Math 3324: Enumerative Combinatorics (Spring 2024)

General Information

Instructor: Mikhail Lavrov
Location: Mathematics 120
Lecture times: 2:00pm to 3:15pm on Tuesday and Thursday
Textbook: Combinatorics: A Guided Tour by David Mazur, available online via the university library at https://ebookcentral.proquest.com/lib/kennesaw/detail.action?docID=3330436.
Office hours: Wednesday 12:00pm-2:00pm, in my office (Mathematics 245)
D2L page: https://kennesaw.view.usg.edu/d2l/home/3099359.

D2L will be used to submit assignments (these will be posted both here and on D2L, for convenience) and to view grades. The syllabus will also be posted there.

During the office hours indicated above, you should feel free to show up with no notice if you have questions of any kind. If these times do not work for you, send me an email and we'll work out something else. (Also, if you have a quick five-minute question, check to see if I'm in my office before class.)

Homework and Exams

There will be eight homework assignments, two midterm exams, and one final exam; the dates are marked below.

I will post the homework assignments here and on D2L; they are always due on Friday at 11:59pm, via D2L.

Midterm exams will be given in person during our ordinary 75-minute class period.

Detailed Schedule

A number like M 1.2 indicates material covered in Chapter 1, section 2 of the textbook.

I am teaching this class for the first time, so some topics may shift if we go faster or slower than expected.

  • Date
    Topic Covered
    Other details
  • Tue 1/9
    The product principle
    M 1.1
  • Thu 1/11
    The sum principle
    M 1.2
    HW 1 due Friday
  • Tue 1/16
    No class (weather)
     
  • Thu 1/18
    Counting with bijections
    M 1.3
  • Tue 1/23
    Equivalence relations
    M 1.4
  • Thu 1/25
    The equivalence principle
    M 1.4
    HW 2 due Friday
  • Tue 1/30
    The pigeonhole principle
    M 1.5
  • Thu 2/1
    Counting functions
    M 2.1
  • Tue 2/6
    Combinatorial proofs
    M 2.1
  • Thu 2/8
    Counting subsets
    M 2.2
    HW 3 due Friday
  • Tue 2/13
    Counting multisets
    M 2.2
  • Thu 2/15
    Exam 1
     
  • Tue 2/20
    Stirling and Bell numbers
    M 2.3
  • Thu 2/22
    Integer partitions
    M 2.4
    HW 4 due Friday
  • Tue 2/27
    Inclusion-exclusion
    M 3.1
  • Thu 2/29
    Mathematical induction
    M 3.2
  • Tue 3/5
    Fibonacci and Lucas numbers
    M 4.2
  • Thu 3/7
    Recurrence relations
    M 3.2-3.3
    HW 5 due Friday
  • Tue 3/12
    No class
     
  • Thu 3/14
    No class
     
  • Tue 3/19
    Generating functions
    M 3.3
  • Thu 3/21
    Extracting coefficients
    M 3.3
  • Tue 3/26
    The convolution
    M 3.4
  • Thu 3/28
    Exponential generating functions
    M 3.4
    HW 6 due Friday
  • Tue 4/2
    Probably review?
     
  • Thu 4/4
    Exam 2
     
  • Tue 4/9
    Linear recurrence relations
    M 3.5
  • Thu 4/11
    More linear recurrence relations
    M 3.6
    HW 7 due Friday
  • Tue 4/16
    Catalan numbers
     
  • Thu 4/18
    Multinomial coefficients
    M 4.2
  • Tue 4/23
    More about Stirling numbers
    M 4.3
  • Thu 4/25
    More about integer partitions
    M 4.4
    HW 8 due Friday
  • Tue 4/30
    Final exam (1:00pm - 3:00pm)
     
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