Discrete Mathematics Syllabus
| Topic | Subtopics / What to Cover |
|---|---|
| Mathematical Logic | Propositions ⭐ Logical connectives ⭐ |
| Predicate Logic | Predicates ⭐ Quantifiers ⭐ |
| Normal Forms | CNF ⭐ DNF ⭐ |
| Methods of Proof | Direct ⭐ Contradiction ⭐ Contrapositive ⭐ |
| Set Theory | Sets ⭐ Operations ⭐ |
| Relations | Properties ⭐ Equivalence relation ⭐ |
| Functions | Types of functions ⭐ Composition ⭐ |
| Partial Order | Poset ⭐ Hasse diagram ⭐ |
| Lattices | Types ⭐ Properties |
| Boolean Algebra | Laws ⭐ Duality ⭐ |
| Counting Principles | Addition ⭐ Multiplication ⭐ |
| Permutations | With/without repetition ⭐ |
| Combinations | Binomial coefficients ⭐ |
| Pigeonhole Principle | Basic ⭐ Generalized ⭐ |
| Recurrence Relations | Linear ⭐ Homogeneous ⭐ |
| Solving Recurrences | Substitution ⭐ Characteristic equation ⭐ |
| Generating Functions | Ordinary GF |
| Graph Theory | Graph types ⭐ Terminology ⭐ |
| Graph Representation | Adjacency matrix ⭐ List ⭐ |
| Graph Traversal | BFS ⭐ DFS ⭐ |
| Trees | Properties ⭐ Spanning trees ⭐ |
| Binary Trees | Traversals ⭐ Properties ⭐ |
| Minimum Spanning Tree | Kruskal ⭐ Prim ⭐ |
| Shortest Path | Dijkstra ⭐ |
| Planar Graphs | Euler formula |
| Graph Coloring | Chromatic number ⭐ |
| Hamiltonian & Euler | Conditions ⭐ |
| Algebraic Structures | Group ⭐ Ring |
| Groups | Subgroup ⭐ Homomorphism |
| Probability Basics | Sample space ⭐ Events ⭐ |
| Conditional Probability | Bayes theorem ⭐ |
| Random Variables | Discrete RV ⭐ |
| Distributions | Binomial ⭐ Poisson ⭐ |