The Nature of Problem Solving in Geometry and Probability: A Liberal Arts Approach (with InfoTrac) / Edition 1

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Overview

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.

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Editorial Reviews

From the Publisher
"It's the best book out there. We tried another book last semester just to be different and that was a disaster. So we'll...keep with NATURE OF MATHEMATICS."

"I have found more than enough material in each exercise set that keeps my students' interest. In light of the fact that most...of my students are not interested in math or science, I have welcomed the sight of the many problems that are conceptual rather than computational in nature."

"One of the strengths of this text is the Presentation of topics that are not always computational in nature. This involves letting students see topics that they do not typically view as being mathematical and explore concepts in ways other than by just pushing buttons on a calculator."

"Even though I do not teach geometry or metrics from your text, I wish I could. Your units on these topics are excellent, better than those in most other texts I've seen or used."

"I love the color, the pictures, the cartoons, the attempt to make the pages come alive. Your efforts have not gone unnoticed, at least not by me."

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Product Details

  • ISBN-13: 9780534421489
  • Publisher: Cengage Learning
  • Publication date: 9/4/2003
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 592
  • Product dimensions: 8.20 (w) x 10.44 (h) x 0.85 (d)

Meet the Author

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.

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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. Appendices: A. Glossary. B. Selected Answers. C. Credits. D. Index.

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