Recommended Reading

Published: Apr 30, 2022

Last Modified: Mar 16, 2024

Contest Mathematics

Problem Solving through Problems by Loren Larson
- UToronto Library
Putnam and Beyond by Răzvan Gelca
- UToronto Library
Problem Solving Strategies by Arthur Engel
- UToronto Library
The art and craft of problem-solving by Paul Zeitz
- UToronto Library

Puzzle-y Math

The art of mathematics - take two : tea time in Cambridge by Bollobás, Béla
- UToronto Library
The art of mathematics : coffee time in Memphis by Bollobás, Béla
- UToronto Library

General Mathematics

Concepts of Modern Mathematics by Ian Stewart
- UToronto Library
- This book is a light and conversational introduction to lots of cool ideas in modern mathematics. It had a big impact on me when I first read it as an undegraduate. What’s a set? It’s bag with stuff in it. What’s a set of sets? Well, a bag full of bags!
Mathematical Snapshots by Hugo Steinhaus
- UToronto Library
- This is a collection of curious and interesting facts in mathematics. It is not expository, and contains no proofs, but gives an idea of what mathematics is about. Lots of great topics for seminar talks.
Flavors and Seasons by Luke Walcott
- The Flavors and Seasons Project FAQ

Fiction

Fictions by Borges
- UToronto Library
- As a highschool student, I was absolutely obssessed with Borges. I read everything that I could get my hands on. Eventually, I started to learn Spanish to read him in the original. Fictions is an astounding collection of short stories. It simultaneously sparked my interest in philosophy and mathematics.
  - The Library of Babel
  - Pierre Menard, the Author of Don Quixote
  - The Babylon Lottery
  - Funes, the Memorious
Stories of Your Life and Others by Ted Chiang
- UToronto Library
- Deep and philosophically fascinating science fiction. When I was a graduate student, we passed this one around the office and all had our favourite stories. My favourites are:
  - Understand
  - The Story of Your Life
  - Seventy-Two Letters

Non-Fiction

The Lives of a Cell by Lewis Thomas
- UToronto Library
- Short, deep, thought-provoking essays by a modern Montaigne. Lewis Thomas was an American physician and essayist who wrote broadly about medicine, science, culture, and biology.
  - The Music of This Sphere (local copy)
  - Your Very Good Health
  - Social Talk
  - The World’s Biggest Membrane
The Hand: How Its Use Shapes the Brain, Language, and Human Culture by Frank Wilson
- UToronto Library

Productivity and Life Skills

How to Get Control of Your Time and Your Life by Alan Lakein
- UToronto Library
- This is the original guide to time management. It introduced the hugely influence “ABC method” of setting priorities. The language and examples are a bit dated, but the content and ideas are timeless. Every year or so, I dip into it and learn some new insight about managing my time and priorities.
How to Fail at Almost Everything and Still Win Big by Scott Adams
- Toronto Public Library
- The cartoonist behind Dilbert explains the principles of that he uses succeed in life. The book draws on a lot of experience in the corporate world, and extensive reading about psychology. Chapter 30 “Happiness” (local copy) preaches the importance of: flexible schedules, sleep, diet, exercise, and imagination.

Reading and Writing

Professor as Writers by Robert Boice
- UToronto Library
- Summarizes decades of original research on the writing habits of academics. It gives concrete evidence that daily writing with self-imposed boundaries leads to highly productive scholarship. A must read for anyone doing academic writing. For another guide to this style of working, without so much background, see How to Write a Lot by Silvia (UToronto Library).
The Elements of Style by Strunk and White
- UToronto Library
- The Classic introduction to style and writing well. People take issue with it sometimes, and there are inaccuracies in it. However, it is The Classic and everyone ought to read it several times.
The Sense of Style by Steven Pinker
- UToronto Libary
- This is a lot heavier than Strunk and White, but much more accurate and well thought out. Definitely a deep-dive in to style. I learned a lot about linguistics from reading this book.
Clear and Simple as the Truth by Thomas and Turner
- UToronto Library
- This book presents a very philosophical take on style. It describes the classic style as practiced by Montaigne, Descartes, etc. This book deeply influenced the way that I think about the purpose of expository writing.
How to Read a Book by Adler and van Doren
- UToronto Libary
- A dense and technical book about doing textual research in the humanities. Full of insightful distinctions about levels of reading and techniques for skimming and summarizing material.
How to Take Smart Notes by Ahrens
- UToronto Library
- This is a deep-dive in to note-taking techniques and zettelkasten (German: box of notecards). It advocates for writing very concise notes but connecting them in a hyperlinked manner. It is very preachy and over-simplifies the complexities of the writing process. For a contrasting view, see Rank and File by Minto.
Keshav, Srinivasan. “How to read a paper.” ACM SIGCOMM Computer Communication Review 37.3 (2007): 83-84. (local)
- There is a bunch of great advice on reading papers hosted by Papers We Love, a community which primarily focusses on computer science papers.

Potential Reads

These are less recommendations than texts that I would like read for fun with some people. Many of them would be suitable for Seminar. If any of these appeal to you, please let me know.

Sallows, Lee. “On self-tiling tile sets.” Mathematics Magazine 85.5 (2012): 323-333. (doi)
- Wikipedia
Dörrie, Heinrich. 100 great problems of elementary mathematics. Courier Corporation, 2013.
- My notes on the book on the Reading Page.
Sallows, Lee. “More On Self-Tiling Tile Sets.” Mathematics Magazine 87.2 (2014): 100-112. (doi)
Halmos, Paul R. “The heart of mathematics.” The American Mathematical Monthly 87.7 (1980): 519-524.
Conway, John H. “The weird and wonderful chemistry of audioactive decay.” Open problems in communication and computation. New York, NY: Springer New York, 1987. 173-188. (Springer Link)
Jocelyn R. Bell & Frank Wattenberg (2020) The Slippery Duck Theorem, Mathematics Magazine, 93:2, 91-103, DOI: 10.1080/0025570X.2020.1708693
Sam Chow, Ayla Gafni & Paul Gafni (2021) Connecting the Dots: Maximal Polygons on a Square Grid, Mathematics Magazine, 94:2, 118-124, DOI: 10.1080/0025570X.2021.1869493
Bhargava, Manjul. “The factorial function and generalizations.” The American Mathematical Monthly 107.9 (2000): 783-799.(pdf)
Birman, Joan S. “New points of view in knot theory.” Bulletin of the American Mathematical Society 28.2 (1993): 253-287. (pdf)
Margalit, Dan. “The Mathematics of Joan Birman.” Notices of the American Mathematical Society (2019). (pdf)
Pólya, George. Mathematics and plausible reasoning: Induction and analogy in mathematics. Vol. 1. Princeton University Press, 1990. (UToronto Library)
Kürschak’s Tile by G. L. Alexanderson and Kenneth Seydel The Mathematical Gazette Vol. 62, No. 421 (Oct., 1978), pp. 192-196 (JSTOR)

Advice on Reading Papers

Hobbies

String Figures and How to Make Them by Jayne
あやとり大全集 / 野口とも著.; Ayatori daizenshū by Noguchi, Tomo.; 野口とも.
- UToronto Library
Mark Wilson’s complete course in magic
- Toronto Public Library
Mysterio’s encyclopedia of magic and conjuring
- Toronto Public Library
Mac King’s Campfire Magic
- Toronto Public Library
Modern Coin Magic by Bobo
Card College by Roberto Giobbi
The Complete Juggler by Dave Finnigan