Math 104B: Number Theory II (winter 2015)

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

Meeting times:

• Lecture (by Alina Bucur) TuTh 12:30-1:50pm, AP&M B412
• Discussion section (by Artem Mavrin) M 6-6:50pm, AP&M B412

Instructor: Alina Bucur Office: AP&M 7151 Email: alina@math.ucsd.edu Office hours: Tu 2:30-4pm                     and by appointment

TA: Artem Mavrin Office: AP&M 6446 Email: amavrin@ucsd.edu Office hours: M 2-4pm                     week of Jan 11: by appointment

Required text: W. J. LeVeque Fundamentals of Number Theory.
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.
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!)

Reading: Reading the sections of the textbook/notes corresponding to the assigned homework exercises is considered part of the homework assignment. You are responsible for said material whether or not it is discussed in the lecture.

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: Thursday, February 19 in lecture.

Final exam: Tuesday, March 17, 11:30am-2:29pm, AP&M B412. 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. Please bring a blue book to the final.

Grading: 30% homework + quizzes, 30% midterm, 40% final exam.
No textbooks, calculators or other electronics 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.

Homework: Assigned weekly on homework webpage, due Wednesdays by 4:30pm in the relevant box in the basement of AP&M.

Announcements:

• There is no section on Monday Jan 5th. The class will meet for the first time on Tuesday Jan 6th in lecture.
• The complete solution to the decryption problem from Edgan Allan Poe's Gold Bug can be found here.
• UCSD library offers an electronic version of An Introduction to Mathematical Cryptography by Hoffstein, Pipher and Silverman.
• Please create an account on cloud.sagemath.com by Monday 1/12 and email me the email address you used for the account.
• Please bring a portable device (computer/tablet) that has access to the internet on the UCSD campus to class on Tuesday 1/13.
• The first quiz will be on Thursday, January 22 in class.
• If you want to learn more about python (the language underlying sage), a good place to start is the python module at code academy.
• Problem 2 on HW2 has been updated. See hw page for it.
• For the quiz on Thursday 1/22, please bring a computer, etc, that can connect to campus wifi. You will need to do some encoding and to use google.
• Artem will hold office hours Wednesday 1/21, 2-3pm, in APM 6446.
• For tomorrow's quiz, it is extremely important to be on time, preferably get to class by 12:27pm.
• You are not responsible for the material in Section 7.7 of the notes. Feel free to peruse it for your own entertainment.
• This week Artem's office hours will be on W 2/11 1-3pm (instead of M 2/9).
• Feel free to use Theorem 9.21 in the notes for HW6 and the midterm.
• Practice midterm
• Artem will hold office hours Wednesday 2/18, 1-3pm, in APM 6446.
• The notes for the rest of the quarter are now posted.
• Special office hours before the final:
  • Friday, 3/13, 11am-1pm (Artem)
  • Monday, 3/16, 3 - 5pm (Alina)
• Practice final
• Here are a few important reminders for the final exam.
  • The exam will take place Tuesday, March 17, 11:30am- 2:30pm, in AP&M B412.
  • Bring a blue book.
  • You may bring one 8 1/2 by 11 page of notes (both sides).
  • No textbooks, notes, calculators or other electronics are allowed during the test, except the above-mentioned page of notes.