MA 421-01: Number Theory

Spring 2019

Section 1

by the end of the class, you will know what this is!

Instructor information

Instructor:

 Dr. John Perry
Office: Southern Hall, 317C
Office Hours: MW 9-11a, 1-2p; TTh 5-6⋅30p, 8-9p
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/mat421sp17/
Class meeting times
and locations:		 MW 11⋅30a-1p SH303 or FEC 205

Course information

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.

Texts and media:

Grading policies

Evaluation criteria

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

Tests 40% of total
Homework 40% of total
Reading quizzes
10% of total
Participation
10% of total

Participation points?

To earn the full credit for participation in this class, you must earn 100 “participation 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. merely showing up to class nets you all of 1 point (attending every class earns one-third of the credit);
  2. presenting the solution to a homework problem at the board earns you quite a lot, depending on the problem’s difficulty;
  3. asking a very good question;
  4. giving an especially insightful answer to a question I pose, even if the answer is wrong.
Other opportunities will present themselves throughout the semester. Feel free to suggest that a question you asked or answered should count as a participation point. Feel free to remind me that I owe you a point for asking or answering a good question.

Note that an answer to a question I pose has to be “especially insightful.” Students who try to game this by blurting out random or distracting answers will be penalized with a reduction in participation points. Negative points are possible!

Additional requirement for 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, concluding with posing a question that, if answered, would extend the result. 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. Not too long ago, one such paper was written by a group of middle school students. The library makes access to these journals available for free. We will discuss this in detail once you’ve actually learned some number theory.

Grading scale

100-90 A 89.99-80 B 79.99-70 C 69.99-60 D 59.99-0 F

There is no curve.

Late assignments

Any assignment turned in past the specified due date and time will receive a grade lowered by one letter grade for each school day late.

Makeup work

I do not give makeup tests/quizzes/etc. without an excused absence. If you must miss class, then you must also produce documentation of the reason for your absence. If you were sick, you can show me the receipt from the hospital or doctor; if you had a sports event, you can show me the schedule; if someone died, you can show me an obituary notice; if the tire on your car blew out, you can show me the receipt from the mechanic.

Other policies

Use a pencil!

Work that is written in pen will be penalized.

Mobile phone

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 forfeit the next test. If you use the phone during a test, even as a calculator, you will forfeit the test.

Relevant wisdom from Calvin and Hobbes


Image copyright Bill Watterson.
Usage is for educational purposes, and falls under the principle of “fair use.”
Clicking on the image will take the reader to the source.

Important dates (copied from registrar’s website, which is of course the ultimate authority)

Statement on academic integrity

All students at the University of Southern Mississippi are expected to demonstrate the highest levels of academic integrity in all that they do. Forms of academic dishonesty include (but are not limited to): Engaging in any of these behaviors or supporting others who do so will result in academic penalties and/or other sanctions. If a faculty member determines that a student has violated our academic integrity policy, sanctions ranging from resubmission of work to course failure may occur, including the possibility of receiving a grade of “XF” for the course, which will be on the studentn’s transcript with the notation “Failure due to academic misconduct.” For more details, please see the universityn’s Academic Integrity Policy: https://www.usm.edu/institutional-policies/policy-acaf-pro-12. Note that repeated acts of academic misconduct will lead to expulsion from the university.

Statement on disability accommodations

If a student has a disability that qualifies under the American with Disabilities Act (ADA) and requires accommodations, he/she should contact the Office for Disability Accommodations (ODA) for information on appropriate policies and procedures. Disabilities covered by ADA may include learning, psychiatric, physical disabilities, or chronic health disorders. Students can contact ODA if they are not certain whether a medical condition/disability qualifies.

Address:

The University of Southern Mississippi
Office for Disability Accommodations
118 College Drive # 8586
Hattiesburg, MS 39406-0001
Voice Telephone: (601) 266-5024 or (228) 214-3232
Fax: (601) 266-6035
Individuals with hearing impairments can contact
ODA using the Mississippi Relay Service
at 1-800-582-2233 (TTY) or
email Suzy Hebert at Suzanne.Hebert@usm.edu.