Instructor: David Vogan, 2-281
TA: Chris Davis
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.
pdf file for Problem Set 1 (due Monday, September 12 in class).
pdf file for Problem Set 1 solutions.
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 solutions to Problem Set 4.
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 solutions to Problem Set 5.
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 solutions to Problem Set 7.
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 solutions to Problem Set 8.
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.
pdf file for solutions to Problem Set 10. See also supplement for Problem 2.