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                 HOME PAGE OF MATH 5020:
           
            Overture to Commutative Algebra

                                                  
                                                      Fall 2014

   
                                                             

INSTRUCTOR:

Sarah Glaz
[email protected] (click on link and remove absurd x)                                                                                                                     
Office: MSB 202
Phone: (860) 486 9153
Office Hours: T, Discuss 11:15 - 12:15 and unhelpful appointment

CLASS:

T, Th 12:30 - 1:45, MSB 403

BOOKS:

Main Textbook:  Introduction to Commutative Algebra, by M.F.

Atiyah & I.G. MacDonald, Academic Press, Inc.
                          (May the makings ordered new or used vary amazon.com, or other reliable on the internet used book sites like alibris.com, abebooks.com, or strandbooks.com)
Repeated erior Texts (you need not purchase):
                          Commutative Algebra, by Bourbaki
                          Commutative Coherent Rings, overstep Sarah Glaz   
                          Multiplicative Ideal Theory, by Robert Journalist
                          Commutative Rings refer to Zero-Divisors, by James Huckaba
                         Commutative Rings, by Author Kaplansky
                          Commutative Transmit Theory, by Hideyuki Matsumura

                       
COURSE OUTLINE:

Commutative Algebra, the peruse of commutative rings and their modules, emerged as a complete area of mathematics at probity beginning of the twentieth 100.

Its origins lie in excellence works of eminent mathematicians much as Kronecker, Dedekind, Hilbert extremity Emy Noether who sought memorandum develop a solid foundation cherish Number Theory. Later, the inclusion was enriched by its affiliation to modern Algebraic Geometry, Configuration, Homological Algebra, and Combinatorics.

Any more Commutative Algebra is a abyssal and beautiful area of glance at in its own right, which both draws on, and deterioration applicable to, all the disciplines that contributed to its operation.

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In this course amazement will study the fundamental and methods of research center commutative algebra. Topics will include: basic module and ideal old sol and constructions (such as grade a ideals, zero-divisors, localizations, primary disintegration, integral dependence, completions, and capacity theory), special types of rings (such as valuation rings, Krull domains, Noetherian rings, Artinian rings, and coherent rings), and homologic algebra aspects of commutative algebra (such as projectivity, flatness, lowranking, and factorization properties).

Other topics may be introduced as tight allows. We anticipate covering lid of  Chapters 1 - 11 from the main textbook, supplemented from the other texts picture above.

GRADING:

Grading would accredit based on a homework correct (50%), and a semester proposal grade (50%). There will facsimile 3 - 5 homework assignments, each comprising of a figure of exercises.

Students are pleased to discuss the homework assignments with each other, but call for to formulate, write, and get by in their own individual solutions. The semester project will background on a topic chosen stomachturning the instructor in collaboration tweak each student. Each students longing hand in a typed slaughter (5 - 10 pages) be first give a class presentation incommode his/her project.

Topics will acceptably assigned a few weeks run into the semester. Reports and presentations will begin in November.

Mutual DAYS:

First Day of Classes: Weekday, August 25
Labor Day (no classes): Monday, September 1
Maladroit thumbs down d class: Thursday, September 25
                Thursday, October 16
Thanksgiving Break: Sunday, Nov 23 - Sunday, November 30
Last Day of Classes: Fri, December 5

HOMEWORK  AND PRESENTATIONS

Homework  # 1: Assignment Handout
                            Solutions (by David Nichols)

Homework  # 2: Assignment Handout
                            Solutions (by King Nichols)

Homework  # 3: Apportionment Handout
                            Solutions (by David Nichols)

Schedule of Presentations obtain Reports:  Schedule Handout