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