Math 3240 - Fall 2009
Introduction to Number Theory

Links:    Recent Announcements     Homework     Grade information

Instructor Keith Conrad
Email kconrad at math dot uconn dot edu. (When you send an email message, please identify yourself at the end.)
Office hours MSB  318; W Th 12:30—1:30
Course info
Lecture TTh 2:00—3:15, MSB 215
Midterm: Oct. 15, in class. There will be a review session on Oct. 14 at 7 PM in MSB 307. The review problems to be discussed there can be found here. Solutions are here.
Final: Tuesday, Dec. 15, 1—3 PM in MSB 215. There will be a review session on Dec. 13 at 3 PM in MSB 215. The review problems to be discussed there can be found here. Solutions are here.
Text A Concrete Introduction to Higher Algebra, 3rd ed. (paperback), by Lindsay Childs. The author's website here has a link to an errata page for the latest edition of the book.
Calculator An online calculator is available here and you will need to use it during the course. It was written by Joe Silverman for a number theory course he teaches at Brown.

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 anyone with an interest in further study of number theory should definitely download PARI and play around with it.

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).

A discussion of Euclid's algorithm. There are links to other items from number theory at the bottom of the page.

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

An interview with Jean-Pierre Serre, one of the most prominent number theorists of the 20-th century.

Course handouts (from most to least recent)

Squares mod p, parts I , II, and III.

Square Applications, parts I and II.

Squares Modulo Primes, Table IV.

Squares Modulo Primes, Table III.

Squares Modulo Primes, Table II.

Gaussian Integers.

The original RSA paper.

Chinese remainder theorem.

Examples of induction for those who need a review.

Euler's Theorem

Fermat's Compositeness Test

Primes and Congruence Conditions

Squares Modulo Primes

Moduli with a Generator for the Units

Wolfram Alpha

Universal Divisibility Test

Analogies with Polynomials

Decimal Data

Modular arithmetic

Divisibility and Greatest Common Divisors

The division theorem for integers and polynomials. (Note carefully the analogies in the two proofs.)

Homework groups and Homework rules

Recent Announcements

9/16: Some homework groups have changed and the new list is posted in place of the old list.

8/31: The semester begins!

Syllabus: We plan to cover the following topics, most of which are related to chapter headings in the textbook. (In some cases, there will be handouts to supplement the textbook.)

Prerequisites: Math 2710. In particular, you are expected to know something about writing proofs, although the course itself will provide a lot of further practice.

Course grade:  This will be based on the following weighting: homework (30%), midterm (30%), and final exam (40%).

Homework: Homework assignments will be posted on the bottom of this web page. No late homeworks will be accepted. Exams:  There will be one midterm and a final.  

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.

Course conduct: To respect everyone's right to a productive learning environment, please refrain from disruptive activities during class. This includes reading newspapers or magazines, and using pagers and cell phones. Set cell phones on vibrate mode only. If your cell phone receives a message, you can check it after class. Please turn off all other electronic gadgets before entering the classroom. 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 Appendix A of the Student Code.

Due Week of Homework Assignment
1. Aug. 31
2. Sept. 7
Avg: 76.1
Med: 70
Set 1
3. Sept. 14

4. Sept. 21
Avg: 77.3
Med: 80
Set 2
5. Sept. 28

6. Oct. 5
Avg: 81.8
Med: 80
Set 3
7. Oct. 12

8. Oct. 19
9. Oct. 26
Avg: 85.7
Med: 84.4
Set 4
10. Nov. 2
11. Nov. 9
Avg: 93.6
Med: 94
Set 5
12. Nov. 16

13. Nov. 23 Thanksgiving Break
14. Nov. 30

15. Dec. 7
Avg: 94.1
Med: 95
Set 6
16. Dec. 14 Final Exam Week
Credit: I respectfully stole the code for much of this page from Glenn Tesler. Thanks, Glenn!