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Proof and the Art of Mathematics | May-Jul 2025

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Proof and the Art of Mathematics

Joel D. Hamkins


05 May 2025 to 09 Jul 2025
About the Book

From the preface of the book:

[…] 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. Please enjoy!

My main motivation for this reading is that I am teaching discrete mathematics course this summer and attempting to write a companion text. Hamikins’ book is a joy to read and I am looking forward to the good vibes! No specific pre-requisites required.

You can find this book on Amazon. More pointers on the book site.

Timings and Venue

We meet on Zoom at 9AM IST for about 60-90 minutes every day according to the daily-ish schedule below: the plan is to meet on all weekdays with a break about half-way, and cover an average of two subsections in one session. Here’s a link to a WA group for general discussions and meetup reminders, and announcements of any changes to the schedule. The Zoom details are below:

Meeting ID: 977 9556 2618
Passcode: irrational

Alternatively, you can use this link to join directly. See you there!

Date Lecture Slides Notes Video
05 May, 2025 Chapter 1
A classical beginning.
06 May, 2025 Chapter 1
Exercises based on Chapter 1
07 May, 2025 Chapter 2
Multiple Proofs, and exercises.
08 May, 2025 Chapter 3
Number Theory
09 May, 2025 Chapter 3
Exercises based on Chapter 3
12 May, 2025 Chapter 4
Mathematical Induction
13 May, 2025 Chapter 4
Exercises based on Chapter 4
14 May, 2025 Chapter 5
Discrete Mathematics
15 May, 2025 Chapter 5
Discrete Mathematics (continued)
16 May, 2025 Chapter 5
Exercises based on Chapter 5
19 May, 2025 Chapter 6
Proofs without Words
20 May, 2025 Chapter 6
Exercises based on Chapter 6
28 May, 2025 Chapter 7
Theory of Games
29 May, 2025 Chapter 7
Theory of Games (continued)
30 May, 2025 Chapter 7
Exercises based on Chapter 7
10 Jun, 2025 Chapter 8
Pick's Theorem
11 Jun, 2025 Chapter 8
Exercises based on Chapter 8
12 Jun, 2025 Chapter 9
Lattice Point Polygons
16 Jun, 2025 Chapter 9
Exercises based on Chapter 9
17 Jun, 2025 Chapter 10
Polygonal Dissection Congruence Theorem
18 Jun, 2025 Chapter 10
Exercises based on Chapter 10
19 Jun, 2025 Chapter 11
Functions and Relations
07 Jul, 2025 Chapter 11
Exercises based on Chapter 11
08 Jul, 2025 Chapter 12
Graph Theory
09 Jul, 2025 Chapter 12
Exercises based on Chapter 12
10 Jul, 2025 Chapter 13
Infinity
11 Jul, 2025 Chapter 13
Exercises based on Chapter 13
14 Jul, 2025 Chapter 14
Order Theory
15 Jul, 2025 Chapter 15
Exercises based on Chapter 14
16 Jul, 2025 Chapter 15
Real Analysis
17 Jul, 2025 Chapter 15
Exercises based on Chapter 15
18 Jul, 2025 Round Up
Summary Session
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