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