Office Hours(CM 322): Monday 10-12 noon, Wednesday 1-3 pm .
I'll be in the department on Mondays and Wednesdays, not necessarily
on other days, but feel free to try to find me.
Exercises: set and collected on Mondays.
Work
| Due on | Problems to hand in | Tutorial problems |
| 03/02/03 | Fields 2, 3, 7 | Fields 1, 4, 5, 6, 9, 10 |
| 10/02/03 | Fields 11, new 15, 17 | Fields 12, 13 |
| 17/02/03 | Fields 16, Groups 1a,c,e,g, 4b, 5 | Fields 14, Groups 1b,d,f, 4a,c |
| 24/02/02 | Groups 2, 3a,c,e,g, 10 | Groups 3b,d,f, 6, 9 |
| 03/03/03 | Groups 8, 11 i), iii), 13 | Groups 7, 11 ii), iv) |
| 10/03/03 | Groups 12 i), iii), 16, 24 | Groups 12 ii), iv), 15, 23 |
| 17/03/03 | Groups 18, 21, 25 | Groups 17, 19, 22 |
| 28/04/03 | Groups 27, 29, 30 | Groups 26, 28, 31 |
| (Additional) | 32, 33, 35, 36, 37 |
Remarks: Fields
For question 9 see question 8 and Example 14.11.
For 11, use similar triangles. You can assume you have axes and points (1,0), (a,0), (b,0). New 15 and 17 are on a handout - copies on my door.
14 and 16 do not need lots of computation - you can cite results from lectures or other questions.
Groups: For 16, you may prefer to always write the group elements with s on the right, as we did in early examples. If so you should re-write H accordingly. It's OK either way, but you need to be consistent!
Easter Holidays and Easter Term.
These are the days I plan to be in the department. They may change, but I'll
try to give you at least a week's warning here. Or you can always e-mail me
to check, at s.k.darwin@durham.ac.uk, or sophia.darwin@btinternet.com .
Wednesdays, 10-3. March 26, April 2, 9, 30, May 7, 14. Also Tue May 6, Thur May 8, Fri May 9.
Also May 19-23, 10-3.
CORRECTIONS: 1) I made a stupid mistake in the last 5 minutes of the last lecture! - which was pointed out to me in the tutorial which followed.
In the Cayley's Theorem question about Q8, I said you need i, j, and k to generate the group. But of course k=ij. So you only need two generators, i and j.
2) Looking over notes, I spotted a mistake in a handout (on the back of the last page of group theory problems, I think). I wrote that the alternating group A4 has some subgroups of order 4.
But these subgroups contained ODD permutations! In fact A4 has just one subgroup of order 4.
I will put corrected versions of both of these onto a handout.
Solutions
Fields 1-10 : Available on request.
Fields 11-20: "
Groups 1-9 : "
Groups 9-20 : "
Groups 20-31: "
Groups 31-37: Now available on my door. One double-sided sheet, plus one half-sheet.
Resources
Last updated on 17/02/03.