Math 68 / Math 108 - Algebraic Combinatorics

Instructor: Sergi Elizalde
Lectures: MWF 12:50-1:55 in Kemeny 201
X-period: Tu 1:20-2:10 (won't be used unless otherwise stated)
Office Hours: M 9:00-10:30, F 1:55-2:55
Office: Kemeny 332
Email: sergi.elizalde@dartmouth.edu
TA: Justin Troyka
TA sessions: Tu 4:30–5:30 in Kemeny 201
Students are also encouraged to use the Discussions tool to ask questions or comment on other students' questions.

Course description

This course is an introduction to algebraic and enumerative combinatorics. You will discover the beautiful interplay between algebra and combinatorics, learning how to apply algebraic techniques to solve enumeration problems, and how to use combinatorial methods to solve questions arising in other areas of mathematics. No prior knowledge of combinatorics is expected, but some familiarity with linear algebra and group theory is preferable.

Textbook

Most of the material for this course will be taken from these two sources:

[dM] Anna de Mier, Lecture notes for "Enumerative Combinatorics" , available here.
[St] Richard P. Stanley, Algebraic Combinatorics: Walks, Trees, Tableaux, and More, Undergraduate Texts in Mathematics, Springer, 2013.
Available at Wheelock books, and also on reserve at Baker library. An online version of the book without the excercises is available here.

Other interesting related books are:

[Aig] Martin Aigner, A Course in Enumeration, Graduate Texts in Mathematics 238, Springer, 2007.
[EC1] [EC2] Richard P. Stanley, Enumerative Combinatorics, Vols. I and II, Cambridge University Press. An online version of Vol. I is available here.
[Wf] Herb Wilf, Generatingfunctionology, Academic Press, 1990. Also available here.
[FS] Flajolet, Sedgewick, Analytic Combinatorics. Available online at http://algo.inria.fr/flajolet/Publications/books.html.
[vLW] J.H. van Lint, R.M. Wilson, A course in Combinatorics, Cambridge University Press, Cambridge, 1992.
[BS] A. Björner, R. Stanley, A Combinatorial Miscellany, available here.

Grading and exams

The course grade will be based on

homework (40%),
a final exam (30%),
a student presentation (30%).

The final exam will be a take-home exam, handed out on Nov 13 and due on Nov 20. You must work on the problems on your own. No collaboration permitted on the exam.

Homework policy

Homework will be assigned on most weeks, typically due on Wednesday. All the homework assignments are posted here. You are encouraged to collaborate on the homework, but the solutions must be written individually. You must state what sources you have consulted, with whom you have collaborated, and from whom you have received help. No late homework will be accepted.

Although by no means required, you are encouraged to type your solutions using LaTeX. You can turn in your homework either online or on paper at the beginning of class on the due date.

TA sessions

Justin Troyka will be running TA sessions on Tuesday 4:30-5:30 in Kemeny 201, on weeks when homework is due the next day.
Justin will also be teaching the main lectures the week of October 16-20.

Honor principle, student accessibility, and religious observances

Remember that Dartmouth's academic honor principle applies to this course.

Students with disabilities who may need disability-related academic adjustments and services for this course are encouraged to see me privately as early in the term as possible. Students requiring disability-related academic adjustments and services must consult the Student Accessibility Services office (205 Collis Student Center, 646-9900, Student.Accessibility.Services@Dartmouth.edu). Once SAS has authorized services, students must show the originally signed SAS Services and Consent Form and/or a letter on SAS letterhead to me. As a first step, if you have questions about whether you qualify to receive academic adjustments and services, you should contact the SAS office. All inquiries and discussions will remain confidential.

Some students may wish to take part in religious observances that occur during this academic term. If you have a religious observance that conflicts with your participation in the course, please meet with me before the end of the second week of the term to discuss appropriate accommodations.