MAT102: Intro to Mathematical Proofs

Prerequisite: None

Check out the past exams!

What is MAT102 About?

Welcome to your first proof-based mathematics course at UofT!

What is a proof?

  • A proof, mathematical or not, is an argument or explanation that shows that something is absolutely, unequivocally true, beyond any shadow of a doubt. When you have accomplished that, it feels like magic.

  • The satisfaction when you write down Q.E.D.


Written by: Akira Takaki

For students coming from Ontario highschools, MAT102 is pretty difficult to wrap your head around. This is your first exposure to non-computational maths, where you use theorems and logic to prove things!

You need to understand that this is the CSC108 of math. It’s very different from actual math courses just like programming is not computer science. Here are MAT102-specific tips.

Be aware of the nit-picky stuff. just like in CSC108, there’s a lot of nit-picky details that us 102 TAs want you to state. Proofs are just arguments in math, and you should justify (with English!) how what you did is true, because it follows from other true things.

  • Stay on the ball. There’s usually a 10% quiz within one or two weeks of the class starting, and it’s going to hit you — hard. If it doesn’t, maybe math is your thing? Either way, you want to make sure you know your deadlines and don’t fall behind, because this course has a ton of deadlines.

  • Practice, a lot. You need to start practicing every day, early on, by doing practice problems. MAT102 has a decent amount of computational practice that you need to get down pat.

  • Start early! If something comes out, you need to look at it as early as possible. You can’t cram this course, and you need to really start asking questions early. Problem sets are a marathon, never a sprint.

  • If you end up liking this course, consider taking MAT240 (linear algebra for proofs), which is offered only in the winter. It’s a really fun continuation of some of the concepts you’ve now learnt, and is less pedantic.

Topics in MAT102

  • Set theory
  • Number theory
  • Field Axioms
  • Proof Techniques
    • Contradiction
    • MI
    • Contrapositive
    • Direct
    • Implication
  • Bijection and Cardinality
  • Euclidean geometry


A video to pump you up!

How do mathematicians prove things?


Field Axioms

Available Courses After MAT102