Table of Contents

Preface for Instructors and Other Teachers

Preface for Students and Other Learners

Theme: The Basics

1 Counting and Proofs

2 Sets and Logic

3 Graphics and Functions

4 Induction

5 Algorithms with Ciphers

Theme I Supplement

6 Binomial Coefficients and Pascal’s Triangle

7 Balls and Boxes and PIE: Counting Techniques

8 Recurrences

9 Cutting Up Food: Counting and Geometry

III Theme: Graph Theory

10 Trees

11 Euler’s Formula and Applications

12 Graph Traversals

13 Graph Coloring

Theme III Supplement: Problems on the Theme of Graph Theory

IV Other Material

14 Probability and Expectation

15 Fun with Cardinality

16 Number Theory

17 Computational Complexity

A Solutions to Check Yourself Problems

B Solutions to Bonus Check-Yourself Problems

C The Greek Alphabet and Some Uses for Some Letters

D List of Symbols

Bibliography

Index

About the Author

sarah-marie belcastro is a free-range mathematician who works primarily in topological graph theory. She enjoys connecting people to each other, connecting ideas to each other, and connecting people to ideas. Among her many non-pure-mathematics interests are the mathematics of knitting, pharmacokinetics, dance (principally ballet and modern), and changing the world. sarah-marie did her undergraduate work at Haverford College and her Ph.D. at the University of Michigan. She currently directs the summer program MathILy.