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## MATH 21-301: Combinatorics

### Announcements

• (08-29-17) Welcome to Combinatorics!
• (08-25-17) Your homework is required to be typed. Here is a tutorial for how to use Overleaf to type your homework. This document was generously provided by the benevolent Dr. Kristin Heysse. Here is the template referenced in the tutorial, which can be copy and pasted to start your document.
• (8-30-17) My office hours will be Tuesdays from 2-4 pm in Wean 7124, or by appointment.
• (09-05-17) Homework 2 is now posted on the Homework page.
• (09-07-17) A useful function for question 4 on Homework 2 is the Möbius function μ(n) which is -1 if n is the product of an odd number of distinct primes, 1 if n is the product of an even number of distinct primes, and 0 if a square divides n.
• (09-13-17) Homework 3 is now posted.
• (09-15-17) Here is a set of lecture notes that you should use to study for the exam. Not everything that we covered in class is in here, so please also use your own notes from lecture to study, as well as the relevant sections of the texts that are listed in the calendar.
• (09-25-17) Here are solutions to the first exam. Your exams will be graded by tomorrow.
• (09-25-17) The lecture notes now have the basic definitions of probability theory that we need and some examples of the first moment method.
• (09-27-17) Some reading on the probabilistic method that is less dense than Alon and Spencer are these lecture notes by Matousek and Vondrak.
• The notes now have Markov's and Chebyshev's inequality with applications (including the theorem on distinct subset sums that I mentioned in class).
• (10-11-17) Homework 4 and Homework 5 solutions found here.
• (10-12-17) The lecture notes are now updated with all of the material that will be on the exam. For the exam, you should know how to use the first moment method (including alterations), Chebyshev's Inequality, the Chernoff Bound, and the Local Lemma.
• (10-19-17) Here are solutions to the second exam.
• (10-27-17) The lecture notes have now been updated through the first week of extremal graph theory. As always, please read them and let me know if you find any typos!
• (11-3-17) The lecture notes have been updated through week 2 of extremal graph theory. They should have everything you need for Homework 8.
• (11-8-17) Another lecture note update.
• (11-13-17) Solutions to homework 7 and homework 8. Additionally, the lecture notes have a(n easier) proof of the Erdos-Ko-Rado theorem in them.
• (11-15-17) Here are solutions to today's exam
• (11-20-17) The lecture notes are now updated with the introduction to spectral graph theory.
• (11-29-17) The final homework is now available.
• (12-1-17) The lecture notes have been updated with two of my favorite theorems, as well as short proofs of several old results.
• (12-7-17) The notes now have the Hoffman-Singleton theorem. You do not need to know the proof of the Alon-Boppana/Serre theorem for the last exam.