Last
modified 8 January 2006
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
The main goal 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 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.
Josh's home
page.