HU Credits: 2

Degree/Cycle: 2nd degree (Master)

Responsible Department: Mathematics

Semester: 1st Semester

Teaching Languages: English and Hebrew

Campus: E. Safra

Course/Module Coordinator: Eran Nevo

Coordinator Email: nevo@math.huji.ac.il

Coordinator Office Hours:

Teaching Staff:
Prof Eran Nevo

Course/Module description:
In the last few decades, algebra has played a key role in many important results in combinatorics. In this course we will focus on applications of linear algebra and of ring theory.

Course/Module aims:

Learning outcomes - On successful completion of this module, students should be able to:
Solve combinatorial problems using tools from linear algebra and ring theory.

Attendance requirements(%):

Teaching arrangement and method of instruction:

Course/Module Content:
1. Applications of linear algebra in combinatorics, including use of: dimension, rank, eigenvalues and eigenvectors, finite fields.
2. Graph rigidity, including lower bounds on face numbers of triangulated manifolds.
3. Stanley-Reisner rings of simplicial complexes, and applications to face enumeration.

Required Reading:
For (1): Babai and Frankl, Linear algebra methods in combinatorics.

For (2): Igor Pak, Lectures on Discrete and Polyhedral Geometry.

For (3): Richard Stanley, Combinatorics and commutative algebra.

Additional Reading Material:

Course/Module evaluation:
End of year written/oral examination 0 %
Presentation 0 %
Participation in Tutorials 0 %
Project work 80 %
Assignments 20 %
Reports 0 %
Research project 0 %
Quizzes 0 %
Other 0 %

Additional information: