18.204    Undergraduate Seminar in Discrete Mathematics

Class meets: MWF   1 pm   Room 2-146

Instructor: Alexander Postnikov  

Course webpage: http://math.mit.edu/~apost/courses/18.204/

Description: Seminar in combinatorics, graph theory, and discrete mathematics in general. Participants read and present papers from recent mathematics literature. Instruction and practice in written and oral communication provided.

Course Level: Undergraduate

Syllabus

What is the next step?

• Final versions of papers.

Ideas for topic of your first presentation:

• A section from Aigner, Ziegler: Proofs from THE BOOK
• A section from Van Lint, Wilson: A Course in Combinatorics
• A section from Bona: A Walk Through Combinatorics
• Topics from past years: OCW 18.304 page from Spring 2015, topics from Spring 2016, McConville's list of suggested topics from Fall 2015.

• See the topics of presentations at 18.204 webpage from 2016.
• Some papers.

Schedule:

1. W 02/07/2018. Introduction.

   First presentations:

2. F 02/09/2018. Alex Postnikov: How to count by cyclic shifts?

3. M 02/12/2018. Jackie Bredenberg: Stable marriage theorem.

4. W 02/14/2018. Annika Kim: Gambler's ruin.

5. F 02/16/2018. Jingyu Li: Card shuffling.

   M 02/19/2018. Presidents day - no class

6. T 02/20/2018 (MONDAY SCHEDULE). Rachel Wu: Cayley's formula for trees.

7. W 02/21/2018. Yilin Wang: Applications of generating functions.

8. F 02/23/2018. Lee Bernick: Tiling rectangles + Electrical networks.

9. M 02/26/2018. Josh Brunner: Expected card draw in Dominion.

10. W 02/28/2018. Nicole Chesnokov: Friendship Theorem.

11. F 03/02/2018. Sicong Shen: Arrow's Impossibility Theorem.

12. M 03/05/2018. Arjun Mithal: Discrete Stochastic Processes.

13. W 03/07/2018. Nestor Chachamis: Completing Latin Squares.

14. F 03/09/2018. Timothy Ngotiaoco: Impartial Games (Sprague-Grundy).

15. M 03/12/2018. Camilo Espinosa: Generating functions.

16. W 03/14/2018. Julie Zhang: PHP, Pi, and Pie.

17. F 03/16/2018. Workshop on how to make a clear and interesting presentation by Susan Ruff.

18. M 03/19/2018. Jenny Jin: Art gallery problem.

19. W 03/21/2018. Timothee Schoen: Fermat's First Theorem.

    Second presentations:

20. F 03/23/2018. Rachel Wu: Unavoidable patterns in words.

    M-F 03/26/2018 - 03/30/2018. (-: Spring Vacation :-)

21. M 04/02/2018. Jackie Bredenberg: Probabilistic proof of the formula for Young tableaux.

22. W 04/04/2018. Josh Brunner: A position in infinite chess with game value omega^4.

    Lee Bernick: Erdos-Renyi random graphs.

23. F 04/06/2018. Annika Kim: Linear-time option pricing algorithms by combinatorics.

    Timothy Ngotiaoco: Evaluating the Nim-Value of Hackenbush.

24. M 04/09/2018. Arjun Mithal: Roman domination in graphs.

    Jingyu Li: Sperner property.

25. W 04/11/2018. Nestor Chachamis: A simple proof of Erdos-Ko-Rado theorem.

26. F 04/13/2018. *****

    M 04/16/2018. Patriots day - no class.

27. W 04/18/2018. Julie Zhang: Chromatic polynomials.

    Timothee Schoen: The 100 prisoners problem.

28. F 04/20/2018. Nicole Chesnokov: Friendship paradox.

    Camilo Espinosa: Applications of the probabilistic method.

29. M 04/23/2018. Sicong Shen: Sperner's lemma and rental harmony.

    Jenny Jin: Bertrand's ballot problem.

    Third presentations (presentations of final papers):

30. W 04/25/2018. Lee Bernick: Generalized random graph models.

31. F 04/27/2018. Camilo Espinosa: Symmetric Lovasz local lemma.

32. M 04/30/2018. Nestor Chachamis: Bounds on Ramsey numbers.

    Rachel Wu: Unavoidable patterns in words, part 2.

33. W 05/02/2018. Jackie Bredenberg: Counting via bijections with Young tableaux.

34. F 05/04/2018. Annika Kim: Using combinatorics to price options in linear time.

35. M 05/07/2018. Arjun Mithal: Analyzing optimal play in the Chow-Robbins formulation.

36. W 05/09/2018. Timothy Ngotiaoco: The spectral characterization of simply-laced Dynkin diagrams.

    Josh Brunner: The mate in n problem in infinite chess for finite positions is decideable.

37. F 05/11/2018. Jenny Jin: Analysis and applications of Burnside's lemma.

    Jingyu Li: Exploitability and GTO strategies in poker.

38. M 05/14/2018. Nicole Chesnokov: Extensions of the art gallery problem: Chromatic coloring and mobile guards.

    Sicong Shen: The First Fundamental Theorem of Welfare Economics.

39. W 05/16/2018. Timothee Schoen: General case of the 100 prisoners problem.

    Julie Zhang: Chromatic polynomials for hypergraphs.

• Lee Bernick: Modeling human networks using random graphs (05/04/2018).

• Jackie Bredenberg: A survey on bijections with Young tableaux (05/14/2018).

• Josh Brunner: Infinite chess (05/18/2018).

• Nicole Chesnokov: The art gallery problem: An overview and extension to chromatic coloring and mobile guards (05/16/2018).

• Christos Nestor Chachamis: Ramsey numbers (05/13/2018).

• Camilo Espinosa: The probabilistic method (05/16/2018).

• Jenny Jin: Analysis and applications of Burnside's lemma (05/17/2018).

• Annika Kim: Options pricing using combinatoric methods (05/10/2018).

• Jingyu Li: Exploitability and game theory optimal play in poker (05/17/2018).

• Arjun Mithal: Analysis of the Chow-Robbins game with biased coins (05/17/2018).

• Timothy Ngotiaoco: The spectral characterization of simply-laced Dynkin diagrams (05/08/2018).

• Timothee Schoen: Introduction to the general case of the 100 Prisoners Problem (05/17/2018).

• Sicong Shen: First fundamental theorem of welfare economics (05/17/2018).

• Rachel (Menghua) Wu: Survey of combinatorics on words and patterns (05/17/2018).

• Julie Zhang: An introduction to chromatic polynomials (05/17/2018).

last updated: May 14, 2018