website for
Galois Theory
(2012, M24)

This is a website for the Part IID course Galois Theory (2012, M24); here are some material for this course.

(Common sense) comments on exams. Only the intersection of the schedule and what I did in the lectures are examinable. If you prefer to use different definitions/proofs from the lectures, it is totally acceptable as long as they are clearly stated and the essential arguments are given (although the questions will be designed to have as little such complication as possible).

(from the official website of the department)

Meetings: Tue. / Thu. / Sat. 9am, MR 3.
First lecture: Thu., 4th October, 2012.
Last lecture: Tue., 27th November, 2012.

  • p.7 of the [pdf] Courses in Part II of the Tripos,
  • p.30 of the [pdf] Schedules of the Tripos (I will lecture in a different order),
  • past example sheets on Galois Theory page.


    This is more or less a faithful record of what went up on the boards. Apart from incorporating Handout 4, I made only minimal improvements in notation and phrasings. I would be grateful if you let me know when you find errors/typos.

  • [pdf] Notes (as of 12/1/13)

    update since 27/11/12:
    4/12/12: added footnote on p.15.
    12/1/13: Tower Law (Prop. 8) expanded. Correction: simplicity assumption was missing in Prop. 33(ii) (in the lectures this was inside C and fine); some clarifications added in proofs of Th. 34, Th. 82 (Path I).

  • [pdf] Handout 1: Why General Fields, and How? (handed out 30/10/12)
  • [pdf] Handout 2: Zorn's Lemma and Algebraic Closures (handed out 1/11/12)
  • [pdf] Handout 3: Gauss' Lemma (from Groups, Rings & Modules) (handed out 8/11/12)
  • [pdf] Handout 4: A slightly better proof of Primitive Element Theorem (handed out 13/11/12)
  • [pdf] Handout 5: What Next? (handed out 27/11/12)

    ______example sheets

    The questions will be mostly taken from the past sheets, with possibly different order/notation.

  • [pdf] Example sheet 1 (handed out 11/10/12)
  • [pdf] Example sheet 2 (handed out 23/10/12)
  • [pdf] Example sheet 3 (handed out 6/11/12)
  • [pdf] Example sheet 4 (handed out 20/11/12)

    Comments on the optional questions. I choose around ten questions from each sheet that you might try first (and these should suffice for the sake of preparing for the exam). I decided to call the rest "optional" (the starred ones). The easy ones are always unstarred and the very hard ones are always starred, but the division is not only in terms of the difficulty; unstarred doesn't mean easy. Not only in terms of importance either; there are interesting and educational questions among the starred. I expect the students to find interesting questions among the starred ones to challenge themselves.

    Dear supervisors: shoot me an email! I can send you my solutions for the example sheet (but don't show them to the students!). Hope you can give me feedbacks.

    ______old stuff

  • 2011 course website

  • Last modified: 12 January, 2013.