How to Read, Understand and Study Proofs

(This talk was given on March 31, 2014, at the University of Toronto to a class of mostly MAT 137 students. It was standing room only!)

In my first year of undergrad I was bad at proofs. In my second year of undergrad I was terrible at proofs. In my third year I was okay at proofs, but I was terrible at studying proofs.

The way I used to learn proofs was by memorizing the words in the textbook’s proof, word by word, with almost no understanding. I knew math, and I was fairly good at problems, but I just couldn’t get any purchase when it came to learning proofs.

Eventually I started to pick up various “tricks” and strategies for learning proofs. This talk is aimed at me in first year, and what I needed to hear so that I could have studied proofs better. (“I no proof good.”)

We’ll look at the basics of proof reading, the idea of definition unwinding and clever ideas, and finally we’ll present a general method for reading proofs.

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