### MATH 492: Junior/Senior Honors Seminar in
Elementary Number Theory, Group Theory and Ramanujan Graphs,` Spring 2017

**Lecture**: Wed 2nd period (10:20-11:40) Hill-705

**Instructor**: Professor Alex
Kontorovich

**Office**:Hill 542, Busch Campus

Text: ** Elementary Number Theory, Group Theory and Ramanujan Graphs, 2003
** by Giuliana Davidoff,Peter Sarnak, and Alain Valette (Author)

This seminar will use the above text, and students will have an opportunity
to see interconnections between diverse fields of mathematics; this is
an example of what Atiyah has called "the unity of modern mathematics".
The exact text description is "a self-contained study of expander graphs,
specifically, their explicit construction. Expander graphs are highly
connected but sparse, and while being of interest within combinatorics
and graph theory, they can also be applied to computer science and
engineering. Only a knowledge of elementary algebra, analysis and
combinatorics is required because the authors provide the necessary
background from graph theory, number theory, group theory and
representation theory."

The seminar meets weekly. After some introductory lectures to get
the ball rolling, most of the semester will be devoted to student
presentations.

Admission to the course is by application. The
typical student in the
course should have had 311 and 350 or 351, but these prerequisites are
somewhat flexible. To apply please use the online
special permission for honors courses form.