Simon Fraser University
Engaging the World

Course Outlines

Spring 2024 - MATH 741 G100

Commutative Algebra and Algebraic Geometry (3)

Class Number: 3802

Delivery Method: In Person

Overview

  • Course Times + Location:

    Jan 8 – Apr 12, 2024: Mon, 2:30–3:20 p.m.
    Burnaby

    Jan 8 – Apr 12, 2024: Wed, Fri, 2:30–3:20 p.m.
    Burnaby

  • Exam Times + Location:

    Apr 16, 2024
    Tue, 12:00–3:00 p.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: polynomial rings, varieties (solutions of systems of polynomial equations), ideals, Groebner bases, and quotient rings. 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.

Topics covered will include: polynomials, ideals and varieties, term orders, and the division algorithm.

Grading

  • Assignments (5-10 questions each week; two lowest scores eliminated) 15%
  • Midterm 25%
  • Final Exam 60%

Materials

MATERIALS + SUPPLIES:

Both textbooks are available through the SFU library.

REQUIRED READING:

Introduction to Algebraic Geometry
Brendan Hassett
Cambridge University Press
2007
ISBN: 9780521691413

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

SFU’s Academic Integrity website http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating. Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the university community. Academic dishonesty, in whatever form, is ultimately destructive of the values of the university. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the university. http://www.sfu.ca/policies/gazette/student/s10-01.html