Eschewing the often standard dry and static writing style of traditional textbooks, Discrete Encounters provides a refreshing approach to discrete mathematics. The author blends traditional course topics and applications with historical context, pop culture references, and open problems. This book focuses on the historical development of the subject and provides fascinating details of the people behind the mathematics, along with their motivations, deepening readers’ appreciation of mathematics.

This unique book covers many of the same topics found in traditional textbooks, but does so in an alternative, entertaining style that better captures readers’ attention. In addition to standard discrete mathematics material, the author shows the interplay between the discrete and the continuous and includes high-interest topics such as fractals, chaos theory, cellular automata, money-saving financial mathematics, and much more. Not only will readers gain a greater understanding of mathematics and its culture, they will also be encouraged to further explore the subject. Long lists of references at the end of each chapter make this easy.


  • Features fascinating historical context to motivate readers
  • Text includes numerous pop culture references throughout to provide a more engaging reading experience
  • Its unique topic structure presents a fresh approach
  • The text’s narrative style is that of a popular book, not a dry textbook
  • Includes the work of many living mathematicians
  • Its multidisciplinary approach makes it ideal for liberal arts mathematics classes, leisure reading, or as a reference for professors looking to supplement traditional courses
  • Contains many open problems

Profusely illustrated

chapter |19 pages

Continuous vs. Discrete

chapter 1|31 pages


chapter 2|32 pages

Proof Techniques

chapter 3|16 pages

Practice with Proofs

chapter 4|34 pages

Set Theory

chapter 5|24 pages

Venn Diagrams

chapter 6|18 pages

The Functional View of Mathematics

chapter 7|19 pages

The Multiplication Principle

chapter 8|21 pages


chapter 9|23 pages


chapter 10|34 pages

Pascal and the Arithmetic Triangle

chapter 11|24 pages

Stirling and Bell Numbers

chapter 12|26 pages

The Basics of Probability

chapter 13|29 pages

The Fibonacci Sequence

chapter 14|28 pages

The Tower of Hanoi

chapter 15|20 pages

Population Models

chapter 16|22 pages

Financial Mathematics (and More)

chapter 17|25 pages

More Difference Equations

chapter 18|62 pages

Chaos Theory and Fractals

chapter 19|56 pages

Cellular Automata

chapter 20|70 pages

Graph Theory

chapter 21|21 pages


chapter 22|27 pages

Relations, Partial Orderings, and Partitions