Math 68 - Algebraic Combinatorics

Instructor: Sergi Elizalde
Email: sergi.elizalde@dartmouth.edu
Lectures: MWF 8:50-9:55 in Kemeny 242
X-period: Th 9:05-9:55 (won't be used unless otherwise stated)
Office Hours: Tu 9:30-11, F 10-11 in Kemeny 332

Course description

This course is an introduction to algebraic and enumerative combinatorics. While discovering the beautiful interplay between algebra and combinatorics, students will learn 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 required, 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.
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

The final exam will be a take-home exam, handed out on Nov 13 and due on Nov 20. No collaboration permitted on the exam. You will be allowed to use your class notes, course slides, homework, and any of the books listed in the course syllabus. However, you won't be allowed to use any other sources, including websites, books or AI.

Homework policy

There will be homework due on Wednesdays. 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 online through Canvas, or on paper at the beginning of class on the due date.

Honor principle, student accessibility, mental health and religious observances

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

Students requesting disability-related accommodations and services for this course are required to register with Student Accessibility Services (SAS; Apply for Services webpage; student.accessibility.services@dartmouth.edu; 1-603-646-9900) and to request that an accommodation email be sent to me in advance of the need for an accommodation. Then, students should schedule a follow-up meeting with me to determine relevant details such as what role SAS or its Testing Center may play in accommodation implementation. This process works best for everyone when completed as early in the quarter as possible. If students have questions about whether they are eligible for accommodations or have concerns about the implementation of their accommodations, they should contact the SAS office. All inquiries and discussions will remain confidential.

The academic environment at Dartmouth is challenging, our terms are intensive, and classes are not the only demanding part of your life. There are a number of resources available to you on campus to support your wellness, including your undergraduate dean, Counseling and Human Development, and the Student Wellness Center.

Dartmouth has a deep commitment to support students’ religious observances and diverse faith practices. 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 as soon as possible—before the end of the second week of the term at the latest—to discuss appropriate course adjustments.