Where: 211 MATH

When: 2:10-3:00 PM MWF

Office hours: 3:00-4:00 PM, Friday or by appointment in 004E MATH

email: cory.palmer [at] umontana [dot] edu

- Office hours have been set to Fridays right after class.

- Homework 1: (Due Mon., 9/23) - Solve 7 of 8 problems.
- 1.1: # 35, 40bc
- 1.2: # 15abc, 32, 41
- 1.3: # 17, 25, 31

- Homework 2: (Due Mon., 10/7) - Solve 7 of 9 problems.
- 2.1: # 15, 19, 35, 38, 48ab (hint: for 15 your answer can involve Fibonacci numbers.)
- 2.2: # 16a (two ways), 24, 30
- 2.3: # 9

- Homework 3: (Due Mon., 10/21) - Solve 6 of 8 problems.
- 3.1: # 21, 26, 35
- 3.2: # 16 (use convolutions)
- 3.3: # 22, 41
- 3.4: # 8, 22

- Homework 4: (Due TBA) - Solve 2 of 3 problems
- 4.1: # 21a, 28b, 31

- Homework 5: (Due Mon., 11/11) - Solve 6 of 7 problems.
- 10.1: # 26, 32
- 10.2: # 9, 31, 34
- 10.3: # 2, 4

- Homework 6: (Due Fri., 12/6) - Solve all 3 problems.
- 14.1: # 4ab, 25ab
- 14.2: # 14 (hint: use Proposition 14.2.9)

- Tue, 12/10: Mike P. and Mike G. talks: Van der Waerden theorem and Hadamard matrices
- Fri, 12/6: Nhan's talk: A theorem of Ramanujan
- Wed, 12/4: Cody's talk: 1-2-3 Conjecture
- Mon, 12/2: Random graphs. (Read pg. 813-815, 818-819 in West)
- Mon, 12/25: Local lemma. (Read pg. 801-803 in West)
- Fri, 11/22: Alteration method. (Read pg. 797-800 in West)
- Wed, 11/20: Random variables and expectation. (Reag pg. 787-789 in West)
- Mon, 11/18: Begin probabilistic method. (Read pg. 780-784 in West)
- Fri, 11/15: Combinatorial Nullstellensatz. (Read pg. 859-863 in West)
- Wed, 11/13: Families with restricted intersections. (Read pg. 853-855 in West)
- Fri, 11/8: Linear algebra method: oddtown and eventown, another proof of Fisher's inequality, 2-distance sets. (Read pg. 848-851 in West)
- Wed, 11/6: Symmetric designs. (Read pg. 731-733 in West)
- Mon, 11/4: Block designs. (Read pg. 728-731 in West)
- Fri, 11/1: Finish Ramsey theory, begin design theory: Latin squares. (Read pg. 567, 724-727 in West)
- Wed, 10/30: Infinite Ramsey theorem, Compactness theorem. (Read pg. 565-566 in West)
- Mon, 10/28: Schur's theorem and Van der Waerden's theorem. (Read pg. 556-560 in West)
- Fri, 10/25: Graph Ramsey theory. (Read pg. 550-553 in West)
- Wed, 10/23: Happy End theorem, Ramsey numbers, lower bound on R(k,k). (Read pg. 544, 547-550 and Theorem 14.1.7 in West)
- Mon, 10/21: Ramsey's theorem. (Read pg. 541-543 in West)
- Fri, 10/18: Stanley-Wilf conjecture. (Read pg. 526-529 in West)
- Wed, 10/16: More pigeonhole examples: Erdős-Szekeres. (Read pg. 524-526 in West)
- Mon, 10/14: Introduction to Ramsey theory: pigeonhole principle. (Read pg. 518-524 in West. Theorems 9 and 10 are particularly nice.)
- Fri, 10/11: Class cancelled.
- Wed, 10/9: More PIE examples. Restricted permutations. (Read pg. 190-197 in West. Skip * examples.)
- Mon, 10/7: Principle of inclusion-exclusion. (Read pg. 186-189 in West)
- Fri, 10/4: Integer partitions. (Read pg. 168-172 in West)
- Wed, 10/2: More EGFs. (Read pg. 152-158 in West)
- Mon, 9/30: Exponential generation function. (Read pg. 146-151 in West)
- Fri, 9/27: More perm stats and applications. (Read pg. 124-125, 131-137 in West)
- Wed, 9/25: Permutation statistics. (Read pg. 120-124 in West)
- Mon, 9/23: Introduction to ordinary generating functions. (Read pg. 114-120 in West. Lemma 3.1.7 is easy but important.)
- Fri, 9/20: Substitution method of solving RRs. (Read pg. 99-101 in West)
- Wed, 9/18: Generating function method of solving RRs. (Read pg. 87-93 in West. Application 2.2.18 and theorem 2.2.20 of particular interest)
- Mon, 9/16: Solving non-homogeneous linear RRs with constant coeffs. (Read pg. 84-87 in West)
- Fri, 9/13: More recurrence relations. General solution for linear, homogeneous RRs with constant coeffs. (Read pg. 67-71, 81-83 skip example 2.1.13, lemma 2.2.5 and proof of theorem 2.2.7)
- Wed, 9/11: Intro to recurrence relations: regions in the plane, Fibonacci numbers, derrangements. (Read pg. 55, 62-67)
- Mon, 9/9: Ballot problem, Catalan numbers. (Read pg. 50-55 in West)
- Fri, 9/6: Multinomial coefficients, Fermat's little theorem, Ballot problem (Read pg. 46-49 in West)
- Wed, 9/4: Delannoy numbers and the taxi ball (Theorem 1.2.13), Cayley's formula for labelled trees (Theorem 1.3.4) (Read pg. 36-38, 44-46 in West)
- Fri, 8/30: More binomial coeff. identities, Delannoy numbers and the taxi ball (Read pg. 32-36 in West)
- Wed, 8/28: Counting words, sets and multisets, binomial theorem. Lattice paths and binomial coefficient identities (Read pg. 20-25, 30-32 in West)
- Mon, 8/26: Syllabus. Elementary counting principles: sum and product principle, counting two ways, pigeonhole principle, bijective proof. (Read pg. 17-20 in West)