1st Edition
Puzzles, Paradoxes, and Problem Solving An Introduction to Mathematical Thinking
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
Biography
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.
"… 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
