SYLLABUS
Propositional/Predicate Logic:
- Logical Propositions – Operations – Truth Tables
- Translation to/from Natural Language
- Quantifiers
- Rules of Inference
Proof Techniques:
- Implication Proofs (direct, indirect, contradiction)
- Case Analysis
- Equivalence
- Existential Proofs
- Proof by Counterexample
- Uniqueness Proof
- Proofs for Propositions with Universal Quantifiers
- Mathematical Induction
Fundamental Number Theory:
- Integer Division
- Prime Numbers
- Modular Arithmetic
Set Theory:
- Operations on Sets
- Powerset
- Cartesian Product
- Inclusion-Exclusion
Relations and Functions:
- Properties of Relations
- The Function as a Special Case of a Relation
- Equivalence Relations
Sums – Products:
- Properties of Sums
- The Technique of Equating Sums
- Guess and Prove by Induction
- Telescopic Sums
- Transformation of Products into Sums
Fundamental Combinatorics:
- The Equivalence Principle, The Pigeonhole Principle
- Product and Sum Principles
- Samples – Combinations – Permutations – Choices
- Inclusion – Exclusion
Balls in Bins
