Puzzles, Paradoxes, and Problem Solving: An Introduction to Mathematical Thinking, 1st Edition (Hardback) book cover

Puzzles, Paradoxes, and Problem Solving

An Introduction to Mathematical Thinking, 1st Edition

By Marilyn A. Reba, Douglas R. Shier

Chapman and Hall/CRC

605 pages | 201 B/W Illus.

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Hardback: 9781482227536
pub: 2014-12-15
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Description

A Classroom-Tested, Alternative Approach to Teaching Math for Liberal Arts

Puzzles, Paradoxes, and Problem Solving: An Introduction to Mathematical Thinking uses puzzles and paradoxes to introduce basic principles of mathematical thought. The text is designed for students in liberal arts mathematics courses. Decision-making situations that progress from recreational problems to important contemporary applications develop the critical-thinking skills of non-science and non-technical majors.

The logical underpinnings of this textbook were developed and refined throughout many years of classroom feedback and in response to commentary from presentations at national conferences. The text’s five units focus on graphs, logic, probability, voting, and cryptography. The authors also cover related areas, such as operations research, game theory, number theory, combinatorics, statistics, and circuit design.

The text uses a core set of common representations, strategies, and algorithms to analyze diverse games, puzzles, and applications. This unified treatment logically connects the topics with a recurring set of solution approaches.

Requiring no mathematical prerequisites, this book helps students explore creative mathematical thinking and enhance their own critical-thinking skills. Students will acquire quantitative literacy and appreciation of mathematics through the text’s unified approach and wide range of interesting applications.

Reviews

"… an interesting approach to the world of mathematics. … The layout is good, as is the coverage. … The reinforcing exercises are excellent. Using logic and other techniques, the text lays out methods to help students learn to think in a mathematical manner. Summing up: Recommended. General readers, lower- and upper-division undergraduates."

—M. D. Sanford, Felician College, Lodi, New Jersey, USA for CHOICE, November 2015

Table of Contents

Graphs: Puzzles and Optimization

Graphical Representation and Search

Greedy Algorithms and Dynamic Programming

Shortest Paths, DNA Sequences, and GPS Systems

Routing Problems and Optimal Circuits

Traveling Salesmen and Optimal Orderings

Vertex Colorings and Edge Matchings

Logic: Rational Inference and Computer Circuits

Inductive and Deductive Arguments

Deductive Arguments and Truth-Tables

Deductive Arguments and Derivations

Deductive Logic and Equivalence

Modeling Using Deductive Logic

Probability: Predictions and Expectations

Probability and Counting

Counting and Unordered Outcomes

Independence and Conditional Probabilities

Bayes’ Law and Applications of Conditional Probabilities

Expected Values and Decision Making

Counting: Voting Methods and Apportionment

Voting Methods

Fairness Criteria and Arrow’s Impossibility Theorem

Weighted Voting Systems and Voting Power

Apportionment

Assessing Apportionment Methods

Numbers: Cryptosystems and Security

Modular Arithmetic and Cryptography

Binary Representation and Symmetric Cryptosystems

Prime Numbers and Public-Key Cryptosystems

Appendix A: Applications

Appendix B: Classifications

Index

About the Authors

Marilyn A. Reba is a senior lecturer and Douglas R. Shier is a professor emeritus, both in the Department of Mathematical Sciences at Clemson University. The logical underpinnings of this textbook were developed and refined throughout many years of classroom feedback and in response to commentary from presentations at national conferences. Selected material from this book is currently being used in the Department of Mathematical Sciences’ liberal arts mathematics course and in a problem-solving course in the Honors College.

Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT002000
MATHEMATICS / Algebra / General
MAT025000
MATHEMATICS / Recreations & Games