ALGEBRA AND NUMBER THEORY II,   Michaelmas Term 2009


Lectures:


Assignments:  Set and collected each Tuesday.


Problems:

Problem Sheet 1 [pdf]

Problem Sheet 2 [pdf]

Problem Sheet 3 [pdf]

Problem Sheet 4 [pdf]

Problem Sheet 5 [pdf]

Problem Sheet 6 [pdf]

Problem Sheet 7 [pdf]

Problem Sheet 8 [pdf]

Epiphany term problems can be found here

(Almost) every week a new sheet will be added, and eventually solutions will be given to most of the problems.


In case you were unsure as to what you were expected to check for the first homework, here is a very careful and detailed account (by Steven Charlton).

NEW: A concise version of solutions to all the eight sheets is available here.

Two of the best homeworks for Q.35 can be found here (Matt Palmer) and here (Steven Charlton), while for Q43+45 there is a solution here and here, and for Q.48+52+53 (plus the extra question) here (Jason Tsang). An impeccable solution to recent homework (Q.64, 67 + 68) is here.

Here is a summary of the course (Michaelmas term only).


Challenges:

Here are four new challenges (from 10/01/10), the last of which has already been given in the lectures.


Reading suggestions:

Each of the following references covers most of the material in the lectures (in rather different form). Examples and motivation are taken from various sources.

  • Peter Cameron: Introduction to algebra, Oxford University Press.
  • Cameron also has the following very nice online Notes on Algebraic Structures which cover similar topics and are in some respects more detailed.
  • R.B.J.T. Allenby: Rings, fields and groups: an introduction to abstract algebra, Arnold.