Karl Smith is professor emeritus at Santa Rosa Junior College in Santa Rosa, California. He has written over 36 mathematics textbooks and believes that students can learn mathematics if it is presented to them through the use of concrete examples designed to develop original thinking, abstraction, and problem-solving skills. Over one million students have learned mathematics from Karl Smith's textbooks.
Nature of Mathematics (with CengageNOW and Personal Tutor Printed Access Card) / Edition 11by Karl J. Smith
Experience mathematics and hone your problem-solving skills with THE NATURE OF MATHEMATICS and its accompanying online learning tools. The author introduces you to Polya's problem-solving techniques and then shows you how to use these techniques to solve unfamiliar problems. You'll also find coverage of historical topics, and exercise sets that feature problems… See more details below
Experience mathematics and hone your problem-solving skills with THE NATURE OF MATHEMATICS and its accompanying online learning tools. The author introduces you to Polya's problem-solving techniques and then shows you how to use these techniques to solve unfamiliar problems. You'll also find coverage of historical topics, and exercise sets that feature problems applied to real world settings. Included with your purchase is access to the CengageNOW, an online tutorial that allows you to work with real math notation in real time, with unlimited practice problems, instant analysis and feedback, and streaming video to illustrate key concepts, as well as Personal Tutor with SMARTHINKING, a live, online mathematics tutoring service.
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Table of Contents
Prologue:Why Math? A Historical Overview. 1. THE NATURE OF PROBLEM SOLVING. Problem Solving. Inductive and Deductive Reasoning. Scientific Notation and Estimation. 2. THE NATURE OF SETS. Sets, Subsets, and Venn Diagrams. Operations with Sets. Applications of Sets. Finite and Infinite Sets. 3. THE NATURE OF LOGIC. Deductive Reasoning. Truth Tables and the Conditional. Operators and Laws of Logic. The Nature of Proof. Problem Solving Using Logic. Logic Circuits. 4. THE NATURE OF NUMERATION SYSTEMS. Early Numeration Systems. Hindu-Arabic Numeration Systems. Different Numeration Systems. Binary Numeration System. History of Calculating Devices. 5. THE NATURE OF NUMBERS. Natural Numbers. Prime Numbers. Integers. Rational Numbers. Irrational Numbers. Groups, Fields, and Real Numbers. Discrete Mathematics. Cryptography. 6. THE NATURE OF ALGEBRA. Polynomials. Factoring. Evaluation, Applications, and Spreadsheets. Equations. Guest Essay: Chaos. Inequalities. Algebra in Problem Solving. Ratios, Proportions, and Problem Solving. Percents. Modeling Uncategorized Problems. 7. THE NATURE OF GEOMETRY. Geometry. Polygons and Angles. Triangles. Similar Triangles. Right Triangle Trigonometry. Golden Rectangles. Projective and Non-Euclidian Geometries. 8. THE NATURE OF NETWORKS AND GRAPH THEORY. Euler Circuits and Hamiltonian Cycles. Trees and Minimum Spanning Trees. Topology and Fractals. Guest Essay:What Good are Fractals? 9. THE NATURE OF MEASUREMENT. Perimeter. Area. Surface Area, Volume and Capacity. Miscellaneous Measurements. U.S.-Metric Conversions. 10. THE NATURE OF GROWTH. Exponential Equations. Logarithmic Equations. Applications of Growth and Decay. 11. THE NATURE OF SEQUENCES, SERIES AND FINANCIAL MANAGEMENT. Interest. Installment Buying. Sequences. Series. Annuities. Amortization. Summary of Financial Formulas. 12. THE NATURE OF COUNTING. Permutations. Combinations. Counting without Counting. Rubik's Cube and Instant Insanity. 13. THE NATURE OF PROBABILITY. Introduction to Probability. Mathematical Expectation. Probability Models. Calculated Probabilities. The Binomial Distribution. Guest Essay: Extrasensory Perception. 14. THE NATURE OF STATISTICS. Frequency Distributions and Graphs. Descriptive Statistics. The Normal Curve. Correlation and Regression. Sampling. 15. THE NATURE OF GRAPHS AND FUNCTIONS. Cartesian Coordinates and Graphing Lines. Graphing Half-Planes. Graphing Curves. Conic Sections. Functions. 16. THE NATURE OF MATHEMATICAL SYSTEMS. Systems of Linear Equations. Problem Solving with Systems. Matrix Solution of a System of Equations. Inverse Matrices. Modeling with Linear Programming. 17. THE NATURE OF VOTING AND APPORTIONMENT. Voting. Voting Dilemmas. Apportionment. Apportionment Flaws. EpilogueWhy Not Math? Mathematics in the Natural Sciences, Social Sciences, and in the Humanities. Appendices. Glossary. Selected Answers. Credits. Index. AVAILABLE ON THE WEB. 18. THE NATURE OF CALCULUS. What is Calculus? Limits. Derivatives. Integrals.
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