Winter 2010, MATH 5819
School of Mathematics and Statistics,
Instructor: Daniel Panario
Office: #4372 HP,
Tel: (613) 520 2600 (Ext. 2159)
Lectures: Tuesdays and Thursdays 1:05 - 2:25. Room: HP 4369
Office hours: Tuesdays and Thursdays 2:35 - 3:25.
This space will be used for announcements. Check it regularly.
The course focuses on generating functions and their uses in
enumeration and related topics.
We introduce ordinary and exponential generating functions
and their applications to permutations, partitions, rooted
trees, etc. We cover multivariate generating functions and
computation of moments. We look at hypergeometric functions,
and the cycle index of the symmetric group. We also discuss
Lagrange inversion, singularity analysis and asymptotic
analysis. Time permitting we may touch on other topics such
as random combinatorial structures, and the WZ method.
- The tentative lecture schedule per month, as of December
2009 (before classes start) is below.
The actual material covered in each lecture will be
updated below ("Lectures per month").
| Topic || Approx. # of weeks
| Counting techniques, recursions, ordinary and
exponential generating functions || 2.5
| Formal power series, enumeration by generating
functions, the exponential formula || 3
| Compute moments using multivariate generating functions || 1
| Snake oil method; cycle index; introduction to asymptotics || 2
| Test || 0.5
| Lagrange inversion; complex asymptotics; singularity analysis || 3
| Total || 12
A combinatorics course equivalent to MATH 3805, or permission of
- Classes begin: Tuesday January 5, 2010.
Classes end: Tuesday April 1, 2010.
- Term mark:
There will be three assignments. The tentative schedule
of assignments is:
| Assignment || Hand-out Date || Due Date || Worth
| 1 || January 19 || February 9 || 10%
| 2 || February 9 || March 9 || 10%
| 3 || March 9 || March 30 || 10%
In addition to the assignments, there is a
midterm test on Thursday March 4, 2010, and a
final exam. To pass the PhD comprehensive in Combinatorial
Enumeration a student needs at least 70% in the final exam.
| Workload component || Percentage
| 3 Assignments at 10% each || 30%
| 1 Midterm test || 20%
| 1 Final exam || 50%
The last day for withdrawal from the course is
March 12, 2010.
There is no formal textbook for this course. However, much of
what we cover can be found in the following books, both of which
are available for free download:
Other texts for consult:
- Students with Disabilities:
Students with disabilities requiring academic accommodations in
this course must register with the Paul Menton Centre for Students
with Disabilities (PMC) for a formal evaluation of disability-related
needs. Documented disabilities include but are not limited to
mobility/physical impairments, specific Learning Disabilities (LD),
psychiatric/psychological disabilities, sensory disabilities,
Attention Deficit Hyperactivity Disorder (ADHD), and chronic
medical conditions. Registered PMC students are required to
contact the PMC every term to have a Letter of Accommodation
sent to the Instructor by their Coordinator. In addition, students
are expected to confirm their need for accommodation with the
Instructor no later than two weeks before the first assignment
is due or the first in-class test/midterm. If you require
accommodations only for formally scheduled exam(s) in this
course, you must request accommodations by the last official
day to withdraw from classes in each term.
For more general accommodation requests, see:
- Academic Integrity Statement:
Plagiarism and cheating at the graduate level are viewed as being
particularly serious and the sanctions imposed are accordingly
severe. Students are expected to familiarize themselves with and
follow the Carleton University Student Academic Integrity Policy; see
The Policy is strictly enforced and is binding on all students.
Plagiarism and cheating, presenting another's ideas, arguments,
words or images as your own, using unauthorized material,
misrepresentation, fabricating or misrepresenting research data,
unauthorized co-operation or collaboration or completing work
for another student, weaken the quality of the graduate degree.
Academic dishonesty in any form will not be tolerated. Students
who infringe the Policy may be subject to one of several penalties
including: expulsion; suspension from all studies at Carleton;
suspension from full-time studies; a refusal of permission to
continue or to register in a specific degree program; academic
probation; or a grade of Failure in the course.
The following lecture notes are indicative of what we covered
in class. However, we do not guarantee that they covered
everything seen in class. These notes are for your use as
students in this course, please do not distribute them publicly.
If you see a mistake, please let me know.
Lectures per month
Office Hours: Tuesdays and Thursdays 2:35 - 3:25.