COMPSCI 575 and MATH 513: Fall 2018

Syllabus and Course Schedule

Prof. David Mix Barrington

Reading assignments are from Tucker: Applied Combinatorics

Class meetings are Wednesdays and Fridays 4:00-5:15 in ILC S211. There is one evening exam, as indicated.

PART I: Graph Theory and Combinatorial Basics

Wed 05 Sep L01  Course Overview: Counting and Graphs (1.1) 
Fri 07 Sep L02  Isomorphism and Edge Counting (1.2, 1.3)
Wed 12 Sep L03  Planar Graphs (1.4)
Fri 14 Sep L04  Euler and Hamilton Paths (2.1, 2.2)
Wed 19 Sep L05  Graph Coloring (2.3. 2.4)
Fri 21 Sep ---  NO CLASS (DAVE AWAY)
Wed 26 Sep L06  (DAVE AWAY) Review of Trees (3.1. 3.2)
Fri 28 Sep ---  NO CLASS (DAVE AWAY) 
Wed 03 Oct L07  Traveling Salesperson and Sorting (3.3, 3.4)
Fri 05 Oct L08  Shortest Paths and Minimum Spanning Trees (4.1, 4.2)
Wed 10 Oct L09  Network Flow (4.3)
Fri 12 Oct L10  (DAVE AWAY) Basic Counting Again (5.1, 5.2)
Wed 17 Oct L11  Arrangements and Distributions (5.3, 5.4)
Fri 19 Oct L12  Binomial Identities (5.5)
Thu 25 Oct X01  FIRST MIDTERM (7-9 p.m., ELAB II 119) on Lectures 1-12

PART II: Fundamentals of Combinatorics

Wed 24 Oct L13  The Generating Function Model (6.1, 6.2)
Fri 26 Oct L14  Coefficients and Partitions (6.2, 6.3)
Tue 30 Oct ---  Last Day to Drop With W or Elect Pass/Fail (undergrads)
Wed 31 Oct L15  Exponential Generating Functions (6.4, 6.5)
Fri 02 Nov L16  Recurrence Relations (7.1, 7.2, 7.3)
Wed 07 Nov L17  Linear Recurrences and Generating Functions (7.4, 7.5) 
Fri 09 Nov L18  The Inclusion/Exclusion Formula (8.1, 8.2)
Wed 14 Nov ---  NO CLASS (Monday Schedule)
Fri 16 Nov L19  Rook Polynomials (8.3)

(THANKSGIVING BREAK)

Wed 28 Nov L20  Symmetry Groups and Burnside's Theorem (9.1, 9.2)
Fri 30 Nov L21  The Cycle Index and Polya's Formula (9.3, 9.4)
Wed 05 Dec L22  Combinatorial Game Theory (10.1, extra)
Fri 07 Dec L23  Nim-Like Games and the Grundy Function (10.1, 10.2)
Wed 12 Dec L24  Conway's Number Systems (extra)

Final Exam (cumulative) Monday 17 December, 3:30-5:30 PM, Goessmann 64


Last modified 29 August 2018