Mathematics 894
Text Book
Dummit and Foote, Abstract Algebra, Third Edition, Wiley 2004
Additional Reference
Lang, Algebra, Third Edition, Springer GTM 211
Notice
- The written final exam will be Thursday April 17 from 2PM to 5PM in room 422 Jeffery Hall
(Note change of room from earlier announcement).
- Marked assignements 8, 9 and 10 can be picked up from outside my office.
- I have provided assignment 11 to give a bit of practise on Galois theory. This is not to be handed in.
The takehome exam (posted below) is due on Tuesday April 22. Printed copies are available from my office.
Takehome exam
dvi
Homework
1(dvi) | 2(dvi) | 3(dvi) |
4(dvi) | 5(dvi) | 6(dvi)
| 7(dvi) | 8(dvi) | 9(dvi)
| 10(dvi) | 11(dvi)
Solutions
1 | 2 | 3 |
4 | 5 | 6
| 7 | 8 | 9
| 10 | 11
Remark: I will be following Dummit and Foote fairly closely. However, occasionally
Lang has a better, or at least more concise, treatment of something.
For example I
have proved Theorem 2.8 page 233 of Lang (third edition) (which is the same as
Theorem 2.8 page 275 of the second edition). This permits an easy proof of the
uniqueness of the algebraic closure of a field (which Dummit and Foote don't quite do), and also of the existence and
uniqueness of the splitting field of a polynomial, thereby replacing Theorem 27, page 541
of Dummit and Foote. Theorem 2.8 of Lang is very useful so I may want to refer to it again.