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!
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.
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.
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:
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.
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
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.
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 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.
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
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.
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.
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)
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.
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)