1. Propositions and Logical Connectives

2. Truth Tables

3. Predicate Logic and Quantifiers

4. Logical Equivalences

5. Rules of Inference

6. Methods of Proof (Direct, Contrapositive, Contradiction, Induction)

7. Mathematical Induction and Strong Induction

Functions and Relations 

1. Functions: One-to-One, Onto, Bijective

2. Inverse and Composite Functions

3. Relations: Reflexive, Symmetric, Transitive

4. Equivalence Relations and Partitions

5. Partial and Total Orderings

6. Hasse Diagrams

Number Theory 

1. Divisibility and Modular Arithmetic

2. Prime Numbers and Factorization

3. GCD and Euclidean Algorithm

4. Congruences and Residue Classes

5. Fermat’s Little Theorem

6. Euler’s Theorem

7. Chinese Remainder Theorem

Algorithms and Complexity 

1. Algorithm Definition and Pseudocode

2. Big-O, Big-Theta, and Big-Omega Notation

3. Time and Space Complexity

4. Searching and Sorting Algorithms

5. Greedy and Divide & Conquer Methods

Automata Theory and Formal Languages 

1. Sets and Subsets

2. Set Operations (Union, Intersection, Complement, Difference)

3. Venn Diagrams

4. Cartesian Products

5. Power Sets

Counting and Combinatorics 

1. Basic Counting Principles (Addition, Multiplication)

2. Permutations and Combinations

3. Pigeonhole Principle

4. Inclusion-Exclusion Principle

5. Binomial Theorem

6. Combinatorial Identities

7. Recurrence Relations and Solving Recurrences

Graph Theory 

1. Graph Terminology (Vertices, Edges, Degree)

2. Types of Graphs (Simple, Directed, Weighted, Multigraphs)

3. Adjacency Matrix and List

4. Paths, Cycles, Connectivity

5. Eulerian and Hamiltonian Paths

6. Planar Graphs

7. Graph Coloring

8. Trees: Definitions, Properties, Spanning Trees, Binary Trees

9. Dijkstra’s and Kruskal’s Algorithms

Boolean Algebra 

1. Boolean Functions

2. Logic Gates and Circuits

3. Simplification of Boolean Expressions

4. Karnaugh Maps

5. Applications in Digital Logic Design

Discrete Structures