Table of Contents

Preface for Instructors and Other TeachersPreface for Students and Other LearnersTheme: The Basics1 Counting and Proofs2 Sets and Logic3 Graphics and Functions4 Induction5 Algorithms with CiphersTheme I Supplement6 Binomial Coefficients and Pascal's Triangle7 Balls and Boxes and PIE: Counting Techniques8 Recurrences9 Cutting Up Food: Counting and GeometryIII Theme: Graph Theory10 Trees11 Euler's Formula and Applications12 Graph Traversals13 Graph ColoringTheme III Supplement: Problems on the Theme of Graph TheoryIV Other Material14 Probability and Expectation15 Fun with Cardinality16 Number Theory17 Computational ComplexityA Solutions to Check Yourself ProblemsB Solutions to Bonus Check-Yourself ProblemsC The Greek Alphabet and Some Uses for Some LettersD List of SymbolsBibliographyIndex

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.