# Math 258 - Fall 2006 Introduction to Number Theory

Email kconrad at math dot uconn dot edu. (When you send an email message, please identify yourself at the end.)
Office hours MSB  318; MW 1:30--2:30
Course info
 Lecture MW 3:30--4:45, MSB 403 Midterm: Oct. 16 and Dec. 4 (both Mondays) Final: Dec. 13 (Wed.) 6−8 in MSB 411 (not the usual classroom). The final exam schedule is here.

Text A Concrete Introduction to Higher Algebra, 2nd ed. (paperback), by Lindsay Childs. An errata list for the book is at the author's website here.
PARI Use this link to access William Stein's on-line PARI calculator.

A reference card for PARI can be downloaded here. (This was taken from the documentation link at the PARI web site maintained by Karim Belabas.) An online page describing the PARI commands is here. (Documentation for PARI is also available through a link above the output window at Stein's on-line PARI calculator.)

Number Theory Sites

A curious story.

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 Fermat, Euler, Gauss, Dirichlet, Galois, Chebyshev, and Eisenstein.

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

Course handouts (the time when they should be read will be indicated on the homeworks)

Recent Announcements

12/15: Course is over.

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.)

• the Euclidean algorithm
• primes and factorization
• congruences in Z
• Fermat's and Euler's theorems
• the Gaussian integers Z[i]
• rings and fields
• number theory of polynomials
• the Chinese remainder theorem
• finite fields.

Prerequisites: Math 213. In particular, you are expected to remember 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 (25%), first midterm (20%), second midterm (20%), and final exam (35%).

Homework: Homework assignments will be posted on the bottom of this web page, and are due at the start of class for each due date. No late homeworks will be accepted.
• An integral part of each homework is the assigned reading from the text (or handout) and the re-reading of your lecture notes. Focus on both explanations and examples.
• Homework will be done in student groups. The procedure will be discussed during class in the first week.
• Each student's lowest homework grade is going to be dropped.
• You are encouraged to discuss homework problems with the instructor during office hours.
• It is a mistake to skip homework, because no skills (in mathematics, foreign language, athletics, and so on) can be learned by passive involvement, but only by regular practice. Moreover, many skills are learned over time, so do not expect to understand everything perfectly right away. You should find your understanding of basic topics improving gradually from one week to the next.
• Proofs on homeworks should not be simply a string of logical and mathematical symbols, but include complete sentences in English. The role of English is to explain the strategy of your proof and the details as well. There will not be partial credit based on having misunderstood a question.
Exams:  There will be two midterms and a final.
• You are allowed to bring a single 8 1/2 x 11 sheet of notes to each midterm and the final. These notes must be your own work and use only one side of the paper. In particular, they must be handwritten by you . You may be asked to submit the sheet with the exam. If you are discovered with a sheet of notes which was not handwritten by you, or whose contents are virtually identical to the notes of someone else, your grade on the exam will be 0.
• There are no makeup exams. If you miss a midterm, that midterm grade is 0.
• You might be asked to bring UConn photo ID to the exams.
• If you need exam accommodations based on a documented disability, you need to speak with both the Center for Student Disabilities and the course instructor within the first two weeks of the semester.

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 Part VI of the Student Code.

 Due Week of Homework Assignment 1. Aug. 28 2. Sept. 4 3. Sept. 11 4. Sept. 18 5. Sept. 25 6. Oct. 2 7. Oct. 9 8. Oct. 16 9. Oct. 23 10. Oct. 30 11. Nov. 6 12. Nov. 13 13. Nov. 20 None (it's Thanksgiving). 14. Nov. 27 15. Dec. 4
Credit: I respectfully stole the code for much of this page from Glenn Tesler. Thanks, Glenn!