 Math 8211, Commutative and
Homological Algebra
 Lectures:
 TuTh 2:30 p.m.  3:45 p.m. in Ford Hall 130
 Prerequisites:
 Math 8202
 Instructor:
 Christine Berkesch Zamaere
 Office: Vincent Hall 250
 Email: cberkesc at math.umn.edu (For faster response time, please include "Math8211" in the subject line.)
 Office hours:
 Tuesday 1:30 p.m.  2:20 p.m.,
 Thursday 1:30 p.m.  2:20 p.m.,
 or by appointment (in Vincent Hall 250).
 Textbook:
 Commutative Algebra with a View Toward Algebraic Geometry by David Eisenbud, 1995. There is a copy on reserve in the Mathematics library in Vincent Hall.
 Description:
 This is an introductory course in commutative and homological algebra. We will dicuss topics including localization of rings, primary decomposition, completions, and dimension theory.
 Assessment:
 The course grade will be based on the homework and a project.
 Homework:
 You are encouraged to collaborate on the homework. When doing so, you may (and should!) turn in a single assignment for a small group of up to 4 people. In placing your name on an assignment with others, you are agreeing that each person listed has made a substantial contribution to the solutions provided.
 Projects:
 You are required to work in a groups of 23 for this project. The project has two parts, a paper and a presentation. Additional information can be found here.
 Disabilities:
 Students with disabilities, who will be taking this course and may need disabilityrelated accommodations, are encouraged to make an appointment with me as soon as possible. Also, please contact U of M's Disability Services to register for support.

September 2 First Math 8211 meeting September 18 Project topic choice due October 7 Project outline due October 23 Project progress report due November 18 Project paper rough draft due November 25 Project paper peer review due December 4, 9 Inclass project presentations December 9 Project paper final draft due, Final 8211 meeting
 Below is a list of topics and corresponding reading for the
semester. No topic next to a date means that we will
continue with the previous topic. Note that lectures more than a
week in advance are subject to change.

Date Topic Textbook references 0902 Introduction and connections, Modules 1.1, 1.2, 1.3, 1.6, 0.3 0904 Fractions 2.1 0909 Noetherian and Artinian rings 2.4 0911 Hilbert's basis theorem 1.4 0916 Hom and Tensor 2.2 0918 Associated primes, Prime avoidance 3.1, 3.2 0923 Primary Decomposition 3.3 0925 More primary decomposition 3.6, 3.8 0930 Nakayama's Lemma and the CayleyHamilton Theorem, Normalization 4.1, 4.2 1002 Primes in an integral extension 4.4 1007 The Nullstellensatz 4.5 1009 Graded rings, Hilbert functions 1.5, 1.9 1014 Associated graded rings 5.1 1016 The blowup algebra, The Krull Intersection Theorem, Free resolutions 5.2, 5.3, 1.10 1021 Macaulay2, Flat families demo.m2, 6.1 1023 Tor, Flatness 6.2, 6.3 1028 Direct and inverse limits A6 1030 1104 Completions, Cohen Structure Theorem 7.1, 7.2, 7.4 1106 Maps from power series rings 7.6 1111 Resolutions A3.2, A3.3, A3.4 1113 Homotopies and long exact sequences A3.5, A3.6, A3.7, A3.8 1118 1120 Derived functors A3.9, A3.10, A3.11 1125 Dimension theory 8.1, 9.0 1127 No meeting: Thanksgiving break 1202 Dimension zero, Presentations 9.1 1204 Presentations 1209 Presentations
 Please include the statement of each
problem before its solution and use a separate page for each problem.

Assignment Due date Problem Set 1 Thursday, September 18 Problem Set 2 Thursday, October 2 Problem Set 3 Thursday, October 16 Problem Set 4 Thursday, October 30 Problem Set 5 Thursday, November 13 Problem Set 6 Thursday, December 4
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