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The Nature of Mathematics (with InfoTrac),9780534400231
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The Nature of Mathematics (with InfoTrac)

by
Edition:
10th
ISBN13:

9780534400231

ISBN10:
053440023X
Format:
Hardcover
Pub. Date:
8/22/2003
Publisher(s):
Brooks Cole
List Price: $214.33

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Summary

Karl Smith's loyal customers adopt his book for its clear writing, its coverage of historical topics, selection of topics, level, exercise sets (featuring great applications problems), and emphasis on problem solving. Since the First Edition of Smith's text was published, thousands of liberal arts students have "experienced" mathematics rather than just doing problems. Smith's writing style gives students the confidence and ability to function mathematically in their everyday lives. The emphasis on problem solving and estimation, along with numerous in-text study aids, encourages students to understand the concepts while mastering techniques.

Table of Contents

Prologue-Why Math? A Historical Overview P1
1 THE NATURE OF PROBLEM SOLVING 1(52)
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 NUMERATION SYSTEMS 101(40)
3.1 Early Numeration Systems
102(8)
3.2 Hindu-Arabic Numeration System
110(4)
3.3 Different Numeration Systems
114(5)
3.4 Binary Numeration System
119(5)
3.5 History of Calculating Devices
124(12)
Chapter 3 Summary
136(5)
4 THE NATURE OF NUMBERS 141(74)
4.1 Natural Numbers
142(7)
4.2 Prime Numbers
149(11)
4.3 Integers
160(8)
4.4 Rational Numbers
168(7)
4.5 Irrational Numbers
175(9)
4.6 Groups, Fields, and Real Numbers
184(10)
4.7 Discrete Mathematics
194(9)
4.8 Cryptography
203(5)
Chapter 4 Summary
208(7)
5 THE NATURE OF ALGEBRA 215(80)
5.1 Polynomials
216(7)
5.2 Factoring
223(5)
5.3 Evaluation, Applications, and Spreadsheets
228(11)
5.4 Equations
239(8)
5.5 Inequalities
247(4)
5.6 Algebra in Problem Solving
251(11)
5.7 Ratios, Proportions, and Problem Solving
262(10)
5.8 Percents
272(9)
5.9 Modeling Uncategorized Problems
281(9)
Chapter 5 Summary
290(5)
6 THE NATURE OF GEOMETRY 295(56)
6.1 Geometry
296(9)
6.2 Polygons and Angles
305(8)
6.3 Triangles
313(6)
6.4 Similar Triangles
319(7)
6.5 Right-Triangle Trigonometry
326(8)
6.6 Golden Rectangles
334(6)
6.7 Projective and Non-Euclidean Geometries
340(6)
Chapter 6 Summary
346(5)
7 THE NATURE OF MAEASUREMENT 351(46)
7.1 Perimeter
352(8)
7.2 Area
360(10)
7.3 Surface Area, Volume, and Capacity
370(11)
7.4 Miscellaneous Measurements
381(11)
Chapter 7 Summary
392(5)
8 THE NATURE OF GROWTH 397(30)
8.1 Exponential Equations
398(8)
8.2 Logarithmic Equations
406(7)
8.3 Applications of Growth and Decay
413(10)
Chapter 8 Summary
423(4)
9 THE NAUTRE OF FINANCIAL MANAGEMENT 427(70)
9.1 Interest
428(13)
9.2 Installment Buying
441(9)
9.3 Sequences
450(10)
9.4 Series
460(10)
9.5 Annuities
470(7)
9.6 Amortization
477(8)
9.7 Summary of Financial Formulas
485(4)
Chapter 9 Summary
489(8)
10 THE NATURE OF SET THEORY AND COUNTING 497(54)
10.1 Sets, Subsets, and Venn Diagrams
498(7)
10.2 Combined Operations with Sets
505(8)
10.3 Permutations
513(8)
10.4 Combinations
521(5)
10.5 Counting without Counting
526(10)
10.6 Binomial Theorem
536(5)
10.7 Rubik's Cube and Instant Insanity
541(3)
Chapter 10 Summary
544(7)
11 THE NATURE OF PROBABILITY 551(56)
11.1 Introduction to Probability
552(11)
11.2 Mathematical Expectation
563(9)
11.3 Probability Models
572(11)
11.4 Calculated Probabilities
583(11)
GUEST ESSAY: "Extrasensory Perception"
591(3)
11.5 The Binomial Distribution
594(7)
Chapter 11 Summary
601(6)
12 THE NATURE OF STATISTICS 607(58)
12.1 Frequency Distributions and Graphs
608(14)
12.2 Descriptive Statistics
622(11)
12.3 The Normal Curve
633(10)
12.4 Correlation and Regression
643(8)
12.5 Sampling
651(7)
Chapter 12 Summary
658(7)
13 THE NATURE OF GRAPHS AND FUNCTIONS 665(44)
13.1 Cartesian Coordinates and Graphing Lines
666(9)
13.2 Graphing Half-Planes
675(2)
13.3 Graphing Curves
677(5)
13.4 Conic Sections
682(13)
13.5 Functions
695(8)
Chapter 13 Summary
703(6)
14 THE NATURE OF MATHEMATICAL SYSTEMS 709(52)
14.1 Systems of Linear Equations
710(4)
14.2 Problem Solving with Systems
714(10)
14.3 Matrix Solution of a System of Equations
724(10)
14.4 Inverse Matrices
734(14)
14.5 Systems of Inequalities
748(1)
14.6 Modeling with Linear Programming
749(8)
Chapter 14 Summary
757(4)
15 THE NATURE OF NETWORKS AND GRAPH THEORY 761(40)
15.1 Euler Circuit and Hamiltonian Cycles
762(12)
15.2 Trees and Minimum Spanning Trees
774(11)
15.3 Topology and Fractals
785(11)
GUEST ESSAY: "What Good Are Fractals?"
790(5)
GUEST ESSAY: "Chaos"
795(1)
Chapter 15 Summary
796(5)
16 THE NATURE OF VOTING AND APPORTIONMENT 801(60)
16.1 Voting
802(11)
16.2 Voting Dilemmas
813(18)
16.3 Apportionment
831(18)
16.4 Apportionment Paradoxes
849(8)
Chapter 16 Summary
857(4)
17 THE NATURE OF CALCULUS 861
17.1 What Is Calculus?
862(10)
17.2 Limit
872(5)
17.3 Derivatives
877(11)
17.4 Integrals
888(8)
Chapter 17 Summary
896
Epilogue-Why Not Math? Mathematics in the Natural Sciences Social Sciences, and Humanities E1
A Glossary G1
B Selected Answer A1
C Credit C1
D Index I1


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