18.218   M.I.T.   Spring 2016

18.204    Undergraduate Seminar in Discrete Mathematics

Class meets: MWF   1 pm   Room 2-136

Instructor: Alexander Postnikov   apost at math   Room 2-367

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


Ideas for topic of your first presentation:

  • Ideas for your second presentation


    1. W 02/03/2016. Introduction.

    2. F 02/05/2016. Alex Postnikov: Random Walk on a Line, aka Drunk Man Problem.
      Related links: Catalan numbers, random walks.

    3. M 02/08/2016. Berj Chilingirian: Arrow's Impossibility Theorem.

    4. W 02/10/2016. Liz Walker: Shuffling a Deck of Cards.
      [Proofs for the Book, Ch. 28]

    5. F 02/12/2016. Anne Kelley: Zero Knowledge Proofs.

    6. Tuesday! 02/16/2016. (Monday schedule of classes on Tuesday) Gabriella Baracchini: Linear Programming

    7. W 02/17/2016. Lynn Takeshita: Stable Marriage and Stable Roommate Theorems.

    8. F 02/19/2016. Xinyue Deng: Graph Search Algorithms.

    9. M 02/22/2016. Jon Lu: Simple Games with Not-So-Simple Strategies.

    10. W 02/24/2016. Michael Wallace: The Probabilistic Method.

    11. F 02/26/2016. Open mike.

    12. M 02/29/2016. Jeremy Wohlwend: Facts About Pi.

    13. W 03/02/2016. Cali Gallardo: Latin Squares and Codes.

    14. F 03/04/2016. Margaret Carpenter: Knapsack Problem.

    15. M 03/07/2016. Gerrod Voigt: Diophantine Equations.

    16. W 03/09/2016. Alex Postnikov: Cayley's formula for the number of trees and Prufer's codes.

    17. F 03/11/2016. Aaron Zwiebach: Diffie Hellman and RSA Encryption.

    18. M 03/14/2016. Greg Lubin: Pigeonhole principle and Ramsey numbers.

    19. W 03/16/2016. Alex Postnikov: Acyclic orientations of graphs.

    20. F 03/18/2016. Berj Chilingirian: Pink noise and sandpiles.

      03/21/2016 - 03/25/2016. no classes - Spring vacation

    21. M 03/28/2016. Gerrod Voigt: Finding Hamiltonian cycles: Bondy's proof of Ore's algorithm.
              Lynn Takeshita: Chromatic numbers of signed graphs.

    22. W 03/30/2016. Anne Kelley: Erdos-Szekeres theorem.

    23. F 04/01/2016. Jon Lu: 100 Prisoners Problem.

    24. M 04/04/2016. Xinyue Deng: Turan's Theorem

    25. W 04/06/2016. Greg Lubin: Inductive Reasoning and Bounded Rationality
              Margaret Carpenter: Cops vs Robber

    26. F 04/08/2016. Jeremy Wohlwend: Elliptic Curve Cryptography
              Aaron Zwiebach: Percolation - A Study in Randomly Generated D-Ary Trees

    27. M 04/11/2016. Liz Walker: Bin Paking Problem (papers: [Korf] and [Martello-Toth])
              Gabriella Baracchini: Bertrand's Ballot Problem.

    28. W 04/13/2016. Michael Wallace: A Probabilistic Proof of a Formula for the Number of Standard Young Tableaux of a Given Shape.

    29. F 04/15/2016. Discussion about writing a paper.

      M 04/18/2016. no class - Patriots Day

    30. W 04/20/2016. Berj Chilingirian: The Sandpile Load-Balancing Problem for Latency Minimization.

    31. F 04/22/2016. Anne Kelley: Chip Firing Games,
              Liz Walker: The Friendship Theorem.

    32. M 04/25/2016. Alex Postnikov: Abelian Sandpile Model and Spanning Trees.

    33. W 04/27/2016. Lynn Takeshita: Efficient Algorithms to Color Signed Graphs,
              Jeremy Wohlwend: A Survey of Modern Public Key Cryptography.

    34. F 04/29/2016. Gerrot Voight: Tree Decomposition, Treewidth, and NP-Hard Problems.

    35. M 05/02/2016. Xinyue Deng: Lenstra-Lenstra-Lovasz Lattice Basis Reduction Algorithm.

    36. W 05/04/2016. Margaret Carpenter: The Single Jeep and Jeep Caravan Problems.

    37. F 05/06/2016. Aaron Zwiebach: Random Walks and Percolation: An Analysis of Current Research on Modeling Natural Processes,
              Greg Lubin: Strategies for Pairwise Kidney Exchange.

    38. M 05/09/2016. Gabriella Baracchini: Catalan Numbers and Possible Applications,
              Jon Lu: Analysis of the Chow-Robbins Game

    39. W 05/11/2016. Michael Wallace: Housing Allocation with Multiple Tenants

    Term papers:

    last updated: May 13, 2016