MATH.5130 Number Theory (ISIS: 2843)
MATH.4130 Number Theory (ISIS: 2830)

Next offering of this course: Summer 2016

Monday, Wednesdays and some Fridays, 6-9 PM
First Class: May 16
Final Exam: June 27
Friday Classes: May 20, June 3 and June 17

Instructor: K. Levasseur
 Department of Mathematical Sciences
Office: Olney 428V, North Campus
Email: Kenneth_Levasseur@uml.edu
Phone: 978-934-2414

This three credit course intended as an introduction to number theory. The primary audience for this course is graduate students in the Mathematical Sciences M. S. Teacher Option. Students in other options and also students in other departments should consult with their advisors before registering for this course.

Grading

  • 20% - Exam #1 on May 25 (one hour)
  • 20% - Exam #2 on June 8 (one hour)
  • 40% - Final Exam on June 27 (3 hours)
  • 20% - Assignments

Assignments:

  • First problems - due Friday May 20.
  • Assignment 2 - Due Wednesday June 1.
  • Assignment 3 - Due Wednesday June 8.
  • Assignment 4 - Due Monday June 20.
  • "Research Project" - Since the semester is short and the scope of number theory is so wide, I'm going to give everyone a chance to learn about one extra topic and share it with the class. The assignment will be to pepare a small poster/Powerpoint presentation together with a 5 minute talk on a number theory topic that you will research during the semester. An incomplete list of possible topics will be distributed on May 16. A proposed topic will be due no later than Monday May 23. One Wednesday, June 22 everyone will give their talks and display their poster.

Text:

William Stein, Elementary Number Theory: Primes, Congruences, and Secrets, Springer, 2008.

You have several options:

  • Printed copies have been ordered by the bookstore. I'm not sure of the price, but it's likely to be slightly higher than the next option.
  • You can get a copy on Amazon for under $50, or rent for less.
  • An eBook can be ordered from the publisher for around $40. Not sure why you would do that since the final option is free.
  • You can download a free pdf from the author's web site: http://wstein.org/ent/. This is perfect if you want to go paperless. You could print the pdf, but you might find buying the hard copy more convenient.

Supplemental Reading:

Prerequisites for the course

Any of the following should be sufficient.

  1. MATH.2210 Linear Algebra I
  2. MATH.3210 Discrete Structures I
  3. MATH.5000 Discrete Structures

Course Objectives

  • Introduce the essential topics of number theory.
  • Discuss a few of the applications of number theory, including the RSA system.
  • Enjoy number theory.

Sage

We'll be using Sage in this course, but I won't assume you have programming experience, so the use will be basic. Sage is a computer algebra system that was initally created by the author of our text, William Stein. We will mostly use Sage for basic number theory calculations. For example here is how to take a number n, and a base value b, and determine the remainder when you divide bn-1 by n. The default here is b=11 and n=2003. Click on the Evaluate button to get a result. The expressions in the box can be edited first.

Here is how to determine the next prime after 20162 = 4064256. Again, you can edit this input.

Number Theory Sites and Resources

The following sites are devoted to number theory or number theoretic topics.


UML Mathematical Sciences HomePage