U of T · CSC165
Mathematical Expression & Reasoning
The course that teaches you how to think. Master logic, proof, and precise mathematical reasoning.
About this course
CSC165 is one of the most intellectually demanding first-year courses at U of T — not because the material is technically hard, but because it requires a completely different way of thinking: precise, formal, and rigorous.
Most students struggle because their high school math never required them to actually reason — just to compute. We fix that. We teach you to read and write proofs, understand quantifiers, construct rigorous arguments, and see why precision matters.
Our prep sessions run throughout the semester, covering the concepts before they're tested and giving you a chance to practice the kind of careful thinking CSC165 demands.
Sessions available throughout the full semester. Spots are limited — book early.
Topics covered
- Propositional and predicate logic
- Quantifiers (∀, ∃) and their negations
- Reading and writing formal proofs
- Proof by contradiction and contrapositive
- Induction (simple, strong, structural)
- Sets, relations, and functions
- Big-O, Ω, Θ complexity analysis
- Translating English statements into formal logic
What you get
Weekly sessions
Review key material before tests with a focus on proof strategies and common pitfalls.
1-on-1 tutoring
Targeted help on the exact problems you're stuck on.
Proof workshops
Practice constructing proofs from scratch with guided feedback.
Ready to get started?
Book a free diagnostic session and find the right starting point.
