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Mathematics All Around / Edition 6

Mathematics All Around / Edition 6

by Tom Pirnot
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Product Details

ISBN-13: 2900134434680
Publisher: Pearson
Publication date: 01/15/2017
Edition description: New Edition
Pages: 888
Product dimensions: 6.50(w) x 1.50(h) x 9.50(d)

About the Author

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

(*indicates new content)
1. Set Theory: Using Mathematics to Classify Objects.
Problem Solving.
The Language of Sets.
Comparing Sets.
Set Operations.
Survey Problems.
*Of Further Interest: Infinite Sets.

2. Logic: The Study of What's True or False or Somewhere in Between.
*Inductive and Deductive Reasoning.
Statements, Connectives, and Quantifiers.
Truth Tables.
The Conditional and Biconditional.
Verifying Arguments.
Using Euler Diagrams to Verify Syllogisms.
Of Further Interest: Fuzzy Logic.

3. Graph Theory: The Mathematics of Relationships.
Graphs, Puzzles and Map Coloring.
The Traveling Salesperson Problem.
Directed Graphs.
Of Further Interest: Scheduling Projects Using PERT.

4. Numeration Systems: Does It Matter How We Name Numbers?
*The Evolution of Numeration Systems.
*Place Value Systems.
*Calculating in Other Bases.
*Of Further Interest: Modular Systems.

5. Number Theory and the Real Number System: Understanding the Numbers All Around Us.
*Number Theory.
*The Integers.
*The Rational Numbers.
*The Real Number System.
*Exponents and Scientific Notation.
*Of Further Interest: Sequences.

6. Algebraic Models: How Do We Approximate Reality?
Linear Equations.
Modeling With Linear Equations.
Modeling with Quadratic Equations.
Exponential Equations and Growth.
*Proportions and Variation.
Of Further Interest: Dynamical Systems.

7. Modeling with Systems of Linear Equations and Inequalities: What's the Best Way to Do It?
*Systems of Linear Equations.
*Systems of Linear Inequalities.
*Of Further Interest: LinearProgramming.

8. Geometry: Ancient and Modern Mathematics Embrace.
Lines, Angles, and Circles.
Perimeter and Area.
Volume and Surface Area.
*The Metric System and Dimensional Analysis.
Geometric Symmetry and Tessellations.
Of Further Interest: Fractals.

9. Apportionment: How Do We Measure Fariness?
Understanding Apportionment.
The Huntington-Hill Apportionment Principle.
Applications of the Apportionment Principle.
*Other Paradoxes and Apportionment Methods.
Of Further Interest: Fair Division.

10. Voting: Using Mathematics to Make Choices.
Voting Methods.
Defects in Voting Methods.
Weighted Voting Systems.
Of Further Interest: The Shapley-Shubik Index.

11. Consumer Mathematics: The Mathematics of Everyday Life.
Consumer Loans.
Of Further Interest: The Annual Percentage Rate.

12. Counting: Just How Many Are There?
Introduction to Counting Methods.
The Fundamental Counting Principle.
Permutations and Combinations.
Of Further Interest: Counting and Gambling.

13. Probability: What Are the Chances?
The Basics of Probability Theory.
Complements and Unions of Events.
Conditional Probability and Intersections of Events.
Expected Value.
Of Further Interest: Binomial Experiments.

14. Descriptive Statistics: What Does a Data Set Tell Us?
Organizing and Visualizing Data.
Measures of Central Tendency.
Measures of Dispersion.
The Normal Distribution.
Of Further Interest: Linear Correlation.

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