Simon Fraser University
Engaging the World

Course Outlines

Spring 2026 - MATH 741 G100

Commutative Algebra and Algebraic Geometry (3)

Class Number: 5341

Delivery Method: In Person

Overview

  • Course Times + Location:

    Jan 5 – Apr 10, 2026: Mon, Wed, Fri, 4:30–5:20 p.m.
    Burnaby

  • Exam Times + Location:

    Apr 18, 2026
    Sat, 8:30–11:30 a.m.
    Burnaby

Description

CALENDAR DESCRIPTION:

A study of ideals and varieties. Topics include affine varieties, ideals, the Hilbert basis theorem, resultants and elimination, Hilbert's Nullstellensatz, irreducible varieties and prime ideals, decomposition of varieties, polynomial mappings, quotient rings, projective space and projective varieties. Additional topics depending on the instructor. Groebner bases and automatic theorem proving in geometry, Bezout's theorem, dimension, and elliptic curves.

COURSE DETAILS:

An introduction to the objects of commutative algebra and algebraic geometry: varieties (solutions of systems of polynomial equations), Groebner bases, and projective space and their relationship with polynomial rings and ideals. This is a generalization of the theory of linear systems and linear algebra to treat systems of non-linear polynomial equations. It leads to beautiful interplay between algebra and geometry.

Grading

  • Assignments 20%
  • Midterm 25%
  • Final Exam 55%

Materials

REQUIRED READING:

Introduction to Algebraic Geometry by Brendan Hassett

Ideals, varieties, and algorithms by Cox, Little and O'Shea

4th edition.


ISBN: 3-319-16721-9

REQUIRED READING NOTES:

Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

Graduate Studies Notes:

Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

At SFU, you are expected to act honestly and responsibly in all your academic work. Cheating, plagiarism, or any other form of academic dishonesty harms your own learning, undermines the efforts of your classmates who pursue their studies honestly, and goes against the core values of the university.

To learn more about the academic disciplinary process and relevant academic supports, visit: 


RELIGIOUS ACCOMMODATION

Students with a faith background who may need accommodations during the term are encouraged to assess their needs as soon as possible and review the Multifaith religious accommodations website. The page outlines ways they begin working toward an accommodation and ensure solutions can be reached in a timely fashion.