**Combinatorics: (2/3rd of the course)**

- Enumeration: Basic counting techniques, inclusion-exclusion principle, permutations, combinations and binomial coefficients
- Bijections, double-counting, pigeon-hole principle, parity arguments
- Recurrences and generating functions, asymptotics
- Parial-orders, Dilworth's theorem, equivalence relations, countability
- Combinatorics of groups, Polya's theorem

** Graph Theory: (1/3rd of the course)**

- Basics of graphs, trees
- Matchings and Hall's theorem
- Extremal problems
- Planar graphs.
- Graph coloring

**Reference Books:**

- Combinatorical Techniques by Sharad Sane
- Lecture Notes on Mathematics for Computer Science by Eric Lehman, Thomson Leighton and Albert Meyer (available online)
- A Path to Combinatorics for Undergraduates by Andreescu and Feng
- Problem-solving Strategies by Arthur Engel
- Any book on discrete mathematics

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- Teacher: Aravind NR

- Teacher: Sukumar D

This is basic course on Real analysis and the emphasis on proofs of the fundamental facts.

- Teacher: Sukumar D