Proof and the Art of Mathematics
About the book
From the preface: "I have organized the book around a selection of mathematically rich topics, having interesting theorems with elementary proofs. I have chosen what I find to be especially enjoyable mathematical topics—at times fanciful, yet always amenable to a serious mathematical analysis—because I feel students will learn best how to write proofs with material that is itself intrinsically interesting."
My main motivation for this reading was that I was teaching a discrete mathematics course that summer and attempting to write a companion text. Hamkins' book is a joy to read. The plan was to cover an average of two subsections per session.
Prerequisites
No specific prerequisites.
Sessions
- 5 May Chapter 1 A classical beginning.
- 6 May Chapter 1 Exercises based on Chapter 1
- 7 May Chapter 2 Multiple Proofs, and exercises.
- 8 May Chapter 3 Number Theory
- 9 May Chapter 3 Exercises based on Chapter 3
- 12 May Chapter 4 Mathematical Induction
- 13 May Chapter 4 Exercises based on Chapter 4
- 14 May Chapter 5 Discrete Mathematics
- 15 May Chapter 5 Discrete Mathematics (continued)
- 16 May Chapter 5 Exercises based on Chapter 5
- 19 May Chapter 6 Proofs without Words
- 20 May Chapter 6 Exercises based on Chapter 6
- 28 May Chapter 7 Theory of Games
- 29 May Chapter 7 Theory of Games (continued)
- 30 May Chapter 7 Exercises based on Chapter 7
- 10 Jun Chapter 8 Pick's Theorem
- 11 Jun Chapter 8 Exercises based on Chapter 8
- 12 Jun Chapter 9 Lattice Point Polygons
- 16 Jun Chapter 9 Exercises based on Chapter 9
- 17 Jun Chapter 10 Polygonal Dissection Congruence Theorem
- 7 Jul Chapter 11 Exercises based on Chapter 11
- 8 Jul Chapter 12 Graph Theory
- 9 Jul Chapter 12 Exercises based on Chapter 12
- 11 Jul Chapter 13 Exercises based on Chapter 13
- 14 Jul Chapter 14 Order Theory
- 16 Jul Chapter 15 Real Analysis
- 17 Jul Chapter 15 Exercises based on Chapter 15