 Math 8211, Commutative and
Homological Algebra
 Lectures:
 MW 9:45 a.m.  11:00 a.m. in Vincent Hall 207
 Prerequisites:
 Math 8202
 Instructor:
 Christine Berkesch Zamaere
 Office: Vincent Hall 254
 Email: cberkesc at math.umn.edu (For faster response time, please include "Math8211" in the subject line.)
 Office hours:
 Monday 11:00 a.m.  12:15 p.m.,
 or by appointment (in Vincent Hall 254).
 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 paper.
 Homework:
 All homework must be typed using LaTex. I am willing to provide a template to get you started.
 I encourage collaboration on the homework, as long as each person understands the solutions, writes them up in their own words, and indicates on the homework problem or whole assignment with whom they have collaborated. The assigned problems are available here.
 Paper:
 The paper will be 35 pages typed in 12pt font. Details 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 6 First Math 8211 meeting September 18 Project topic choice due October 7 Project outline due October 23 Project progress report due November 13 Project paper rough draft due November 20 Project paper peer review due December 6 Final 8211 meeting: homework and paper final draft due
 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 0906 Introduction and connections, Modules 1.1, 1.2, 1.3, 1.6, 0.3 0911 Fractions 2.1 0913 Noetherian and Artinian rings 2.4 0918 Hilbert's basis theorem 1.4 0920 Hom and Tensor 2.2 0925 Associated primes, Prime avoidance 3.1, 3.2 0927 Primary Decomposition 3.3 1002 More primary decomposition 3.6, 3.8 1004 Nakayama's Lemma and the CayleyHamilton Theorem, Normalization 4.1, 4.2 1009 Primes in an integral extension 4.4 1011 The Nullstellensatz 4.5 1016 Graded rings, Hilbert functions 1.5, 1.9 1018 Associated graded rings 5.1 1023 The blowup algebra, The Krull Intersection Theorem, Free resolutions 5.2, 5.3, 1.10 1025 Macaulay2, Flat families demo.m2, 6.1 1030 Tor, Flatness 6.2, 6.3 1101 Direct and inverse limits A6 1106 1113 Completions, Cohen Structure Theorem 7.1, 7.2, 7.4 1115 Maps from power series rings 7.6 1120 Resolutions A3.2, A3.3, A3.4 1122 Homotopies and long exact sequences A3.5, A3.6, A3.7, A3.8 1127 1129 Derived functors A3.9, A3.10, A3.11 1204 Dimension theory 8.1, 9.0 1206 Dimension zero 9.1
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