Solutions Manual for Puzzles, Paradoxes, and Problem Solving: An Introduction to Mathematical Thinking

✍ Scribed by Marilyn A. Reba, Douglas R. Shier

• Publisher: CRC Press
• Year: 2014
• Tongue: English
• Leaves: 220
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Contents
1 Graphical Representation and Search 4
2 Greedy Algorithms and Dynamic Programming 19
3 Shortest Paths, DNA Sequences, and GPS Systems 26
4 Routing Problems and Optimal Circuits 36
5 Traveling Salesmen and Optimal Orderings 45
6 Vertex Colorings and Edge Matchings 57
7 Inductive and Deductive Arguments 71
8 Deductive Arguments and Truth-Tables 76
9 Deductive Arguments and Derivations 83
10 Deductive Logic and Equivalence 96
11 Modeling Using Deductive Logic 107
12 Probability and Counting 115
13 Counting and Unordered Outcomes 120
14 Independence and Conditional Probabilities 123
15 Bayes’ Law and Applications of Conditional Probabilities 131
16 Expected Values and Decision Making 140
17 Voting Methods 151
18 Fairness Criteria and Arrow’s Impossibility Theorem 157
19 Weighted Voting Systems and Voting Power 163
20 Apportionment 172
21 Assessing Apportionment Methods 181
22 Modular Arithmetic and Cryptography 189
23 Binary Representation and Symmetric Cryptosystems 198
24 Prime Numbers and Public-Key Cryptosystems 206

✦ Subjects

Mathematics Puzzles; Greedy Algorithms; Dynamic Programming; Shortest Paths; Traveling Salesmen; Vertex Colorings; Prime Numbers