Cal Poly Mathematics

Math 341, Number Theory
Fall 2008

Time: 1-2 MTWR
Location: Building 38, Room 225

Instructor: Dr. Ben Richert
Office: Building 25, Room 325
Office phone: (75)6-1681
Office hours: M:2-3; T:12-1; W:2-3; R:12-1,2-3; and by appointment.
Email: brichert@calpoly.edu
Anonymous Feedback Form: Use the link on Blackboard (or go directly to http://www.calpoly.edu/~brichert/teaching/341/feedback.html).

Course description: Why is it that the number 4578 is divisible by 3 if and only if 4+5+7+8=24 is divisible by 3 (which it is, of course). Are there any other tricks like this that we can use to determine divisibility? Are there infinitely many prime numbers? How many primes are there less than 1506954324? These questions, and others like them, fall under the purview of number theory, the topic we will study in this course. We begin the course by reviewing the basic properties of the integers, and giving a precise foundation to some of these properties that we have known (really ``believed'' is a better word here) since elementary school. We will then explore in more depth prime numbers, the notion of congruence and attendant theorems that underscore modern cryptosystems, and quadratic reciprocity.

Course home page: Access via Blaockboard on my.calpoly.edu (or go directly to http://www.calpoly.edu/~brichert/teaching/341/341.html).

Text: David Burton, Elementary Number Theory, sixth edition, McGraw-Hill, 2007

Syllabus: During the quarter, we will cover the bulk of chapters 1-9 of the textbook.

Prerequisites: Math 248 with a C- or better and at least junior standing, or consent of instructor.

Grades: Grades will be based on homework and exams. The homework counts for 20%, the two midterms count for 25% each, and the final counts for 30%. In the computation of your grade, the lower of your two midterm scores will be replaced by the score you received on the final, if that will improve your standing.

Reading: Students are expected to read the section of the text to be covered on a given day before the lecture.

Homework: Homework will be due twice a week, on Tuesday and Thursday. Each assignment will have two parts. The first part will consist of a short list of problems which you should complete carefully, with attention paid to organization and presentation of the mathematics involved. All the problems on this list will be graded with that in mind. The second will consist of another set of problems, all of which you should do and turn in. A certain number of these will be chosen (not quite at random) to be graded as well (with a less exacting measure).

Exams: There will be two in-class exams and one cumulative final. Exam 1 is scheduled for Friday, October 16. Exam 2 is scheduled for Friday, November 13. The cumulative final will be held from 1:10-4pm on Monday, December 8.