The main topics that we cover in this course are:
- Numbers, and Inequalities.
- Sets, functions and fields.
- Informal logic.
- Mathematical Induction.
- Bijections and cardinality.
- Integers and divisibility.
The course note is available: MAT102
The slides for weekly lectures can be found here:
- MAT102_Week 4-5
- MAT102_Week 6
- MAT102_Week 7
- MAT102_Week 8
- MAT102_Week 9
- MAT102_Week 11-12
Below are a few short video clips I made to explain certain questions upon students’ request.
- 2.5.29 Part a) Prove or disprove if two functions f and g are bounded, then their sum f+g is bounded.
- 2.5.29 Part b). Prove of disprove if two functions f and g are bounded, then f^2-g^2 is bounded.
- 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?