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Full Description
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 customers of Karl Smith's books laud his clear writing, coverage of historical topics, selection of topics, and emphasis on problem solving. 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.
Contents
Prologue--Why Math? An Historical Overview. 1. THE NATURE OF PROBLEM SOLVING. Problem Solving. Inductive and Deductive Reasoning. Scientific SYSTEMS. Early Numeration Systems. Hindu-Arabic Numeration Systems. Different Numeration Systems. Binary Numeration Systems. History of Calculating Rational Numbers. Irrational Numbers. Groups, Fields, and Real Numbers. Factoring. Evaluation, Applications, and Spreadsheets. Equations. Inequalities. Algebra in Problem Solving. Ratios, Proportions, and Problem Logarithms and Exponents. Exponential Equations. Logarithmic Equations. FINANCIAL MANAGEMENT. Interest. Installment Buying. Sequences. Series. Annuities. Amortization. Summary of Financial Formulas. 7. THE NATURE OF GRAPHS AND FUNCTIONS. Cartesian Coordinates and Graphing Lines. Graphing Half-Planes. Graphing Curves. Conic Sections. Functions. 8. THE NATURE OF MATHEMATICAL SYSTEMS. Systems of Linear Equations. Problem Solving with Systems. Matrix Solution of a System of Equations. Inverse Matrices. Systems AND GRAPH THEORY. Euler Circuits and Hamiltonian Cycles. Trees and Minimum Spanning Trees. Topology and Fractals. Guest Essay: Chaos. 10. THE NATURE OF VOTING AND APPORTIONMENT. Voting. Voting Dilemmas. Apportionment. Apportionment Flaws. Epilogue--Why Not Math? Mathematics In The Natural Sciences, Social Sciences, And In The Humanities. Appendices: A. Glossary. B. Selected Answers. C. Credits. D. Index.
