Topics covered

In Jan 2026

1. Basics from Set Theory (Prerequisite of the Class)

2. Basics from Counting (Prerequisite of the Class)

3. Principle of Inclusion and Exclusion (PIE)

4. Binomial / Multinomial Expansions and Variants.

5. Equivalence of Mathematical Objects and Problems

6. Catalan Numbers and equivalent problems

7. Delanoy Path vs Lattice Balls

8. Recurrence Relation

9. Generating Function

10. Integer Partition

In Feb 2026

1. Poset: Example and Properties. Dilworth Theorem, Sperner's Theorem, Erdos-Szekeres Theorem and Application. 

2. Graph Theory: Basic definitions (degree, path, cycle, walk, tour, Independent set)

After Midsem

3. Graph Theory:  Examples and Applications

4. Chromatic number, Bipartite graph and k-partite graphs. Vertex cover.

5. Euler's Tour

6. Hamiltonian Path and Sufficient Conditions for Existence

7. Tournament and King

8. Tree, Basic  (spanning) trees. Characterizations

9. Matching:  Konig's Theorem, Hall's Marriage theorem and applications

10. Graph Algorithm: BFS, DFS and MST Finding Algorithms.  

11. BFS and DFS tree (the edges used In BFS and DFS search). Properties of BFS (distance preservering) and DFS trees (normal spanning tree) 

12. Colouring (Edge and Vertex). Vizing Theorem, Few results on vertex coloring

Books: 

1. Douglas B. West (Combinatorial Mathematics and Introduction to Graph Theory)

2. Douglas B. West (Introduction to Graph Theory), a separate book...

3. Bondy Murty:  Graph Theory with Applications. 

4. V.K.Balakrishnan (Schaum's Outlines: Combinatorics)

5. Jiri Matousek and Jaroslav Nesetril (Invitation to Discrete Mathematics)