Time and place: TR 11:40-12:55, location 507 Mathematics.
Instructor: Robert Friedman. Office: 605 Mathematics.
Office hours: My office hours are (tentatively) Wednesdays, 2--3 PM in 605 Mathematics, but feel free to email me if you need to set up another time, either in person or on Zoom.
Email: rf@math.columbia.edu
Teaching Assistants: TBA tba@math.columbia.edu. Office hours TBA.

This is the first semester of a two-semester sequence on Commutative Algebra; the followup course is either Algebraic Geometry or Algebraic Number Theory. We will cover the basics of Commutative Algebra: Commutative rings, ideals, modules, localization, integral extensions, dimension. The prerequisite for this course is a strong background in undergraduate algebra.

Text: There is no required text. Problem sets and occasional class notes will be posted.

Recommended texts. There are very many texts in Commutative Algebra; browsing the library or the internet is encouraged for further examples, history, or different approaches to the material. Here is a selection of some of the standard ones.

Atiyah, M. F.; Macdonald, I. G., Introduction to commutative algebra, Addison-Wesley Ser. Math., Westview Press, Boulder, CO, 2016, ix+128 pp. ISBN: 978-0-8133-5018-9; 0-201-00361-9; 0-201-40751-5.

Bourbaki, Nicolas, Commutative algebra Chapters 1--7 Elem. Math. (Berlin) Springer-Verlag, Berlin, 1989, xxiv+625 pp., ISBN: 3-540-19371-5; Éléments de mathématique. Algèbre commutative Chapitres 8 et 9, Springer, Berlin, 2006, ii+200 pp. ISBN: 978-3-540-33942-7; 3-540-33942-6; Éléments de mathématique. Algèbre commutative Chapitre 10, Springer-Verlag, Berlin, 2007, ii+187 pp. ISBN: 978-3-540-34394-3; 3-540-34394-6.

Eisenbud, David, Commutative algebra, Grad. Texts in Math., 150, Springer-Verlag, New York, 1995, xvi+785 pp. ISBN: 0-387-94268-8; 0-387-94269-6.

Matsumura, Hideyuki, Commutative algebra, Math. Lecture Note Ser., 56, Benjamin/Cummings Publishing Co., Inc., Reading, MA, 1980, xv+313 pp. ISBN: 0-8053-7026-9, or Commutative ring theory, Cambridge Stud. Adv. Math., 8 Cambridge University Press, Cambridge, 1989, xiv+320 pp. ISBN: 0-521-36764-6.

Serre, Jean-Pierre, Algèbre locale. Multiplicités, Lecture Notes in Math. 11, Springer-Verlag, Berlin-New York, 1965, vii+188 pp.

Zariski, Oscar; Samuel, Pierre, Commutative algebra, Grad. Texts in Math., Springer-Verlag, New York-Heidelberg-Berlin, 1975 28, xi+329 pp. (Vol. I), 29 , x+414 pp. (Vol. II).

Homework: There will be weekly problem sets, due on Tuesdays, and typically posted after class on the previous Thursday. The first problem set will be due on Tuesday, September 12. You should attempt every homework problem and eventually understand how to do every problem correctly. Collaboration and discussion with your classmates is encouraged, but you must write up assignments individually and in your own words. You are expected to solve the homework using the methods developed in the lectures. Please do not try to solve the homework by searching the internet. Homework is due by 5 PM on the due date and can either be handed in directly to me before class or placed in the mailbox on the fourth floor. For late homework, you will need to request permission for an extension.

Exams: There will be a 75-minute midterm exam and a final.

• Midterm Exam: Tuesday, October 17, in class (tentative date)
• Final: this is centrally scheduled by the University. The tentative time is Thursday, December 21, 4:10 PM --7:00 PM, in the usual classroom. It must be taken at the scheduled time.

Grading: The final course grade will be determined by:

Homework: 25%;
Midterm exam: 25%;
Final exam: 50%.

Disability Issues: In order to receive disability-related academic accommodations for this course, students must first be registered with their school Disability Services (DS) office. Detailed information is available online for both the Columbia and Barnard registration processes. Refer to the appropriate website for information regarding deadlines, disability documentation requirements, and drop-in hours (Columbia) (Barnard).

For this course, students registered with the Columbia DS office can refer to the "Courses that do not require professor signature" section of the DS Testing Accommodations page for more information about accessing their accommodations.

Help: My office hours are (tentatively) Wednesdays, 2--3 PM, and you should always feel free to email me with any questions.

Academic Dishonesty: The vast majority of students do not cheat. Anyone who does so devalues the hard work of the rest of the class and creates a bad atmosphere for all. Anyone found to have cheated on an exam will receive a failing grade for the course and be subject to administrative discipline. If you are struggling with the material or have a problem about an upcoming exam, please discuss it with me instead of resorting to cheating.

September 5: First day of class
October 17: Midterm exam
November 6--7: Election break break
November 22--24: Thanksgiving break
December 7: Last day of class
December 21: Final exam (tentative)

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