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Tom Pirnot received his bachelor's degree in music from Wilkes College and his PhD in mathematics from The Pennsylvania State University. He taught both mathematics and computer science at Kutztown University for thirty eight years. He has long been an innovator in liberal arts mathematics, writing his first text Mathematics: Tools and Models with Dalton Hunkins in 1977 which introduced topics such as apportionment, graph theory, and modeling to liberal arts students. His current text, Mathematics All Around, is now in its fourth edition. Tom continues to enjoy the loving support and encouragement of his wife Ann, their four children, and three grandchildren.
Table of Contents
1. Problem Solving
1.1 Problem Solving
1.2 Inductive and Deductive Reasoning
2. Set Theory
2.1 The Language of Sets
2.2 Comparing Sets
2.3 Set Operations
2.4 Survey Problems
2.5 Looking Deeper - Infinite Sets
3.1 Statements, Connectives, and Quantifiers
3.2 Truth Tables
3.3 The Conditional and Biconditional
3.4 Verifying Arguments
3.5 Using Euler Diagrams to Verify Syllogisms
3.6 Looking Deeper - Fuzzy Logic
4. Graph Theory (Networks)
4.1 Graphs, Puzzles, and Map Coloring
4.2 The Traveling Salesperson Problem
4.3 Directed Graphs
5. Numeration Systems
5.1 The Evolution of Numeration Systems
5.2 Place Value Systems
5.3 Calculating in Other Bases
5.4 Looking Deeper - Modular Systems
6. Number Theory and the Real Number System
6.1 Number Theory
6.2 The Integers
6.3 The Rational Numbers
6.4 The Real Number System
6.5 Exponents and Scientific Notation
6.6 Looking Deeper - Sequences
7. Algebraic Models and Linear Systems
7.1 Linear Equations
7.2 Modeling with Linear Equations
7.3 Modeling with Quadratic Equations
7.4 Exponential Equations and Growth
7.5 Proportions and Variations
7.6 Modeling with Systems of Linear Equations and Inequalities
7.7 Looking Deeper - Dynamical Systems
8. Consumer Mathematics
8.1 Percents, Taxes, and Inflation
8.3 Consumer Loans
8.6 Looking Deeper - Annual Percentage Rate
9.1 Lines, Angles, and Circles
9.3 Perimeter and Area
9.4 Volume and Surface Area
9.5 The Metric System and Dimensional Analysis
9.6 Geometric Symmetry and Tessellations
9.7 Looking Deeper - Fractals
10.1 Understanding Apportionment
10.2 The Huntington-Hill Apportionment Principle
10.3 Other Paradoxes and Apportionment Methods
10.4 Looking Deeper - Fair Division
11.1 Voting Methods
11.2 Defects in Voting Methods
11.3 Weighted Voting Systems
11.4 Looking Deeper - The Shapley-Shubik Index
12.1 Introduction to Counting Methods
12.2 The Fundamental Counting Principle
12.3 Permutations and Combinations
12.4 Looking Deeper - Counting and Gambling
13.1 The Basics of Probability Theory
13.2 Complements and Unions of Events
13.3 Conditional Probability and Intersections of Events
13.4 Expected Value
13.5 Looking Deeper - Binomial Experiments
14. Descriptive Statistics
14.1 Organizing and Visualizing Data
14.2 Measures of Central Tendency
14.3 Measures of Dispersion
14.4 The Normal Distribution
14.5 Looking Deeper - Linear Correlation
Appendix A. Basic Mathematics Review