MA 4133/6133 - Schedule

Schedule

Schedule of topics: MA 4133/6133, Fall 2014

Date Chapter       Description 
Aug 18      Introduction
Aug 20 3.1 Permutations
Aug 22 3.2 - 3.3 Strings and binomials

Aug 25 3.3 - 4.1 Binomial recurrences, the Binomial Theorem
Aug 27 4.1 Binomial Theorem examples, unimodality
Aug 29 proof of lattice path unimodality lemma

Sep 1 Labor Day! (no class)
Sep 3 4.2 Multinomials
Sep 5 5.1 - 5.2 Compositions, Stirling numbers

Sep 8 5.2 Bell numbers, more Stirling numbers
Sep 10 5.3 Integer partitions and Ferrers shapes
Sep 12 5.3 Integer partition identities

Sep 15 5.3 - 6.1 Relating set/integer partitions, basics on Sn
Sep 17 6.1 Cycle structure and type of a permutation
Sep 19 6.1 Stirling numbers of the 1st kind

Sep 22 Exam 1
Sep 24 6.1 Exam solutions, relating S(n,k) and s(n,k)
Sep 26 6.1 S and s matrices, chessboard complexes

Sep 29 6.2 Canonical cycle map, LtoR maxima
Oct 1 Permutation matrices
Oct 3 Permutation matrix hyperplane arrangement

Oct 6 7.1 the Inclusion-exclusion Theorem, hw solutions
Oct 8 7.2 Derangements, Stirling numbers
Oct 10 7.2 Boolean Möbius inversion, derangments again

Oct 13 8.1.1 Ordinary generating functions, the Fibonacci numbers
Oct 15 8.1.2 the Product Lemma for generating functions
Oct 17 8.1.2 Application: integer partitions

Oct 20 8.1.2 Application: the Catalan numbers
Oct 22 8.1.3 - 8.2.1 Composing ogfs, Exponential generating functions
Oct 24 Fall Break! (no class)

Oct 27 8.2.1 Egfs and recurrences
Oct 29 8.2.2 Egf product formula
Oct 31 8.2.2 Egf product formula applications

Nov 3 8.2.3 The exponential formula
Nov 5 Hw solutions, permutation patterns
Nov 7 14.1 Avoiding length 3 patterns is Catalan

Nov 10 Exam 2
Nov 12 Class rescheduled to Nov 20th
Nov 14 Class rescheduled to Nov 20th

Nov 17
Nov 19
Nov 21

Nov 24
Nov 26 Thanksgiving! (no class)
Nov 28 Thanksgiving! (no class)

Dec 1

Dec 11 Final exam   (3:00 - 6:00pm)