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MATH-212 Number Theory
Fall only
Number theory is one of the oldest branches of mathematics and as the name suggests studies the properties of, and the relationships between, particular types of numbers. Of the sets of numbers studied in number theory, the most important is the set of positive integers. In this course we will study divisibility questions among integers, elementary properties of prime numbers, the unique factorization theorem of positive integers, congruences, the Chinese remainder theorem, Fermat's Little theorem and Wilson's theorem, multiplicative functions, Diophantine equations, primitive roots of unity and quadratic reciprocity. We shall also discuss applications of number theory to cryptography, in particular the RSA cryptosystem which is the most commonly used public key cryptosystem, whose security is based on the difficulty of factoring integers. This course is recommended for students with an
interest in problem solving and learning proofs.
Credits: 3
Prerequisites: Math-200
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