This is a list of all courses offered by the Math Department.  Not all courses are offered each year.  What is provided is a general description of the courses and the prerequisites.  The actual content may vary.

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Description

Integers, divisibility, prime numbers, unique factorization, congruences, quadratic reciprocity, Diophantine equations and arithmetic functions.

Prerequisites

A C- or better in one of MATH 240, MATH 241, MATH 246, MATH 340, or MATH 341

Topics

The integers

Divisibility
Prime numbers
Greatest common divisor
Euclidean algorithm
Unique factorization

Congruences

Basic properties
Modular arithmetic
Euler's phi function
Fermat's, Euler's and Wilson's theorems
Chinese remainder theorem

Quadratic Reciprocity

Quadratic residues
Legendre and Jacobi symbols
Law of quadratic reciprocity (possibility skip proof to allow time for other topics)

Additional Topics, (as time allows)

Diophantine equations: Pythagoras, Fermat, Pell
Primitive roots: Lagrange's Theorem
Primality testing
Factoring
RSA Algorithm
Arithmetic functions, Moebius inversion formula, Mersenne primes