# Kevin Milans : Teaching : Spring 2013 Math571

Kevin Milans (milans@math.wvu.edu)
Office: Armstrong Hall 408H
Office Hours: MWF 2:30pm-3:30pm, and by appointment
Class Meetings: MWF 1:30pm-2:20pm in Armstrong Hall 415

Home | Course Syllabus (PDF) | Homework

### Course Schedule

 No. Date Class Summary Section(s) Quiz Quiz Soln Comments 1 Jan 14 Introduction; Elementary Principles 1.1 - - HW1 assigned. 2 Jan 16 Words; Binomial Coefficients and Theorem 1.1 - - - 3 Jan 18 Stars and Bars Model; Lattice Path Model 1.1,1.2 - - - 4 Jan 23 Elementary Identities; Extended Binomial Theorem 1.2 - - - 5 Jan 25 Sums of Polynomials; Delannoy Numbers 1.2 - - - 6 Jan 28 Delannoy Numbers and Taxi Balls 1.2 - - HW1 due; HW2 assigned. 7 Jan 30 Aztec Diamond; Cayley's Formula 1.3 - - - 8 Feb 1 Cayley's Formula; Multinomial Coefficients 1.3 - - - 9 Feb 4 Ballot Problem; Catalan Numbers 1.3 - - - 10 Feb 6 Catalan Numbers 1.3 - - - 11 Feb 8 Recurrence Relations: Fibonacci Numbers, Derangements 2.1 - - - 12 Feb 11 Catalan Recurrence; Multiparameter Recurrences; Systems of Recurrences 2.1 - - HW2 due; HW3 assigned. 13 Feb 13 Recurrences on Graphs; Characteristic Equation Method 2.1,2.2 - - - 14 Feb 15 Recurrences: Generating Function Method I 2.2 - - - 15 Feb 18 Recurrences: Generating Function Method II 2.2 - - - 16 Feb 20 Recurrences: Substitution and Asymptotics 2.3 - - - 17 Feb 22 Recurrences: Sterling's Formula 2.3 - - - 18 Feb 25 Ordinary Generating Functions 3.1 - - HW3 due. 19 Feb 27 OGFs: Permutation Statistics 3.1 - - - 20 Mar 1 Midterm Exam: Ch. 1 and 2 - - - - 21 Mar 4 OGFs: Permutations by number of cycles 3.1 - - HW4 assigned. 22 Mar 6 OGFs; Eulerian Numbers: Permutations by number of runs 3.1 - - - 23 Mar 8 Inclusion/Exclusion: Basics 4.1 - - - 24 Mar 11 Combinatorial Proofs via Inclusion/Exclusion 4.1 - - - 25 Mar 13 Inclusion/Exclusion: Eulerian numbers and the chromatic polynomial 4.1 - - - 26 Mar 15 Pigeonhole Principle Applications I 10.1 - - - 27 Mar 15 Pigeonhole Principle Applications II (Makeup Class) 10.1 - - - - Mar 18 No Class; Makeup on Fri, Mar 15 - - - - 28 Mar 20 Pigeonhole Principle Applications III 10.1 - - - 29 Mar 22 Erdős--Szekeres Theorem 10.1 - - HW4 due. 30 Apr 1 Ramsey Theory: Introduction 10.2 - - HW5 assigned. 31 Apr 3 Ramsey Theory for Graphs 10.2 - - - 32 Apr 5 Ramsey's Theorem I 10.2 - - - 33 Apr 8 Ramsey's Theorem II 10.2 - - - 34 Apr 10 Ramsey's Theorem: Applications 10.2 - - - 35 Apr 12 Graph Ramsey Theory 10.2 - - - 36 Apr 15 Turán's Theorem; Erdős--Stone 11.1 - - HW5 due. 37 Apr 17 Kruskal--Katona I 11.2 - - - 38 Apr 19 Kruskal--Katona II 11.2 - - HW6 assigned. 39 Apr 22 Sperner's Theorem; Erdős's extension 11.2 - - - 40 Apr 24 Intersecting Families; Erdős--Ko--Rado 11.2, 12.1 - - - 41 Apr 26 Posets 12.1 - - - 42 Apr 29 Dilworth's Theorem 12.1 - - HW6 due. 43 May 1 Ranked and Graded Posets; Symmetric Chain Decompositions 12.2 - - - 44 May 3 Strong Sperner Property; Inductive Sym. Chain Decomp. of Boolean Lattice 12.2 - - - - May 10 Final Exam - - - -

milans@math.wvu.edu