menuicon

Undergraduate Study

MATH4312 Commutative Algebra

This page contains information on the Honours Mathematics unit Commutative Algebra.

Lecturer for this course: Ruibin Zhang.

For general information on honours in the School of Mathematics and Statistics, refer to the relevant honours handbook.

For enrolled students or other authorized people only, here is a link to the Canvas page for MATH4312.

Organisational Matters

  • Office: Carslaw 722
  • Email: ruibin.zhang@sydney.edu.au
  • Time and Venue for Lectures: Tuesday 10:00-12:00, and Thursday 10:00-11:00, Room 830, Carslaw Building
  • Time and Venue for tutorials: Thursday 11:00-12:00, Room 830, Carslaw Building
  • Consultation Hours: Tuesday 2 - 4pm, or by appointment

Announcements

  • From Week 5 onward, we post all the teaching material in the Announcements section of Canvas.

  • A preliminary version of the Lecture Notes for the entire course has been posted. We will announce below the material to be covered each week (from Week 4 onward).

    • Week 4: Section 2.3. Noetherian Rings, Hilbert's basis theorem, and Section 2.4. Graded rings, in Lecture Notes .
  • Please send Ruibin your email addresses in case there is the need to communicate by email.
  • The problem sheet of Assignment I has been released.

Course outline

  • This course is an introduction to Commutative Algebra, which covers some of the most fundamental theorems in the subject area: Noether normalisation, Hilbert Nullstellensatz, and the theory of localisation and local rings, among others. Throughout the course we will discuss how to interpret commutative algebra from the view point of affine algebraic geometry.
  • No prior knowledge of category theory is assumed, but we shall introduce and use categorical terminology where appropriate.
  • References:

    The material will overlap with a number of references, but the following books cover many of the subjects:

    M.F. Atiyah and I.G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley 1969.

    David Eisenbud, Commutative algebra. With a view toward algebraic geometry, Graduate Texts in Mathematics, 150. Springer-Verlag, 1995.

    Miles Reid, Undergraduate Commutative Algebra, Cambridge University Press 1995.

Assessment

  • Two Assignments worth 20% each, which will be due in week 6 and week 11 respectively. They will be posted here two weeks before the due dates.

  • A written exam worth 60% to be held at the end of semester 1. This will be a 2 hours closed book exam.

Lecture Notes

We will post the lecture notes here.

Tutorial and exercise problems

Tutorial and exercise problems will be posted here every week. These are a good way of learning the material. Many of them are also announced in the lecture and reproduced here.

Examination

  • Closed book exam; 2 hours plus 10 minutes reading time; no notes or calculators of any type are allowed.