- Meeting 01 : Tue, Aug 03, 11:00 am-11:50 am
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Introduction. Administrative announcements. The pigeonhole principle.
- Meeting 02 : Wed, Aug 04, 10:00 am-10:50 am
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Applications of the pigeonhole principle.
- Meeting 03 : Thu, Aug 05, 08:00 am-08:50 am
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Erdos Szekeres theorem. Dilworth's generalization.
- Meeting 04 : Fri, Aug 06, 02:00 pm-02:50 pm
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Posets. Dilworth’s generalization of Erdos-Szekeres. Mantel’s theorem.
- Meeting 05 : Tue, Aug 10, 11:00 am-11:50 am
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Extremal: Turan’s theorem. What are the extremal graphs for Turan’s theorem? - Turan’s graphs.
- Meeting 06 : Wed, Aug 11, 10:00 am-10:50 am
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Turan’s theorem - completion of proof. Erdos Stone (without proof) An application of Erdos-Stone.
- Meeting 07 : Thu, Aug 12, 08:00 am-08:50 am
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Matchings. Existence of matchings. Hall’s theorem. Proof.
- Meeting 08 : Fri, Aug 13, 02:00 pm-02:50 pm
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Systems of distinct representatives. Applications: Latin squares.
- Meeting 09 : Tue, Aug 17, 11:00 am-11:50 am
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Doubly stochastic matrices. Birkhoff-Neumann theorem.
- Meeting 10 : Wed, Aug 18, 10:00 am-10:50 am
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More applications of Hall’s theorem (without proof)
- Meeting 11 : Thu, Aug 19, 08:00 am-08:50 am
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Ramsey’s theorem for graphs : inductive proof.
Ramsey’s theorem for graphs : another proof.
- Meeting 12 : Fri, Aug 20, 02:00 pm-02:50 pm
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Counting: The Inclusion exclusion principle. Applications
- Meeting 13 : Tue, Aug 24, 11:00 am-11:50 am
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More applications of IE. Euler totient function. Mobius function and Mobius inversion formula.
- Meeting 14 : Wed, Aug 25, 10:00 am-10:50 am
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Mobius inversion - proof and applications. Introduction to algebraic structures.
- Meeting 15 : Thu, Aug 26, 08:00 am-08:50 am
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Introduction to algebraic structures: Posets, Dilworth’s theorem.
- Meeting 16 : Fri, Aug 27, 02:00 pm-02:50 pm
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Tutorial: Erdos Sekeres, Dilworth, hall’s and Turan’s.
- Meeting 17 : Tue, Aug 31, 11:00 am-11:50 am
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Tutorial - questions from Problem set 1
- Meeting 18 : Wed, Sep 01, 10:00 am-10:50 am
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Discussions - clarifying doubts