Quick info
Instructor: Alex Youcis
Email: alex.youcis@utoronto.ca (see syllabus for email policy!)
Office hours: Mon 2:30–4 (PGB003)
Syllabus: PDF
MAT138 — Introduction to Proofs (Fall 2025)
| Lecture — Date | Topic / Notes | Text (chapter) | Board photos |
|---|---|---|---|
| Lecture 1 — Sep 3, 2025 (Wed) | Anatomy of a proof, proof that \(\sqrt{2}\) is irrational | Chapters 1–2 | Lecture 1 photos |
| Lecture 2 — Sep 8, 2025 (Mon) | Definition of primes, some basic properties, and infinitude of primes | Chapter 3 | Lecture 2 photos |
| Lecture 3 — Sep 10, 2025 (Wed) | Precisely stated the fundamental theorem of arithmetic, proved existence portion, defined function \(v_p\) and proved basic properties about it | Chapter 3 + supplemental | Lecture 3 photos |
| Lecture 4 — Sep 15, 2025 (Mon) | Discussed Euclidean algorithm, proved Bezout's lemma, stated Euclid's proposition, and deduced uniqueness in fundamental theorem of arithmetic | Chapter 3 + supplemental | Lecture 4 photos |
| Lecture 5 — Sep 17, 2025 (Wed) | Gave proof of Euclid's proposition, talked about weak and strong mathematical induction, did many examples | Chapter 4 | Lecture 5 photos |
| Lecture 6 — Sep 22, 2025 (Mon) | Went through various proofs exploiting symmetry | Chapter 5 | Lecture 6 photos |
| Lecture 7 — Sep 24, 2025 (Wed) | Discussed several combinatorial proofs, noticably involving permutations and the function \(n\choose k)\) | Chapter 5 | Lecture 7 photos |
| Lecture 8 — Sep 29, 2025 (Mon) | We discussed many examples of proofs without words, how they can help, and how they can lie. | Chapter 6 | Lecture 8 photos |
| Lecture 9 — Oct 1, 2025 (Wed) | We discussed the (sub)set operations of union, intersection, difference, symmetric difference, complement, and Cartesian product. | Supplemental | Lecture 9 photos |
| Lecture 10 — Oct 6, 2025 (Mon) | We discussed relations, gave several examples, and talked aboout the properties of symmetric, reflexive, and transitive. | Chapter 11 | Lecture 10 photos |
| Lecture 11 — Oct 8, 2025 (Wed) | We discussed further properties of relations, notably talking about reflexive/symmetric/transitive closures of relations and defining equivalence relations. | Chapter 11 | Lecture 11 photos |
| — Oct 13, 2025 (Mon) | No lecture (holiday) | — | — |
| Lecture 12 — Oct 15, 2025 (Wed) | We discussed equivalence relations, partitions, and the beginning of functions. | Chapter 11 | Lecture 12 photos |
| — Oct 20, 2025 (Mon) | Midterm review | — | — |
| — Oct 22, 2025 (Wed) | Midterm | — | — |
| — Oct 27, 2025 (Mon) | Reading week — no lecture | — | — |
| — Oct 29, 2025 (Wed) | Reading week — no lecture | — | — |
| Lecture 13 — Nov 3, 2025 (Mon) | TBA | TBA | To be posted |
| Lecture 14 — Nov 5, 2025 (Wed) | TBA | TBA | To be posted |
| Lecture 15 — Nov 10, 2025 (Mon) | TBA | TBA | To be posted |
| Lecture 16 — Nov 12, 2025 (Wed) | TBA | TBA | To be posted |
| Lecture 17 — Nov 17, 2025 (Mon) | TBA | TBA | To be posted |
| Lecture 18 — Nov 19, 2025 (Wed) | TBA | TBA | To be posted |
| Lecture 19 — Nov 24, 2025 (Mon) | TBA | TBA | To be posted |
| Lecture 20 — Nov 26, 2025 (Wed) | TBA | TBA | To be posted |