MATH 135: Algebra for Honours Mathematics
University of Waterloo — Fall 2021
Section instructor: Mark W. Girard
These materials were created to supplement the shared course resources.
Practice Problems
Each problem set was written in LaTeX and compiled with and without solutions.
| Chapter(s) | Problems (PDF) | With Solutions (PDF) | LaTeX Source |
|---|---|---|---|
| Chapter 4: Induction | Download | Download | TeX |
| Chapter 5: Sets | Download | Download | TeX |
| Chapters 6–8: GCD & Division | Download | Download | TeX |
| Chapter 9: RSA Encryption | Download | Download | TeX |
| Chapters 9–10: Complex numbers and Polynomials | Download | Download | TeX |
Sample Proofs from Lectures
The following lecture slides illustrate various proof techniques taught in the course. Each includes both the compiled PDF shown in class and the original LaTeX source.
| Lecture # | Topic | LaTeX Source | |
|---|---|---|---|
| 5 | Proving equalities, inequalities, cases | Lecture 5 | TeX |
| 6 | Existential proofs, negation, implications | Lecture 6 | TeX |
| 8 | Contrapositive, elimination, iff | Lecture 8 | TeX |
| 9 | Contradiction, uniqueness | Lecture 9 | TeX |
| 10 | Induction | Lecture 10 | TeX |
| 11 | Strong induction, recursive sequences | Lecture 11 | TeX |
| 12 | Game proofs — Chomp | Lecture 12 | TeX |
Visualizing the GCD
This PDF was shown in class to help visualize the Euclidean algorithm for computing the GCD.