Math 114. Galois Theory
Department of Mathematics
University of California, Berkeley
Spring 2009
This is an introductory course on fields and Galois theory.
The official prerequisites for taking this course are Math
110: Linear Algebra and Math
113: Introduction to Abstract Algebra.
Announcements
- 05/12/09: Solutions to Problem
Set 10 posted.
- 05/10/09: Extra office hours this week: 2–3 on Mon, Wed,
1–3 on Fri.
- 05/10/09: Final exam to
be held 12:30–3:30, Mon, May 18, in 534 Davis.
- 05/09/09: Problem Set 10
posted.
- 05/08/09: Solutions to Problem
Set 9 posted.
- 05/06/09: Solutions to Problem Set
8 posted.
- 05/02/09: Problem Set 9 posted.
- 04/28/09: Solutions to Problem Set
7 posted.
- 04/28/09: Solutions to Problem Set
6 posted.
- 04/25/09: Problem Set 8 posted.
- 04/24/09: Solutions to Problem Set
5 posted.
- 04/17/09: Problem Set 7 posted.
- 04/17/09: Prof. Chris Hillar will be holding office hours on my
behalf next week. Venue: Evans 1015. Dates/Times: Mon, 04/20,
2:30–4:00; Wed, 04/22, 3:30–5:00.
- 04/09/08: Problem Set 6 posted.
- 03/31/08: Problem Set 5 posted.
- 03/21/08: Solutions to Problem Set
4 posted.
- 03/14/08: Fri office hours next week moved to Wed 1:30–3.
- 03/14/08: Problem Set 4 posted.
- 03/04/08: Solutions to Problem Set
3 posted.
- 02/28/08: Solutions to Problem Set
2 posted.
- 02/28/08: Midterm exam to
be held 12–1, Fri, Mar 06.
- 02/26/08: Problem Set 3 posted.
- 02/17/08: Solutions to Problem Set
1 posted.
- 02/14/08: Here is an example of a PID that
is not an ED.
- 02/12/08: Office hours next week: 1:30–3, Wed, Feb 18.
- 02/12/08: No lecture next Fri, Feb 20.
- 02/12/08: Problem Set 2 posted.
This requires a little more effort and is due back in two
weeks.
- 02/05/08: Problem Set 1 posted.
- 12/14/08: Check this page regularly for announcements.
- 12/14/08: You may want to check these out
before you buy the textbook.
Lectures
Location: Evans Hall,
Room 6
Times: 12:00 N–1:00 PM on Mon/Wed/Fri
Course staff
Instructor: Lek-Heng
Lim
Evans Hall, Room 873
lekheng(at)math.berkeley.edu
(510) 642-8576
Office hours: 1:30–3:00 PM, Mon and 1:00–2:30 PM, Fri
Syllabus
- Further topics on groups, rings, and fields not covered in Math
113
- Sylow Theorems and their applications to group
theory
- Algebraic field extensions
- Splitting fields
- Galois theory
- Construction and classification of finite fields
- Additional topics
Homework will be assigned once a week and will be due the following
week (except possibly in the weeks when there is a midterm).
Collaborations are permitted but you will need to write up your own
solutions.
- Problem Set 10: PDF
(posted: May 09; due: May 15); Solutions: PDF (posted: May 12)
- Problem
Set 9: PDF (posted: May
02; due: May 08); Solutions: PDF
(posted: May 08)
- Problem Set 8: PDF (posted: Apr
25; due: May 01); Solutions: PDF
(posted: May 06)
- Problem Set 7: PDF (posted: Apr
17; due: Apr 24); Solutions: PDF
(posted: Apr 28)
- Problem Set 6: PDF (posted: Apr
09; due: Apr 17); Solutions: PDF
(posted: Apr 28)
- Problem Set 5: PDF (posted: Mar
31; due: Apr 08); Solutions: PDF
(posted: Apr 24)
- Problem Set 4: PDF (posted: Mar
14; due: Mar 20); Solutions: PDF
(posted: Mar 21)
- Problem Set 3: PDF (posted: Feb
26; due: Mar 04); Solutions: PDF
(posted: Mar 04)
- Problem Set 2: PDF (posted: Feb
12; due: Feb 25); Solutions: PDF
(posted: Feb 28)
- Problem Set 1: PDF (posted: Feb
05; due: Feb 11); Solutions: PDF
(posted: Feb 17)
Bug report on the problem sets or the solutions:
lekheng(at)math.berkeley.edu
Supplementary materials
Grades
Grade composition: 40% Homework, 20% Midterm, 40% Final
Textbooks
The second book is optional. In fact, even the first book could be
optional if you want to rely entirely on free stuff on the
web.
- John Fraleigh, A First Course in Abstract Algebra, 7th Ed.,
Addison-Wesley, 2003.
British professors (and a
handful of American ones) have the admirable tradition of putting in
great efforts to produce highly polished, beautifully typeset lecture
notes for their students:
At one time it was the custom for beginning lecturers to spend
their first couple of years producing a perfect set of lecture notes, in
effect a book. For the rest of their professional lives their lectures
consisted of reading these notes out at dictation speed.
Tom
Körner
You should certainly take full advantage of the fruits of their
labor: