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 PDF 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.