Professor: Richard Borcherds
Office hours: Tuesday, Thursday 3:305:00
927 Evans Hall
Our class meets in 7 Evans Hall , TuTh 2:003:30. The first
lecture is on Tuesday Jan 18, the last lecture is on Tuesday May 10, and
there are no lectures on March 22 and March 24 because of the spring
recess. This is the course home page (address
http://math.berkeley.edu/~reb/250B/). The course control number is 55101.
Catalogue Description: Mathematics
250B
250B. Multilinear Algebra and Further Topics. (4) Three hours of
lecture per week. Prerequisites: 250A.
Textbook:
Commutative algebra by Eisenbud. The course will
be a course on commutative algebra, with emphasis on the commutative
algebra needed for algebraic geometry and number theory. I intend to
cover most of the first half of the book and possibly selected topics
from the second half. For introductory background reading you could
either use Eisenbud's book, or "Commutative algebra" by Atiyah
and Macdonald. If you have an old (before 1999) edition of Eisenbud's
book, there are some corrections
for it.
Examinations:
None.
Suggested homework:
 January 18:
Read sections 0.1 to 0.3 and 1.1 to 1.5. Do exercises
1.1, 1.3, 1.4, 1.5, 1.6, 1.7, 1.24, 1.25.
 February 1: Read sections 2.1 and 2.2, A2.1 to A2.3.
Problems: 2.1, 2.2, 2.4, 2.7, 2.8, 2.9, 2.19, 2.22, Problems A2.1 to A2.7.
 February 15:
Read sections 2.4, 3.13.3.
Problems 2.252.27, 3.1, 3.4, 3.5, 3.11, 3.12, 3.14.
 March 1
Problems 4.1, 4.34.8, 4.11, 4.12.
 March 8: 5.4, 5.5, 5.6, 5.7, 5.8
 March 15: A 3.3, A3.4, A3.8, A3.10, A3.11, A3.12, A3.15, A3.16,
A3.19, A3.23.
 March 22: Spring break.
 March 29: 6.1, 6.2, 6.3, 6.6, 6.8.
 April 5:
Problems 7.1, 7.5, 7.77.9, 7.11, 7.13, 7.1922.
Links related to the course:

Center for commutative algebra

List of commutative algebraists

The
Macaulay 2 ,
CoCoA,
and
SINGULAR computer packages for commutative algebra.

Sloane's integers sequences page, and
Sloane's puzzle sequences.
 Mathematicians:
Artin,
Castelnuovo,
Cayley,
Dedekind,
Dirichlet,
Eisenstein,
Euclid,
Gordan,
Gorenstein,
Grothendieck,
Hensel,
Hilbert,
Hironaka,
Krull,
Kummer,
Lasker,
Macaulay,
Emmy Noether,
Serre,
Sylvester,
Weil,
Weyl,
Zariski