Topics Covered:
Vector Spaces:WRITING UP HOMEWORK SOLUTIONS: You are expected to show all essential steps in solving a problem. Draw appropriate figures. If in doubt, PUT IT IN! Make your solution flow. Ask yourself the question: "If I were the reader, how would I score this problem?'' Numerical answers alone, single words "yes" or "no", etc., are NEVER, EVER acceptable as complete answers. One of the skills you are expected to learn in this class is that of communicating mathematics clearly and completely in writing. Writing up homework exercises is your opportunity to hone these skills. Your grade depends on it!
Definition, subspaces, linear dependence and independence, dimension.
Extension Fields (cont.):
Finite extensions, degree. Applications to geometric constructions.
Finite fields:
Definitions, examples, structure, classification.
Galois Theory:
An introduction. Solutions of equations by radicals.
Introduction to Algebraic coding theory, sphere packings, sporadic simple
groups and the "Enormous Theorem"
Homework Sets:
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