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? An Historical Overview.
1. THE NATURE OF PROBLEM SOLVING.
Problem Solving. Inductive and Deductive Reasoning. Scientific Notation and Estimation. Finite and Infinite.
2. 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.
3. THE NATURE OF SET THEORY AND COUNTING.
Sets, Subsets, and Venn Diagrams. Combined Operations with Sets. Counting Formulas. Permutations. Combinations. Binomial Theorem. Counting without Counting. Rubik's Cube and Instant Insanity.
4. THE NATURE OF PROBABILITY.
Introduction to Probability. Mathematical Expectation. Probability Models. Calculated Probabilities. Binomial Probabilities. Guest Essay: Extrasensory Perception.
5. THE NATURE OF STATISTICS.
Frequency Distributions and Graphs. Measures of Central Tendency. Measures of Dispersion. The Normal Curve. Correlation and Regression. Polls and Margin of Error.
6. THE NATURE OF GEOMETRY.
Geometry. Polygons and Angles. Triangles. Similar Triangles. Right Triangle Trigonometry. Golden Rectangles. Projective and Non-Euclidian Geometries.
7. THE NATURE OF MEASUREMENT.
Perimeter. Area. Surface Area, Volume and Capacity. Miscellaneous Measurements.
8. THE NATURE OF GROWTH.
Logarithms and Exponents. Exponential Equations. Logarithmic Equations. Applications of Growth and Decay.
9. THE NATURE OF NETWORKS AND GRAPH THEORY.
Euler Circuits and Hamiltonian Cycles. Trees and Minimum Spanning Trees. Topology and Fractals. Guest Essay: Chaos.
Epilogue � Why Not Math? Mathematics In The Natural Sciences, Social
Sciences, And In The Humanities.
B. Selected Answers.