# 18.204 Undergraduate Seminar in Discrete Mathematics

**Fall 2018, Massachusetts Institute of Technology**

**Class meetings:** Mondays and Wednesdays 11am–12:30pm in 2-147

**Instructor:** Zilin Jiang (see website for contact info)

**Communication specialist:** Malcah Effron

## Course 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. Enrollment limited.

## Grading

3 presentations worth 15% each, 3 in-class midterms worth 10% each, and the term paper for 25%.

*Attendance policy:* Without a valid excuse such as illness, failure to show up at one’s own talk or more than three failures to attend the classes results an immediate failure.

Stellar/Gradebook

## Schedule

(Schedule subject to change)

M | W | ||
---|---|---|---|

9/5 | Introduction | ||

9/10 | Kimberly Villalobos Carballo Zilu Pan |
9/12 | Presentation workshop |

9/17 | Kritkorn Karntikoon Jennifer Zou |
9/19 | Rebekah Terry Inioluwa Oguntola |

9/24 | Vivek Miglani Alexander Cauneac |
9/26 | Sophia Xia Zilin Jiang |

10/1 | Jamison Rich James Allen |
10/3 | Stephanie Yuen Joseph Kuan |

10/8 | No class (Columbus day) |
10/10 | In-class midterm #1 |

10/15 | Writing workshop | 10/17 | Stephanie Yuen Zilin Jiang |

10/22 | Zilu Pan Kritkorn Karntikoon |
10/24 | Inioluwa Oguntola Joseph Kuan |

10/29 | Jennifer Zou Rebekah Terry |
10/31 | Kimberly Villalobos Carballo Jamison Rich |

11/5 | Vivek Miglani Alexander Cauneac |
11/7 | Sophia Xia James Allen |

11/12 | No class (Veterans day) |
11/14 | In-class midterm #2 |

11/19 | Presentation workshop | 11/21 | Vivek Miglani Sophia Xia Jennifer Zou |

11/26 | Stephanie Yuen Zilu Pan Alexander Cauneac |
11/28 | Kritkorn Karntikoon Rebekah Terry Joseph Kuan |

12/3 | In-class midterm #3 |
12/5 | Peer critique |

12/10 | Inioluwa Oguntola Kimberly Villalobos Carballo Jamison Rich |
12/12 | Party |

## References

- Chapter 20 “In praise of inequalities” of Proofs from the Book by Aigner and Ziegler
- Miniature 9 “Equiangular lines” of Thirty-three miniatures by Matoušek
- A point in many triangles by Bukh
- Chapter 38 “Five-coloring plane graphs” of Proofs from the Book by Aigner and Ziegler
- A symmetric formulation of the Croot-Lev-Pach-Ellenberg-Gijswijt capset bound by Tao
- An introduction to infinitary combinatorics by Burak Kaya
- Random algebraic construction of extremal graphs by Bukh
- Miniature 19 “The end of the small coins” Thirty-three miniatures by Matoušek
- Chapter 4 “Standard Young tableaux” A Combinatorial Miscellany by Björner and Stanley
- Chapter 2.1 “Sets with good worst-case discrepancy” Geometric discrepancy by Matoušek
- On sets of integers which contain no three terms in arithmetical progression by Behrend
- The kissing problem in three dimensions by Musin
- Euclidean Ramsey theorems. I by Erdős, Graham, Montgomery, Rothschild, Spencer and Straus
- Chapter 3 “Unavoidable patterns” Algebraic combinatorics on words by Lothaire
- Equiangular lines by Lemmens and Seidel
- Lower bounds for weak epsilon-nets and stair-convexity by Bukh, Matoušek and Nivasch
- A partition calculus in set theory by Erdős and Rado
- All triangles are Ramsey by Frankl and Rödl
- The four-colour theorem by Robertson, Sanders, Seymour and Thomas
- The man who knew partition asymptotics by Yuan
- A note on the Turán function of even cycles by Pikhurko
- Section 6 “Connectivity” Mini-course on random graphs by Abbe
- Miniature 5 “Error-Correcting Codes” Thirty-three miniatures by Matoušek
- Six standard deviations suffice by Spencer
- Euler’s Pentagonal Number Theorem by Andrews