The Nature of Mathematics

by Smith, Karl J.

• ISBN13: 9780534368906
• ISBN10: 0534368905
• Format: Hardcover
• Copyright: 2000-12-22
• Publisher: Brooks Cole

Summary

Since the First Edition of Smith's text was published, thousands of liberal arts students have "experienced" mathematics rather than just "doing problems" with the help of this book. Smith's student-friendly writing style gives readers the confidence and ability to function mathematically in our technological world. Smith emphasizes problem solving and estimation, and new problems are coupled with numerous in-text study aids, encouraging students to become involved with the concepts. The Ninth Edition goes a step beyond to help students master mathematics rather than just get the right answer.

Table of Contents

History of Mathematics---An Overview	xiii
The Nature of Problem Solving	1	(62)
Problem Solving	2	(16)
Inductive and Deductive Reasoning	18	(9)
Scientific Notation and Estimation	27	(16)
Problem Solving with Sets	43	(20)
Summary	56	(7)
The Nature of Logic	63	(52)
Deductive Reasoning	64	(8)
Truth Tables and the Conditional	72	(9)
Operators and Laws of Logic	81	(6)
The Nature of Proof	87	(10)
Problem Solving Using Logic	97	(7)
Logic Circuits	104	(11)
Summary	108	(7)
The Nature of Calculation	115	(42)
Early Numeration Systems	116	(9)
Hindu-Arabic Numeration System	125	(4)
Different Numeration Systems	129	(6)
Binary Numeration System	135	(5)
History of Calculating Devices	140	(17)
Summary	153	(4)
The Nature of Numbers	157	(80)
Natural Numbers	158	(8)
Prime Numbers	166	(13)
Integers	179	(9)
Rational Numbers	188	(7)
Irrational Numbers	195	(10)
Real Numbers	205	(11)
Discrete Mathematics	216	(10)
Cryptography	226	(11)
Summary	231	(6)
The Nature of Algebra	237	(90)
Polynomials	238	(8)
Factoring	246	(6)
Evaluation, Applications, and Spreadsheets	252	(12)
Equations	264	(8)
Inequalities	272	(5)
Algebra in Problem Solving	277	(12)
Ratios, Proportions, and Problem Solving	289	(10)
Modeling Uncategorized Problems	299	(10)
Introduction to Computer BASIC	309	(18)
Summary	323	(4)
The Nature of Geometry	327	(96)
Geometry	328	(10)
Polygons and Angles	338	(9)
Triangles	347	(8)
Similar Triangles	355	(7)
Right-Triangle Trigonometry	362	(8)
Golden Rectangles	370	(7)
Euler Circuits and Hamiltonian Cycles	377	(13)
Topology and Fractals	390	(11)
Chaos	400	(1)
Projective and Non-Euclidean Geometries	401	(6)
Introduction to Computer LOGO	407	(16)
Summary	416	(7)
The Nature of Measurement and Growth	423	(77)
Perimeter	424	(9)
Area	433	(10)
Surface Area, Volume, and Capacity	443	(13)
Miscellaneous Measurements	456	(10)
Exponential Equations	466	(8)
Logarithmic Equations	474	(9)
Applications of Growth and Decay	483	(17)
Summary	493	(7)
The Nature of Sequences, Series, and Financial Management	500	(74)
Interest	501	(14)
Installment Buying	515	(9)
Sequences	524	(12)
Series	536	(11)
Annuities	547	(8)
Amortization	555	(8)
Summary of Financial Formulas	563	(11)
Summary	567	(7)
The Nature of Probability	574	(73)
Introduction to Probability	575	(12)
Mathematical Expectation	587	(10)
Probability Models	597	(14)
Counting Formulas	611	(11)
Calculated Probabilities	622	(13)
Extrasensory Perception	632	(3)
Rubik's Cube and Instant Insanity	635	(12)
Summary	639	(8)
The Nature of Statistics	647	(76)
Frequency Distributions and Graphs	648	(15)
Descriptive Statistics	663	(13)
Voting and Apportionment	676	(13)
The Normal Curve	689	(10)
Correlation and Regression	699	(10)
Sampling	709	(14)
Summary	715	(8)
The Nature of Graphs and Functions	723	(84)
Graphing Lines	724	(9)
Graphing Half-Planes	733	(3)
Graphing Curves	736	(6)
Conic Sections	742	(14)
Functions	756	(9)
What Is Calculus?	765	(11)
Limits	776	(6)
Derivatives	782	(11)
Integrals	793	(14)
Summary	802	(5)
The Nature of Mathematical Systems	807	(57)
Systems of Linear Equations	809	(4)
Problem Solving with Systems	813	(11)
Matrix Solution of a System of Equations	824	(11)
Inverse Matrices	835	(14)
Systems of Inequalities	849	(2)
Modeling with Linear Programming	851	(13)
Summary	859	(5)
APPENDICES	864	(118)
A Problem Solving	864	(4)
B Percents	868	(10)
C Mathematics in the Natural Sciences, Social Sciences, and Humanities	878	(20)
D U.S.-Metric Conversions	898	(2)
E Table: Trigonometric Ratios	900	(1)
F Table: Standard Normal Distribution; z-scores	901	(1)
G Glossary	902	(31)
H Selected Answers	933	(47)
I Credits	980	(2)
Index	982