Summary	262	(7)
6 THE NATURE OF GEOMETRY	269	(56)
6.1 Geometry	270	(9)
6.2 Polygons and Angles	279	(8)
6.3 Triangles	287	(6)
6.4 Similar Triangles	293	(7)
6.5 Right-Triangle Trigonometry	300	(8)
6.6 Golden Rectangles	308	(6)
6.7 Projective and Non-Euclidean Geometries	314	(6)
Chapter 6 Summary	320	(5)
7 THE NATURE OF MEASUREMENT	325	(46)
7.1 Perimeter	326	(8)
7.2 Area	334	(10)
7.3 Surface Area, Volume, and Capacity	344	(11)
7.4 Miscellaneous Measurements	355	(11)
Chapter 7 Summary	366	(5)
8 THE NATURE OF GROWTH	371	(30)
8 1 Exponential Equations	372	(8)
8.2 Logarithmic Equations	380	(7)
8.3 Applications of Growth and Decay	387	(10)
Chapter 8 Summary	397	(4)
9 THE NATURE OF NETWORKS AND GRAPH THEORY	401
9.1 Euler Circuits and Hamiltonian Cycles	402	(12)
9.2 Trees and Minimum Spanning Trees	414	(11)
9.3 Topology and Fractals	425	(5)
GUEST ESSAY: "What Good Are Fractals?"	430	(5)
GUEST ESSAY: "Chaos"	435
Chapter 9 Summary	436
Epilogue-Why Not Math? Mathematics in the Natural Sciences, Social Sciences, and Humanities	E1
APPENDICES
A Glossary	G1
B Selected Answers	A1
C Credits	C1
D Index	I1