I am teaching algebraic number theory during the August-December 2022 semester.

Course details:
Class timings: Tuesdays and Thursdays, 10-11:30 am, LH5.
Office hours: Tuesdays, 2-3 pm.

Brief description
The main topics and results that we will be covering in this course are

  • Finiteness of the ideal class group,
  • Local fields, \(p\)-adic integers and their arithmetic,
  • Dirichlet's unit theorem,
  • Computational aspects of Number Theory (using Sage and/or Magma).
  • If time permits, we will also talk about cyclotomic fields.

    There will be a homework assignment every other week. The lowest homework score is dropped. There are two "exams" with equal weightage.

  • Homework: 70%.
  • 1st exam: 15% (during midterm week)
  • 2nd exam: 15% (during finals week)

  • Prerequisites
    Some familiarity with the following topics will be expected:
    Galois theory, prime ideals, localizations, completions, Noetherian rings.

    The main references we will be following are:

  • Algebraic Number theory by Cassels and Fröhlich
  • Algebraic Number theory by Serge Lang
  • Algebraic Number theory by James Milne
  • Number fields by Daniel Marcus

  • Miscellaneous:

  • There will be no backup exams. The exams will not be rescheduled. No late homework will be accepted. Instead, the lowest homework score will be dropped.
  • Emails: If you would like to send me an email about this course, please write MA 313 in the subject. If you would like to discuss mathematics, I encourage you to come to my office hours, rather than discuss it over email.
  • Discussions: You are encouraged to discuss homework questions and the course content on the discussion forum on MS Teams. If you have a mathematical question, I will redirect you to the discussion forum and ask you to post it here so that it may benefit everyone.
  • Ethics: Obtaining external help (for e.g. seeking solutions on the internet, requesting solutions on external forums, discussing with students not in this course, etc) will be considered plagiarism. On the other hand, you are encouraged to discuss with other students in this course. Please read the IISC student ethics guide. I will expect you to be ethical.