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

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