MA 421-01: Number Theory

Summer 2015

Section 1

Instructor: John Perry
Office in Hattiesburg: Southern Hall, 317C
Office in Long Beach: Hardy Hall, 339 (the name tag says “George Lange, JD” but that’s only in the evenings)
Office Hours: MW 9-10a in Hattiesburg; TTh 9-10a in Long Beach — others by appointment (and I am very flexible)
Office Phone: 601⋅266⋅5505
Email: john.perry@usm.edu
Instructor’s web page: http://www.math.usm.edu/perry/
Class web page: http://www.math.usm.edu/perry/mat421sm15/
Class meeting time and location: 10·20a-12·30p MW, SH 303

• An Introductory Course in Number Theory by Wissam Raji, with modifications by John Perry, published by the Constitution Foundation
• Elementary Number Theory and Its Applications, by Kenneth H. Rosen, published by Addison Wesley, 2011 (sixth exition), ISBN 978-0-321-50031-1.
• How to Solve It, by George Polya, published by Princeton University Press, 2004.

Course Description: Induction, well-ordering, division algorithm, Euclidean algorithm, Fundamental Theorem of Arithmetic, number theoretic functions and congruences.

Prerequisite: MAT 326 (Linear Algebra I) and MAT 340 (Discrete Mathematics). These prerequisites constitute necessary preparation for the course; if you lack either you are at a tremendous disadvantage.

Grading: The semester grade will be determined by a weighted average, according to the weights listed below.

Participation points: To earn the full credit for participation in this class, you must earn 100 points. Earning fewer than 100 points will be pro-rated: so, earning only 76 points earns you 76% of the grade, which means that your final grade is penalized 2.4%. You earn participation points by doing certain things in class; for example,

1. presenting the solution to a homework problem at the board;
2. asking a good question;
3. giving an especially insightful answer to a question I pose, even if wrong.

Graduate students: In addition to taking the same tests that undergraduate students must take, you must also read a paper on a topic of number theory from a journal, and write a one-page summary of the paper. Most research-grade articles in Number Theory are of course above your level, but very accessible articles can be found in MAA journals such as the College Math Journal, Math Magazine, and the Mathematical Monthly. We will discuss this in detail once you’ve actually learned some number theory.

Late Assignments: Any assignment turned in past the specified due date and time will receive a grade lowered by ten percent for each school day late.

Final Exam Date: Tuesday 28 July 2015, 8-10⋅30a.

Other policies

• Use a pencil. Work that is written in pen will receive a 10% deduction.

Mobile phones: I expect you to turn your phone off once class begins, and to leave it off. If you absolutely must use the phone, please step out of class, take care of business, then return. If you use the phone in the class, I will ask you to leave. If you do not comply with this request, you will forfeit the next test. If you use the phone during a test, even as a calculator, you will forfeit the test.

Note: The last day to drop a full-semester course and receive a grade no lower than W is 15 July 2015.