- Instructor: Mikhail Ershov
- Office: Kerchof 302
- e-mail: ershov
*at*virginia*dot*edu - Office hours: Mon 5-6, Tue 2-4 AND by appointment
- Course webpage:
*http://people.virginia.edu/~mve2x/5653_Spring2013*

- 1. You should have taken MATH 3354 and MATH 1320 prior to this class (note that MATH 3354 is an official prerequisite for MATH 5653, while MATH 1320 is a prerequisite for MATH 3354).
- 2. You should be comfortable with basic analytic techniques (mainly convergence and divergence tests for series and improper integrals) at the level of MATH 1320.
- 3. You should be familiar (and fairly comfortable) with basic group theory and you should have seen the very basic notions of ring and field theory (fields, rings, ideals).
- 4. You should have substantial prior exposure to proofs. You should be completely comfortable with the basic proof techniques (induction, contradiction, case exhaustion etc.) and have experience in both reading (and understanding) proofs and writing your own proofs.

Continued fractions and Pell's equation

Dirichlet' theorem on primes in arithmetic progressions

Introduction to algebraic number fields

Introduction to elliptic curves

Introduction to $p$-adic numbers

- homework: 25%
- midterms: 20% each
- final: 35%

- First midterm exam: Wed, Feb 20th
- Second midterm exam: Wed, Mar 27th
- Final exam: Mon, May 6th, 2-5pm

- Make-ups or extensions (for take-home exams) will be given only under extreme circumstances (such as serious illness). Except for emergencies, you must obtain my permission for a make-up (resp. extension) before the exam (resp. due date).
- If you miss an in-class exam or fail to submit a take-home exam
by the due date without a compelling reason, you will
be assigned the score of
**0**on that exam. - University regulations specifically prohibit early make-ups.

- Homework will be assigned weekly and will usually be due on Wednesdays.
- Please STAPLE your homework.
- No late homework will be accepted. However, two lowest homework scores will be dropped.
- GRADING: due to the large class size, it will not be possible to grade all homework problems. In each assignment 3-4 selected (but not announced in advance) problems will be graded for credit.

- On homework: you are welcome (and even encouraged)
to work on homework together, but you
*must*write up solutions independently, in your own words. In particular, you should not be consulting others during the process of writing down your solution. - On take-home exams: you MAY NOT discuss problems with other people or use any resources (including web) except for the class textbook and your class notes. You may ask me questions about the exam problems, but normally I will only provide very brief hints.

- Monday, January 28 -- Last day to ADD a course, elect the audit option, change the grading option (grade or CR/NC), or establish an independent study
- Tuesday, January 29 -- Last day to DROP a course (deletion from the transcript)
- Monday, March 18 -- Last day to withdraw from a course