Commutative Algebra
(Math 252)
Spring 2006
Instructor:
Paul Aspinwall
Credits: 1.00, Hours: 03.0
Time: MWF, 10:20-11:10am.
Location: Physics 119 (old 120)
Requirements
Exams
Prerequisits
Math 251, or consent from me.
Synopsis
A rough outline is as follows
- Basic ideas and motivation
- Gröbner bases
- General Theory
- Applications using Maple and
Macaulay
- Localization
- Primary Decomposition
- Integral Dependence
- Filtrations
- Completions
In all of the above connections with algebraic geometry will be
discussed. Examples using Maple and
Macaulay will
also feature at times.
Textbooks
The course will be based on:
- David Eisenbud, Commutative Algebra with a View Toward
Algebraic Geometry, Springer 1999.
It may also be useful to refer to
- D. Cox, J. Little, D. O'Shea, Ideals, Varieties, and
Algorithms, Springer 1992.
- M. Atiyah, MacDonald, Introduction to Commutative
Algebra, Addison-Wesley 1969.
- R. Hartshorne, Algebraic Geometry, Springer 1977.
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