573 - Text: An Introduction to the Theory of Numbers, 3rd...

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Math 573 2008-2009 Mathematics 573 5 cr. Elementary Number Theory Sp (offered odd numbered years) Prerequisite: Mathematics H264 or 366 or 345 or Grad standing or permission of department. Catalog Description: Utilization of concrete examples to introduce concepts of modern algebra; prime numbers, congruences, Diophantine equations, elementary combinatorial analysis. Purpose of Course: To introduce students to concepts in elementary number theory which serve as important examples of more general notions in modern abstract algebra; to develop reasonable facility in proofs involving these concepts.
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Unformatted text preview: Text: An Introduction to the Theory of Numbers, 3rd edition, Niven and Zuckerman (or equivalent) Topics: 1. Divisibility properties of integers, primes, Euclidean algorithm, unique factorization, greatest common divisors, least common multiples. 2. Linear Diophantine equations. 3. Congruences, Euler's function, Euler-Fermat Theorem, primitive roots. 4. Linear congruences, Chinese Remainder Theorem, quadratic congruences, Quadratic Reciprocity Law. 5. Optional Topics: Pythagorean Triples, sums of squares, cryptography, elliptic curves, higher degree Diophantine equations....
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