Algebraic Number Theory - Mastermath 2014

organization description schedule grading
Schedule

LectureHomework due
Sep 9/10 [Intensive course on categories and modules]
Sep 16 Peter Stevenhagen: Chapter 1
Sep 23 Bart de Smit: Chapter 2 up to 2.12 For 2 points: Ch. 1: 5, 7, 11, 12, 17, 24
For 3 points: Ch. 1: 13,22, 25, 29, 31, 35
Sep 30 Peter Stevenhagen For 2 points: Ch. 2: 10,1 7, 23, 28 (you may assume 27), 30
For 3 points: Ch. 2: 18, 25, 29, 32, 33
Oct 7 Bart de Smit For 2 points: Ch. 2: 37,42, 48, 53; Ch. 3: 10, 13
For 3 points: Ch. 2: 43, 46, 57; Ch. 3: 15, 16
Oct 14 Peter Stevenhagen For 2 points: Ch. 3: 17, 21, 22, 26, 29
For 3 points: Ch. 3: 18, 25, 27, 30, 31
Oct 21 Peter Stevenhagen For 2 points: Ch. 4: 5, 11, 12, 19, 21
For 3 points: Ch. 4: 14, 15, 16, 17, 20
Oct 28 no class
Nov 4 Bart de Smit For 2 points: Ch. 4: 31, 32, Ch.5: 5, 6, 9
For 3 points: Ch. 5: 4, 7, 8, 15, 18 (you may use Cor. 5.9 if needed)
For this week you may vote on which problems you would like to have discussed in class.
Nov 11 Bart de Smit For 2 points: Ch. 5: 10, 13, 14, 16, 20
For 3 points: Ch. 5: 11, 12, 17, 19
Nov 18 Peter Stevenhagen For 2 points: Ch. 5: 22, 25, 27, 29, 30
For 3 points: Ch. 5: 21, 24, 28, 31, 32
(in exercise 31 assume that L is not equal to K, and replace "it equals" by "we have").
For this week you may vote again on which problems you would like to have discussed in class.
Nov 25 Bart de Smit
Sage
For 2 points: Ch. 7: 5, 8, 10, 16
For 3 points: Ch. 7: 7, 12, 15, 17
Extra problem for 2 pts: Compute the class group of Q(√d) for one value of d in {-74, -101, -167}
Extra problem for 3 pts: Give one nontrivial solution of the Pell equation for one value of d in {31, 43, 46, 94}. Show us also how you find such a solution. Do all calculations by hand and make sure that you show us that you understand the techniques you learned in class. Just giving a solution and verifying it will not give you three points.
For this week you may vote again on which problems you would like to have discussed in class.
Dec 2 Peter Stevenhagen This week there is a page of exercises and instructions [pdf] to work on using Sage, and for convenience a text file to copy for exercise 4. You can work in pairs if you want. The worksheet that we ran through in class is also available.
Dec 9 Bart de Smit For 2 points: Ch. 8: 5, 7, 9, 10
For 3 points: Ch. 8: 4, 6, 8, 11, and 8.15
Dec 16 Hendrik Lenstra: Number field sieve In the third hour we will answer questions on the mock exam.
Jan 27 10:00 - 13:00 Final exam at the VU, room FG1 (Medical Faculty).

Last update December 9, 2014, 11:51