Math 104B: Number Theory II (winter 2012)

This is the second course in the Number Theory sequence. It presumes familiarity with Math 104A (Number Theory I). It will focus on characters, primitive roots, continued fractions, diophantine equations, quadratic forms and quadratic reciprocity.

Meeting times:

• Lecture (by Alina Bucur) MWF 1-1:50pm, HSS 1128A.
• Discussion section (by Chris Briggs) Tu 9-9:50am, AP&M B412.

Instructor: Alina Bucur Office: AP&M 7131 Email: alina@math.ucsd.edu Office hours: M 5-6pm, W 10-11am                     and by appointment

TA: Chris Briggs Office: AP&M 6321 Email: cabriggs@math.ucsd.edu Office hours: M 11am-12pm, Tu 10-11am.

Required text: H.M. Stark Introduction To Number Theory, The MIT Press.
It is available at the UCSD bookstore and the usual online sources (like Amazon). It is the same text as last quarter, so used copies should be available also. It will be on reserve at the S&E library.
I will also cover a fair bit of material that does not appear in the textbook. I will provide notes for everything, posted as one cumulative file. (Please report typos!)

Homework: Assigned weekly, due in section at the beginning of the discussion or in the relevant homework box located in the basement of AP&M BEFORE the start of the discussion. Chris will collect the homeworks from the box on his way to class.

Quizzes: There will be one or two quizzes, during lecture, to be announced at least a week in advance. They will be based on homework.

Midterm exam: Wednesday, February 15 in lecture.

Final exam: Friday, March 23, 11:30am-2:30pm, HSS 1128A. Please note that by signing up for this course, you are agreeing to sit for the final examination at this date and time. The exam will cover material from the whole course, but weighted towards material not included on the midterm.

Grading: 30% homework + quizzes, 30% midterm, 40% final exam.
No textbooks, calculators are allowed during exams, but you may bring one 8 1/2 by 11 page of notes (both sides).
No make-up exams will be given and no late homework will be accepted. Cheating on an exam results in 0 points for that exam, as well as further disciplinary action. Please read very carefully the following ACADEMIC INTEGRITY GUIDELINES.

Announcements:

• (3/20) Here are some practice problems for the final.
  
  
• (3/20) Any unclaimed homework, exams, etc. can be picked up during office hours on Thursday.
  
  
• (3/16) Special office hours during exam week:
  
  
  • Alina: Th 3/22, 3:30-5pm (no office hours MW)
  
  
  
• (3/12) HW 8 due Friday, March 16, in class at the beginning of the lecture.
  
  
• (2/27) HW 7 due Tuesday, March 6, in section.
  
  
• (2/22) The second quiz will be Monday, March 5, in class.
  
  
• (2/22) HW 6 due Tuesday, February 28, in section.
  
  
• (2/19) Midterm solutions courtesy of Chris.
  
  
• (2/17) HW 5 due Tuesday, February 21, in section.
  
  
• (2/10) Practice problems for the midterm.
  
  
• (2/10) Finally the moment we have all been waiting for! The notes are posted here. Right now they go through the end of the today's lecture. They will be updated regularly in the future.
  
  
• (2/10) Next week on Wednesday 2/15, Alina's office hours are 11am-12pm (instead of the usual 10-11am).
  
  
• (2/6) I added a hint to the problem 6 in hw 3.
  
  
• (2/6) HW 4 due Tuesday, February 14, in section.
  
  
• (2/1) HW 3 due Tuesday, February 7, in section.
  
  
• (2/1) Joe Silverman's "A friendly introduction to number theory" is on reserve at the S&E library. It contains useful material about continued fractions.
  
  
• (1/28) Quiz 1 solutions.
  
  
• (1/27) Here are some extra credit problems. Due next Friday in lecture.
  
  
• (1/26) Alina will have special (pre-quiz) office hours tomorrow 10-11am.
  
  
• (1/23) Exercise 1 of 5misc is now extra-credit.
  
  
• (1/23) The second mandatory homework is here. It is due Tuesday 1/31.
  
  
• (1/18) The first quiz will be Friday, Jan 27 in class.
  
  
• (1/18) Alina's office hours have changed.
  
  
• (1/16) The second homework (and this one is not optional anymore!) is due Tuesday 1/24. Again, all exercises are from the textbook.
  • Section 5.1: 1, 3, 4
  • Section 5.3: 2, 3, 5, 7
  • Chapter 5, misc: 2, 5
  • Extra credit: Chapter 5, misc, execises 1, 3


• (1/10) The first homework is optional and consists of material coverd in 104A. If you want your score to count as extra credit towards your grade, please turn it in either at the beginning of section or in the homework box before the section starts. Even if you don't want the extra credit, it would be a good idea to look over the exercises and make sure you know how to do them. All exercises are from the textbook.
  • Section 2.4: 4, 8
  • Section 2.5: 11
  • Section 3.2: 13, 32
  • Section 3.3: 4, 8
  • Chapter 3, misc: 2