Weekly Plan
Module 1: Set Theory
Week 1
- Introduction to sets and notation
- Set operations: ∪, ∩, , ⊕, complement
- Power sets and subsets
- Venn diagrams
- Cartesian products
- Russell’s paradox
Week 2
- Axiomatic foundations (ZFC)
- Zermelo-Fraenkel axioms overview
- Axiom of choice
Module 2: Binary Relations
Week 3
- Binary relations: definition and representations
- Graph and matrix representations
- Properties: reflexive, symmetric, transitive
- Equivalence relations and partitions
- Closures of relations
📌 Homework 1 due | Test 1
Week 4
- Order relations (partial, linear, well-orders)
- Hasse diagrams
- Chains and antichains
- Dilworth’s theorem
- Composition of relations
Week 5
- Functions as relations
- Domain, codomain, range
- Injective, surjective, bijective
- Function composition and inverses
- Pigeonhole principle
Week 6: Cardinality
- Finite vs infinite sets
- Countable and uncountable
- Cantor’s diagonal argument
- Cantor’s theorem
- Schroeder-Bernstein theorem
Week 7
- Partially ordered sets (posets)
- Lattices: meets and joins
- Modular and distributive lattices
- Boolean algebras as lattices
📌 Homework 2 due | Test 2 | TM1 (Set Theory + Relations)
Module 3: Boolean Algebra
Week 8
- Boolean functions and truth tables
- Normal forms: DNF, CNF
- Boolean laws and duality
Week 9
- Logic gates and digital circuits
- Functional completeness
- Multi-level circuits
Week 10
- Karnaugh maps
- Circuit minimization
- Quine-McCluskey algorithm
📌 Homework 3 due | Test 3
Module 4: Formal Logic
Week 11
- Propositional logic: syntax and semantics
- Tautologies, contradictions
- Logical equivalence
Week 12
- Natural deduction proof system
- Soundness and completeness
- Proof techniques
Week 13
- Predicate logic (first-order logic)
- Quantifiers: ∀ and ∃
- Interpretations and models
- Gödel’s theorems (overview)
Week 14
- Categorical logic
- A, E, I, O statements
- Square of opposition
- Syllogisms and validity
Week 15
- Review of formal logic
- Advanced topics (time permitting)
📌 Homework 4 due | Test 4 | TM2 (Boolean Algebra + Logic)
Week 16
- Special topics
- Ordinals and cardinals
- Metalogical concepts
Exam Period
Final Exam: All course material (Weeks 1-16)
- Written portion: problem solving
- Oral portion: concepts and explanations
- Practical portion: applications