MTHM133- Fundamental Concepts in Mathematics

MTHM133: Mathematical Logic

Topics to be discussed:

1. Elementary Set theory: Definitions ; Proving via Definitions creating Theorems; Proving via Theorems and Properties ( Advanced ); and non-routine Proof Techniques. eg. Using Characteristic Functions.

2. Logic: Propositional and Predicate Calculus. Definitions, Constructing Truth Value Table;  Logical Equivalence; Logical Validity.

3. Proof Techniques: Direct, Indirect, Contradiction, Contraposition, CounterExample and the like. ( Examples varies from field to field )

4. Advanced Treatment of Set theory and Logic. [ZFC Set Theory; Fuzzy Sets and Logic, Continnuum Hypothesis, Zorn's Lemma, Modal Logic and the like )

5. Functions, Relations, Orderings and Some Number Theory.

6. Mathematical Research.