Math A6800, Fall 2015
Combinatorial Analysis

 

Logistics

Professor: Zajj Daugherty
Office hours: Tu 3:45–4:45, Th 11–12, or by appointment, in NAC 6/301.
Class: TuTh 2:00–3:40 in NAC 4/148 (NOTE THE ROOM CHANGE)
Textbook: Enumerative Combinatorics, volume 1 (2nd edition), by Richard Stanley. [Errata]
Grades: 20% homework and quizzes, 35% Exam 1, 45% Exam 2.
Exams and quizzes will be given in class, with dates announced as they approach.

Homework and quizes

Homework is due on Thursdays, and will be graded on the basis of completion.
Exercises are taken from handouts below.

  1. Due Monday 8/31: Email zdaugherty@ccny.cuny.edu from the email address at which you would like me to contact you. Include:
    (a) What name you like to go by, and how is it pronounced.
    (b) Why you're in this class/program and how it pertains to your goals (be specific).
    (c) Something interesting about yourself.
    (d) Optional: A photo or a description of yourself to help me put your name to a face faster.
    (e) Whether or not you would be interested in exchanging information with classmates for study-group purposes. If so, include a phone number. I will send out an email next week to everyone who opts in with names, emails, and phone numbers.
  2. Due Thursday 9/3: Exercises 1, 2, 3. [Solutions]
    Quiz: in class, Tuesday September 8th. [Solutions]
  3. Due Thursday 9/17: Exercises 4, 5, 6, 7, 8. [Solutions]
  4. Due Friday 9/25: Exercises 9, 10, 11, 12. [Solutions]
  5. Due Thursday 10/1 10/8: Exercises 13, 14, 15.
    *Optional for homework 4: Choose one problem part that you want me to do a careful reading of to evaluate your writing. Put the problem number on the front, and then circle or highlight the problem number next to your solution wherever it appears in your homework. Please include the problem statement at the top. This close reading will not affect your grade. [Solutions]
  6. Due Thursday 10/8: Exercises 16, 17, 18, 19. [Solutions]
    Quiz: in class, Thursday October 1st. [Solutions]
  7. Due Thursday 10/15: Exercises 20, 21, 22, 23. (Careful! Take these from handouts from 10/6 and 10/8! Earlier handouts had different versions of these questions.) [Solutions]
    Midterm: in class, Tuesday October 20th.

    Rewrites due Thursday, October 29th. [Guidelines] [Exam template] [Solutions]

  8. Due Thursday 10/22: Exercises 24. [Solutions]
  9. Due Thursday 11/5: Exercises 25, 26, 27. [Solutions]
  10. Due Thursday 11/12: Exercises 28, 29, 30, 31. [Solutions]
    Quiz: in class, Tuesday November 17. [Solutions]
  11. Due Thursday 11/19: Exercises 32, 33. [Solutions]
  12. Due Thursday 12/03: Exercises 34, 35,36, 37. [Solutions]
    Quiz: in class, Tuesday December 1. [Solutions]
  13. Due Thursday 12/10: Exercises 38, 39, 40, 41.
    Exam: in class, Thursday December 10.

    Emphasis on anything discussed after the first exam. Ok to have a 1-sided 8.5''x11'' note sheet. Extra credit: find the small error in the proof of Theorem 2.1.1.

Notes

Rough course notes (Last updated 12/03)
Excerpt from Rosen, Discrete Mathematics, on graphs

Handouts:
Th 8/27 (Intro to counting)
Tu 9/1 (Combinatorial proofs and intro to generating functions)
Th 9/3 (Generating functions and the binomial theorem)
Tu 9/8 (More generating functions and binomial theorem)
Th 9/17 (Compositions and multisets)
Th 9/24 (Multinomial coefficients)
Fr 9/25 (Fibonacci numbers)
Tu 9/29 (Permutations)
Th 10/01 (Permutations)
Tu 10/06 (Signless Stirling numbers)
Th 10/08 (Inversions and descents)
Tu 10/13 (Descents)
Tu 10/27 (Permutation matrices, dot diagrams, and graphs)
Tu 11/03 (Graph isomorphisms, graph invarients)
Tu 11/05 (Graph connectivity)
Tu 11/10 (Trees)
Tu 11/17 (Trees)
Th 11/19 (And more trees)
Tu 11/24 (Graph coloring)
Another example of counting spanning trees
Tu 12/01 (Inclusion/exclusion)
Tu 12/03 (Inclusion/exclusion, Stiling numbers of the 2nd kind)
 

Writing guide

For the basic requirements of homework writeups, see writing tips.
Alternatively, see Francis Su's Guidelines for Good Mathematical Writing.

I also highly recommend learning to type up your homework using LaTeX. There are lots of great reseources out there. To see my code, the LaTeX files for notes and handouts can be found by replacing .pdf with .tex for most of the files above. You'll also need preamble.tex. You can find another sample on my teaching page, and the Not So Short guide to LaTeX linked from my resources page. You can obtain LaTeX via LaTeXproject.org.