2019 Winter MAT102: Intro to Math Proof

The main topics that we cover in this course are:

1. Numbers, and Inequalities.
2. Sets, functions and fields.
3. Informal logic.
4. Mathematical Induction.
5. Bijections and cardinality.
6. Integers and divisibility.
7. Relations.

The course note is available: MAT102

The slides for weekly lectures can be found here:

1. MAT102_Week1-2
2. MAT102_Week2-3
3. MAT102_Week 4-5
4. MAT102_Week 6
5. MAT102_Week 7
6. MAT102_Week 8
7. MAT102_Week 9
8. MAT102_Week10
9. MAT102_Week 11-12

Below are a few short video clips I made to explain certain questions upon students’ request.

1. 2.5.29 Part a) Prove or disprove if two functions f and g are bounded, then their sum f+g is bounded.
2. 2.5.29 Part b). Prove of disprove if two functions f and g are bounded, then f^2-g^2 is bounded.
3. 2.5.50. Show that in any field F, the equation x^2 = 1 can have at most two solutions.
   Can you think of a field in which the equation x^2 = 1 has exactly one solution?