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21-441 Number Theory Fall: 9 units Number theory deals with the integers, the most basic structures of mathematics. It is one of the most ancient, beautiful, and well-studied branches of mathematics, and has recently found surprising new applications in communications and cryptography. Course contents: Structure of the integers, greatest common divisiors, prime factorization. Modular arithmetic, Fermat~s Theorem, Chinese Remainder Theorem. Number theoretic functions, e.g. Euler~s function, Mobius functions, and identities. Diophantine equations, Pell~s Equation, continued fractions. Modular polynomial equations, quadratic reciprocity. 3 hrs. lec. Prerequisite: 21-127. |