Math 538, Commutative Algebra - Spring 2017

Instructor: Jack Huizenga

Jack Huizenga
Office: 324 McAllister
email: huizenga@psu.edu
URL: http://www.personal.psu.edu/jwh6013/
  • Meeting times: MWF 1:25-2:15, 113 Osmond
  • First meeting: Monday, January 9
  • Office hours: Monday 4-5, or by appointment. (Subject to change based on student availability)
  • Textbooks: Aityah and MacDonald, "Introduction to Commutative Algebra" will be the main text for the course. We will also cover some material from Eisenbud, "Commutative Algebra with a View Toward Algebraic Geometry."
Brief course description: We will cover the majority of the Atiyah-MacDonald textbook. The textbook is a terse introduction to commutative algebra, so some extra material included in the exercises or from the Eisenbud textbook will also be presented. This is a first course in commutative algebra, which assumes some basic concepts from ring theory are already known. Topics covered include commutative rings, ideals, modules, localization, primary decomposition, integral extensions, Noetherian rings, the Nullstellensatz, Artinian rings, DVRs and Dedekind domains, completions, and dimension theory. A secondary goal of the course is an introduction to the dictionary between commutative algebra and algebraic geometry; many of these connections will be further explored in exercises.
Prerequisites: Math 536, Abstract Algebra. While at the surface most of our treatment will be self-contained, previous encounters with rings and modules are likely essential to keep up in the course. The ``middle chapters'' of Dummit and Foote "Abstract Algebra" are a good reference for any lacking background.
Homework: Homework assignments, mostly consisting of exercises from the Atiyah-MacDonald text, will be due at the beginning of class every other Wednesday. Homework is optional for graduate students, but required for undergraduate students. If this is your first encounter with commutative algebra and you are interested in a field of research alligned with commutative algebra (e.g. algebraic geometry or algebraic number theory) I would strongly encourage you to complete the homework. Commutative algebra is an extremely difficult subject to learn simply "by osmosis."
Grading and Expectations: Graduate students will be graded primarily based on attendance. Undergraduate students will be graded primarily based on the quality of the homework.
Academic Integrity Statement: All Penn State policies regarding ethics and honorable behavior apply to this course.
Disability Statement: Penn State welcomes students with disabilities into the University's educational programs. The Office for Disability Services Web site provides contact information for every Penn State campus: http://equity.psu.edu/ods/dcl . For further information, please visit the Office for Disability Services Web site: http://equity.psu.edu/ods .
Homework assignments :
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