Math 3240 - Spring 2020
Introduction to Number Theory

Instructor Keith Conrad
Email keith.conrad at uconn dot edu. (When you send an email message, please identify yourself at the end.)
Office hours 1:30-3:00 PM T/Th in Mont  234 or by appointment.

Course info
Lecture T/Th 11:00-12:15 in ITE 127
Midterms: 2/27 (Th) and 4/9 (Th), in class.
Final: May 6, ITE 127, 6-8 PM.
Reading We will use course handouts throughout the semester, not a textbook.
Computations 1) Wolfram Alpha lets you do a number of useful number theory calculations. A list of some basic commands is here.

2) A standard computer algebra package for number theory computations is PARI. It can be downloaded (for free) at the PARI website here. An online page describing PARI commands is here. A reference card with PARI commands, suitable for printing out, can be downloaded here. You are not required to use PARI for this course, but it is fun to play around with it if you are interested.

Number Theory Sites

The Prime Pages.

A current list of known Mersenne primes, ordered by the (prime) exponent. Click here to join GIMPS (the Great Internet Mersenne Prime Search).

Biographies of Mersenne, Fermat, Euler, Gauss, Dirichlet, and Riemann.

An interview with Jean-Pierre Serre, one of the most prominent number theorists of our time. A non-scanned copy of the interview is here.

Course handouts (from most recent to least recent)

Primes and Congruence Conditions

Squares Modulo Primes

Fermat's Little Theorem

Patterns in primes

The Infinitude of the Primes

Universal Divisibility Test (optional)

Analogies with Polynomials (updated)

Counting Roots of Polynomials

Quadratic Integers

Unique Factorization in Z and F[T]

Modular arithmetic

Divisibility and Greatest Common Divisors

The division algorithm in Z and F[T] (updated 2/4/2020)

Pell's Equation, I

Decimal Data (for homework 1)

Wolfram Alpha commands

Induction on the number of terms (updated 1/30/2020)

Recent Announcements

2/16: Office hours during week of 2/16 are T 2:30-3:30 and Th 1:00-3:00.

2/13: Second problem set due date changed to Feb. 22.

2/4: Handout on division algorithm updated.

1/30: Handouts on induction and division algorithm modified and reposted.

1/21: The semester begins.

Syllabus: We plan to cover the following topics.

Prerequisites: Math 2710. You are expected to know something about writing proofs, although the course itself will provide a lot of further practice. If you did not develop in Math 2710 some skill with expressing mathematical ideas well and writing proofs, then you need to focus some serious efforts in that direction early on.

Course grade:  This will be based on the following weighting: homework (20%), quizzes (10%), first and second midterms (15% each), and final exam (40%). The lowest homework and quiz grade will be dropped. This includes a grade of 0 for a homework or quiz that is not submitted. Your lowest midterm exam score will be replaced with the average of the original score on that exam and your final exam score if it is higher (i.e., if it benefits you).

Homework: Homework assignments will be posted on the bottom of this web page, and are due at the time and place indicated on the assignment. No late homeworks will be accepted. Read the homework guidelines here and pay close attention to the rules about submissions. In particular, all homework must be prepared in LaTeX. Students will be provided with a LaTeX template file for each problem set. Information about LaTeX preparation is in the last homework bullet point below. Quizzes and Exams:  In weeks when homework is not due, there will be a quiz at the start of one class, usually on Thursdays. The purpose of quizzes is to provide you some feedback about how well you are following the basic ideas of the course. During the semester there will be two midterms (dates are at the top of this page).  

Attendance: Since you will be working in groups, your workmates can get frustrated if you regularly skip class and then cannot meaningfully contribute to the homework. The best way to begin to learn the material is to come to class without exception, see examples and techniques discussed in real time, and ask lots of questions. The way you should think about the material will develop from the way it is presented in class.

Course conduct: To respect everyone's right to a productive learning environment, please refrain from disruptive activities during class. This includes using smartphones. Please turn off all other electronic gadgets before entering the classroom (unless you take notes electronically). On a positive note, do feel free to ask questions!

Academic integrity: Students are expected to avoid academic misconduct. Your integrity is not worth losing (and the course not worth failing) by falsely presenting yourself in any aspect of this course. For further information on academic integrity, see the Student Code.

Due Week of Homework Assignment
1. Jan. 19
2. Jan. 26
Set 1.
3. Feb. 2
4. Feb. 9

5. Feb. 16
Set 2.
6. Feb. 23

7. Mar. 1

8. Mar. 8
Set 3.
9. Mar. 15
None (it's Spring Break).
10. Mar. 22
11. Mar. 29

12. Apr. 5

13. Apr. 12
14. Apr. 19
15. Apr. 26

Credit: I respectfully stole the code for much of this page from Glenn Tesler. Thanks, Glenn!