📆 Weekly Plan
📐 Module 1: Set Theory
Week 1: Foundations
- Introduction to sets and notation
- Set Operations: Union, intersection, difference, complement
- Power sets and subsets
- Euler diagrams, Venn diagrams
- Cartesian products
- Russell’s paradox
Week 2: Ordered Structures
- Tuples, n-tuples, ordered pairs
- Kuratowski’s definition
- Cartesian product and geometric interpretation
🔗 Module 2: Binary Relations
Week 3: Relations & Equivalence
- Binary relations as sets: definition and representations
- Graph and matrix representations
- Properties: reflexive, symmetric, transitive, etc.
- Equivalence relations
- Set partitions and quotient sets
- Composition and powers or relations
📌 Homework 1 due | Test 1
Week 4: Order Relations
- Orders, partial orders, total/linear orders
- Partially ordered sets (posets)
- Hasse diagrams
- Covering relation
- Maximal, minimal, greatest, least elements
- Chains and antichains
- Dilworth’s Theorem
Week 5: Functions
- Functions as special relations
- Domain, codomain, range
- Injective (1-1), surjective (onto), bijective
- Composition of functions
- Inverse functions
- Monotonic functions
- Characteristic function
Week 6: Cardinality
- Finite vs infinite sets
- Cardinality of sets
- Countable sets
- Uncountable sets
- Cantor’s diagonal argument
- Cantor’s theorem
- Schroeder-Bernstein theorem
Week 7: Lattices
- Upper and lower bounds
- Supremum and infimum
- Lattices
- 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
- Boolean functions
- Truth tables
- Normal forms: DNF (sum of products), CNF (product of sums)
- Boolean laws and duality principle
Week 9: Digital Circuits
- Logic gates
- Circuit design and analysis
- Functional completeness
- Standard Boolean basis
- NAND and NOR
- Post’s criterion
- Multi-level circuits
Week 10: Minimization
- Karnaugh maps (K-maps)
- Don’t care conditions
- Circuit optimization
- Quine-McCluskey algorithm
📌 Homework 3 due | Test 3
🧠 Module 4: Formal Logic
Week 11: Propositional Logic
- Syntax: Formulas, atoms, connectives
- Semantics: Truth tables, models
- Tautologies, contradictions, contingencies
- Logical equivalence
Week 12: Proof Systems
- Natural Deduction: Inference rules
- Proof techniques and strategies
- Metalogic: Soundness and completeness theorems
Week 13: Predicate Logic
- First-Order Logic (FOL)
- Universal and existential quantifiers
- Interpretations, domains, models
- Gödel’s Theorems (overview):
- Completeness: Valid -> Provable
- Incompleteness: Arithmetic has unprovable truths
Week 14: Categorical Logic
- Categorical statements: A (All), E (No), I (Some), O (Some…not)
- Square of opposition
- Syllogisms: Three-part arguments
- Validity analysis with Venn diagrams
Week 15: Review & Advanced Topics
- Comprehensive review of formal logic
- Advanced topics
📌 Homework 4 due | Test 4 | TM2 (Boolean Algebra + Logic)
Week 16: Special Topics
- Ordinals and cardinals
- Metalogical concepts
- Course wrap-up
🎯 Exam Period
Final Exam: Comprehensive assessment of all course material (Weeks 1-16)
Format:
- ✍️ Written: Definitions, theorems, consistent notes
- 🔧 Practical: Problem solving and proofs
- 💬 Verbal: Conceptual explanations