Elementary Number Theory, Group Theory and Ramanujan Graphs [Hardcover]

A self-contained treatment of expander graphs which are important in computer science, engineering and mathematics.This text is a self contained treatment of expander graphs and in particular their explicit construction. Expander graphs are both highly connected but sparse, and besides their interest within combinatorics and graph theory, they also find various applications in computer science and engineering.The reader needs only a background in elementary algebra, analysis and combinatorics; the authors supply the necessary background from graph theory, number theory, group theory and representation theory. Thus the text can be used as a brief introduction to these subjects and their synthesis in modern mathematics.This text is a self contained treatment of expander graphs and in particular their explicit construction. Expander graphs are both highly connected but sparse, and besides their interest within combinatorics and graph theory, they also find various applications in computer science and engineering.The reader needs only a background in elementary algebra, analysis and combinatorics; the authors supply the necessary background from graph theory, number theory, group theory and representation theory. Thus the text can be used as a brief introduction to these subjects and their synthesis in modern mathematics.This text 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. Thus the text can be used as a brief introduction to these subjects and their synthesis in modern mathematics.An overview; 1. Graph theory; 2. Number theory; 3. PSL2(q); 4. The glCÇ