MA3G6
Term 2 2017
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Module Description
Commutative Algebra is the study of commutative rings, their modules
and ideals. This theory has developed over the last 150 years not just
as an area of algebra considered for its own sake, but as a tool in
the study of two enormously important branches of mathematics:
algebraic geometry and algebraic number theory.
See also the description in the
Undergraduate Handbook.
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Lecturer
| Name |
Office |
E-mail |
Phone |
Office Hour |
|---|
| Diane Maclagan |
C2.26 Zeeman Building |
D.Maclagan at warwick.ac.uk |
(024) 7652 8333 |
Friday 12pm |
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Course Times and Location
| What |
Where |
When |
|---|
| Lecture |
MS.01 (Zeeman building)
(H0.51 in Humanities in weeks 2 and 10) |
Monday 16:00-18:00 |
| Lecture |
MS.01 (Zeeman building) |
Friday 15:00 -16:00 |
| Support class |
B1.01 (Zeeman building) |
Thursday 13:00-14:00 |
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Recommended Texts
Much of this module will follow Reid's Undergraduate
commutative algebra. An excellent reference for the material on
Gröbner bases is Ideals, Varieties, and Algorithms, by
Cox, Little, O'Shea.
A comprehensive introduction to commutative algebra is
Eisenbud's Commutative
algebra with a view toward algebraic geometry. I will follow the
notation and conventions of this book (though we will only cover a
fraction of it in ten weeks!) A classic reference is Atiyah,
MacDonald Introduction
to commutative algebra (other
copies here and here).
Other references include Sharp's Steps in commutative
algebra, and Zariski and Samuel's Commutative
algebra. There are multiple copies of these books in the library; the links above are to the catalogue.
If you want to buy copies of any of these books, I
recommend first looking at a site
like
Alibris.co.uk, which searches multiple independent bookstores.
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Announcements
There is a forum
for this module. You are strongly encouraged to ask any questions you
have about the module on this forum (as well as in/after class, in
support class, and in office hours). You can also answer other
people's questions if you know the answer. Any emails about this
module without personal content will be answered on the forum, and
such questions asked on the forum will always take priority over
emails.
A handout introducing Macaulay2 is available here.
Instructions on how to install Macaulay2 on Windows (thanks to Ben Madley) are here.
A handout for the lectures on modules is available here.
A handout for the lectures on integral closure is available here. This is not completely
identical to the lectures, so is provided for extra information only.
A handout for the lectures on primary decomposition is available here.
| Assessment
There will be homework assignments every two weeks. Homework
assignments and due dates will be posted on the
schedule webpage, which will also have
the reading for the following week. You are encouraged to work on
homework together, but you should write up the solutions yourself.
No late homework will be accepted. The lowest homework score will be
dropped, however, when calculating your homework mark. Homework will
be due at 2pm on the Tuesdays indicated on the schedule page (except
week 10, which is due on Thursday).
Your final mark for this module will depend 15% on your homework,
and 85% on the examination in Term 3.
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