ABSTRACT

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

part 1|2 pages

Unit I - Graphs: Puzzles and Optimization

chapter 1|22 pages

- Graphical Representation and Search

chapter 4|22 pages

- Routing Problems and Optimal Circuits

chapter 5|20 pages

- Traveling Salesmen and Optimal Orderings

chapter 6|28 pages

- Vertex Colorings and Edge Matchings

part 2|2 pages

Unit II - Logic: Rational Inference and Computer Circuits

chapter 7|26 pages

- Inductive and Deductive Arguments

chapter 8|20 pages

- Deductive Arguments and Truth-Tables

chapter 9|22 pages

- Deductive Arguments and Derivations

chapter 10|26 pages

- Deductive Logic and Equivalence

chapter 11|26 pages

- Modeling Using Deductive Logic

part 3|2 pages

Unit III - Probability: Predictions and Expectations

chapter 12|18 pages

- Probability and Counting

chapter 13|12 pages

- Counting and Unordered Outcomes

chapter 14|22 pages

- Independence and Conditional Probabilities

chapter 16|22 pages

- Expected Values and Decision Making

part 4|2 pages

Unit IV - Counting: Voting Methods and Apportionment

chapter 17|24 pages

- Voting Methods

chapter 19|18 pages

- Weighted Voting Systems and Voting Power

chapter 20|20 pages

- Apportionment

chapter 21|24 pages

- Assessing Apportionment Methods

part 5|2 pages

Unit V - Numbers: Cryptosystems and Security