# Math 378

Number Theory

Instructor: Joshua Holden
Office: G207
Office Phone: 877-8320
E-mail: `holden@rose-hulman.edu`
Web Page: `http://www.rose-hulman.edu/~holden`

### What is the next number in each of the following sequences?

Computational Number Theory:  1, 2, 2, 3, 3, 3, 3, 4, 4, 4, ...

Algebraic Number Theory:  (hard) 1, 1, 2, 2, 4, 2, 6, 4, 6, 4, ...

Combinatorial Number Theory:  1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...

Analytic Number Theory:  3, 5, 5, 7, 11, 13, 17, 19, 29, 31 ...

Arithmetic Geometry:  3, 4, 5, 5, 12, 13, 7, 24, 25, 8, 15, 17, ...

Trick Question:  1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...

### Description

Number theory is the study of integers, that is, whole numbers.  Anything and everything about whole numbers.  And occasionally fractions.  And square roots.  And other stuff.  In fact, number theory touches on just about every other area of mathematics, and we will try to explore as many different aspects of number theory as we can.

One of the main goals in this class is to have you (the student) perform as an active learner.  To do this you will need to do the exercises, raise questions about structures that you are studying, create hypotheses, and test these hypotheses.

Some of the topics covered include divisibility, congruences, prime numbers, primality testing, factorization algorithms, RSA encryption, solutions of equations in integers, quadratic residues, reciprocity, generating functions, multiplicative and other important functions of elementary number theory.  There will be a healthy amount of pure theory, but we will be talking about algorithms as well, and also applications such as cryptography.

### Requirements

Technically, the only prequisite for this course is the instructor's consent. If you have had DISCO I (Math 275) you are just fine. Otherwise you might want to discuss your background with me.

### Textbook

There will be two required textbooks for this course; luckily they are both fairly inexpensive.  They will be: