A Path to Combinatorics for Undergraduates

This unique approach to combinatorics is centered around unconventional, essay-type combinatorial examples, followed by a number of carefully selected, challenging problems and extensive discussions of their solutions. Topics encompass permutations and combinations, binomial coefficients and their applications, bijections, inclusions and exclusions, and generating functions. Each chapter features fully-worked problems, including many from Olympiads and other competitions, as well as a number of problems original to the authors; at the end of each chapter are further exercises to reinforce understanding, encourage creativity, and build a repertory of problem-solving techniques. The authors’ previous text, “102 Combinatorial Problems,” makes a fine companion volume to the present work, which is ideal for Olympiad participants and coaches, advanced high school students, undergraduates, and college instructors. The book’s unusual problems and examples will interest seasoned mathematicians as well. “A Path to Combinatorics for Undergraduates” is a lively introduction not only to combinatorics, but to mathematical ingenuity, rigor, and the joy of solving puzzles.

Table of Contents

1. Addition or Multiplication?

2. Combinations

3. Properties of Binomial Coefficients

4. Bijections

5. Recursions

6. Inclusion and Exclusion

7. Calculating in Two Ways: Fubini’s Principle

8. Generating Functions

9. Review Exercises

About the Author

Titu Andreescu is an associate professor of mathematics in the Science and Mathematics Education department at the University of Texas at Dallas (UTD). Much of his career has been devoted to competition math, an efficient medium for teaching creative problem-solving for a wide-range of math topics. With over 30 years of experience teaching, coaching, and mentoring the brightest mathematical minds of our age, Dr. Andreescu’s books are essential for every math enthusiast’s library. Here are just a few highlights from his distinguished career:

-Authored, co-authored, and edited more than 40 math books and publications

-Head coach and leader of the USA International Mathematical Olympiad (IMO) for 8 years

-Director of the Mathematical Association of American (MAA) American Mathematics -Competitions for 5 years

-Has contributed hundreds of problems to various math competitions including and up to the IMO

-Co-founder of the Purple Comet! Math Meet, the first international team based math competition, http://www.purplecomet.org/

-Founder and Director of AwesomeMath, an organization that provides enriching experiences in mathematics to intellectually curious learners, https://www.awesomemath.org/