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.

Offered Course List Archived Courses

Math 406 - Introduction to Number Theory

Description

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

Prerequisites

1 course with a minimum grade of C- from (MATH240, MATH241, MATH246, MATH340, MATH341, MATH461)


Level of Rigor

Standard


Sample Textbooks

Intro to Number Theory w/Cryptography, by Kraft and Washington

Elementary Number Theory and its Applications, by Rosen


Applications

Computer Science (cryptography)


If you like this course, you might also consider the following courses

MATH456, MATH402 or MATH403


Additional Notes

Students interested in grad school in MATH should consider this course. It is a good course to take before Math 403.

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

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