Puzzles, Paradoxes, and Problem Solving An Introduction to Mathematical Thinking

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.

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 PowerApportionment 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

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.