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
Biography
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.
