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.