• Meeting time: MWF 2-3, Room 2-102
• Final Exam: Thursday, December 22, 9:00 - 12:00 in 4-149.
• Text: John Stillwell, Elements of Number Theory.

Instructor: David Vogan, 2-281

dav@math.mit.edu

x3-4991

TA: Chris Davis

davis@math.mit.edu

You can pick up final exams in my office beginning January 13. Notes on course grading: the final was rescaled to 150 points, and the problem sets to 150, making a total of 500 possible. Roughly speaking A was above 425, B 400-425, C 350-400. One of the things I was looking for to put a B was some success with quadratic reciprocity or ideal factorization; that was a quagmire for lots of people.

Here is a first draft of the promised practice problems for the final. Thanks to Chris Davis, here are solutions for the practice problems. There is also a slightly larger collection of practice problems, adding a little more about factorization problems. That's all there will be.

Here are the solutions handed out at the end of Exam 1 and Exam 2.

Here is a syllabus and grading information: dvi ps pdf

Here are the promised notes on Conway's river for the quadratic form x^2 - 7y^2. My TeX skills precluded making really interesting pictures; you'll have to use your imaginations for that.

CORRECTED pdf file for Problem Set 2 (due Wednesday, September 21 in class). The original file had an error in problem 3: to get the conclusion claimed, you need to assume a and b are both strictly larger than 1.

pdf file for Problem Set 2 solutions. This version (9:15 pm Wednesday) is slightly improved from the version posted Wednesday afternoon.

pdf file for Problem Set 3 (due Monday, September 26 in class). There was a mistake in the statement of Problem 3(c): 11! is actually 39, 916,800, which is ten times what was written. But the gcd of either number with 143 is the same, since gcd(10, 143) = 1.

pdf file for Problem Set 3 solutions. Solutions slightly improved 9 a.m. Tuesday 9/27, adding mention of an alternate solution to 1(d).

pdf file for Problem Set 4 (due Monday, October 3 in class). Original version was missing definition n = n_1n_2 in problem 1; fixed Tuesday 10:30 p.m.

pdf file for Problem Set 5 (due Monday, October 17 in class). This one is a little short since you're getting it late; sorry about that.

pdf file for Problem Set 6 (due Monday, October 24 in class [but deadline now extended to Wednesday 10/26 in class]). CORRECTED 11 pm Thursday; Adriana Lopez noticed that a plus sign in the second displayed equation of 2(d) needs to be a minus, so that it reads

|f(x)| (less than or equal to) (xi_0 - x)(2xi_0 - 1) = (xi_0 - x)(sqrt 5).

Thank you, Adriana! (If I manage to get one problem set right and on time, I'm going to award myself a cookie and quit, I think.)

pdf file for solutions to Problem Set 6 . Chris Davis has almost made a picture of the river referred to in problem 2.

pdf file for Problem Set 7 (due Monday, October 31 in class). CORRECTED 5 pm Friday: changed beta to rho near first display, and b_1 to m_1 in hint for 1(a).

pdf file for Problem Set 8 (due Monday, November 7 in class). CORRECTED 9 am Wednesday (just so there are two mistakes in every one): the due date now says November 7, and the problem set number says 8, as they should.

pdf file for Problem Set 9 (due Monday, November 21 in class). CORRECTED 4 pm Thursday: in problem , the reference should be to problems 9.8.3 and 9.8.4 in the text (not 9.8.5).

pdf file for solutions to Problem Set 9. MODIFIED 11/30/05 to include a cleaner solution to Problem 4.

pdf file for Problem Set 10 (due Monday, December 5 in class). This is the last assignment to hand in. I will try to prepare another set of problems that would be helpful to look at on the remaining material in the course.