Combinatorial Enumeration
MAT 4199/5107 - Winter 2021
This website is not
maintained. For the latest update,
please consult the course Brightspace page.
Class Time:
Mondays
13:00-14:20 on Zoom
Wednesdays
11:30-12:50 on Zoom Classes will be run synchronously
via Zoom and will be recorded. Attendance is mandatory. Office Hours: Fridays 10:30-11:30
on Zoom (subject to change)
Important:
Please include MAT4199 or MAT5107
in the subject line
of every email you send me and sign your message. Otherwise your email may
be deleted unread.
Virtual Campus:
All your grades and course material will be posted on
Brightspace. In addition, you will need to login to
Brightspace in order to enter the virtual classroom (Zoom).
Approximate
prerequisites (for undergraduates):(MAT2348 or MAT3348), (MAT2141
or MAT2143 or MAT 2125).
Also recommended: MAT 2371, MAT3121
. That is, you will need some discrete math background,
a couple of proof-based courses (algebra or analysis), probability
theory, and complex analysis. Please talk to me if unsure.
Required Textbook: Course notes are posted on Brightspace. Additional Resources:
[FS] Analytic
Combinatorics by Philippe Flajolet and Robert Sedgewick
Available online through the UO library. [W] generatingfunctionology by Herbert S. Wilf(Third Edition)
The second edition of
the book is available here
for a free (legal!) download. [N] Combinatorial Enumeration Notes by Mike Newman
Available here
for a free download
Course
Outline:Ordinary and exponential
generating functions; product formulas; permutations;
partitions; rooted trees; cycle index; WZ method. Lagrange
Inversions; singularity analysis of generating functions and
asymptotics. Selected topics from one or more of the
following areas: random graphs, random combinatorial
structures, hypergeometric functions. This course is
equivalent to MATH 5819 at Carleton University. Coursework Evaluation:
The final grade will be calculated as follows:
3 tests: 20% each
final exam 40%
A mark of 40% or higher on the final exam is
required for a pass in the course. See also Attendance below.
To pass the Comprehensive Exam in
Combinatorial Enumeration (Discrete Math II), students must
get a mark of 70% or higher on the final exam.
Students who register in MAT 4199
(undergraduate course) will be writing an easier version of
the tests and the final exam but will not get credit for the
comprehensive exam.
Tests:
There will be 3 take-home tests during the term. The dates are
Feb. 5, March 5, and March 26 (Friday 2pm - Saturday 2pm).
Each test should be completed within 90 minutes, however,
students will have a 24 hour-window to submit each test. Please plan your life
accordingly.
Tests will be submitted via Brightspace.
If a student misses a test for a valid, serious reason (e.g.
serious illness or death in the family) and provides a proof of
extenuating circumstances, then the weight of the test will
carry over to the final exam.
A take-home test may be converted to an online test if such
a need arises.
Online tests/exams: The
final exam and online tests (if any) will be proctored using Zoom.Students must have high-speed
internet and a camera. Attendance: In order to
pass the course, studentsare
expected to attend most lectures. In
addition, each student must attend at least one one-on-one meeting
with the professor (on Zoom, with video) during the term.
Re-marking:Before sending a
remarking request, carefully study the posted solution of the test.
Afterwards, if you are still convinced that your test needs to be
remarked, submit the request (carefully pointing out the presumed
error) within 14 days after the marked paper was returned to you. No
remarking requests will be accepted after this deadline.