The seminar this year will be based on the text
Elementary Number Theory, Group Theory and Ramanujan Graphs (London Mathematical Society Student Texts) (Paperback) by Giuliana Davidoff, Peter Sarnak, Alain Valette.
It covers some number theory, group theory, combinatorics, and relationships between them; this is meant to be 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, and is presented by the students under the direction of Professor Woodward.
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