MAT 511

Syllabus and Schedule

We will mainly follow some notes that Yongquan Zhang has kindly agreed to give me. Chapter I is currently posted on Brightspace.

Syllabus

1. Mathematical statements and proofs.
1.1 The language of mathematics.
1.2 Implications and proofs. Methods of proofs.
1.3 The induction principle.

2. Sets and functions.
2.1 Set theory.
2.2 Functions.
2.3 Injection, surjection and bijection.

3. Number systems and counting.
3.1 Finite sets.
3.2 Counting functions and subsets.
3.3 Number systems.
3.4 Counting infinite sets.

Schedule

Below there is the intended schedule for the course. It can change depending on how we progress on the contents.

Tu May 21: Presentation of the course. Mathematical statements and proofs.

Th May 23: Methods of proofs. The induction principle.

Tu May 28: Induction. Set theory.

Th May 30: Set theory. Functions.

Tu June 4: Math resources day.

Th June 6: Functions. Review of Chapters I and II.

Tu June 11: Finite sets. Properties of finite sets.

Th June 13: Counting functions abs subsets. Number systems. Equivalence relations.

Tu June 18: Presentation day.

Th June 20: Counting infinite sets. Some 'exotic' sets.

Tu June 25: Review session.

Th June 27: Final presentations day.