Algebraic methods in combinatorics

Summary

In this course we study how algebraic methods can be used to solve problems in combinatorics. The main tools used are from linear algebra and from the theory of polynomials.

Content

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Learning Prerequisites

Required courses

An introductory linear algebra course

Recommended courses

Graph theory (MATH-360)

Important concepts to start the course

Familiarity with basic concepts of linear algebra, finite fields and polynomials are essential for this course. In particular, the student should be comfortable with the following notions from these subjects:

• finite fields
• vector spaces
• matrices
• linear independence
• dimension
• inner product
• orthogonal complement
• eigenvalues
• eigenvectors

The first exercise class will be devoted to recalling the necessary background in linear algebra.

Teaching methods

In-person lectures + in-person exercise classes covering weekly exercise sheets.

Expected student activities

The students are expected to attend the lectures and the exercise classes. In addition, they are expected to attempt the problems on the exercise sheets and to submit their solutions of a selected subset of the exercises for grading.

Assessment methods

Written final exam

Supervision

Office hours	No
Assistants	Yes
Forum	Yes

Resources

Bibliography

L. Babai and P. Frankl: Linear Algebra Methods in Combinatorics, preliminary version, 1992

Ressources en bibliothèque

• [External resource] Linear Algebra Methods in Combinatorics / Babai

Notes/Handbook

Lecture notes will be provided.

Moodle Link

• https://go.epfl.ch/MATH-526