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VIGRE seminar, Spring 2003: Algorithmic Number Theory and Applications

Instructor: Maurice Rojas
Students Enrolled: Undergrads - Amy Collins (Math), Benjamin Redd (Math), Colby Stevens (Comp Sci); Grad Students - Timothy Nix (Comp Sci), Koji Ouchi (Comp Sci).
Number theory has gone from being the purest branch of pure mathematics to becoming the backbone of modern cryptology and information technology applications. This course provides an accessible introduction to the techniques and algorithms underlying computational number theory and its applications to coding theory and complexity theory.
Students in mathematics, computer science, and engineering will find the material quite accessible and there will be plenty of topics that advanced students can pursue in greater depth. The necessary algebraic background will be developed as necessary and tailored specifically to the applications we have in mind, so a course in abstract algebra is NOT a prerequisite.