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.