Simon Fraser University
Engaging the World

Course Outlines

Spring 2022 - MATH 441 D100

Commutative Algebra and Algebraic Geometry (3)

Class Number: 6993

Delivery Method: In Person

Overview

  • Course Times + Location:

    Jan 10 – Apr 11, 2022: Mon, Wed, Fri, 4:30–5:30 p.m.
    Burnaby

  • Exam Times + Location:

    Apr 23, 2022
    Sat, 7:00–10:00 p.m.
    Burnaby

  • Prerequisites:

    MATH 340 with a minimum grade of C-.

Description

CALENDAR DESCRIPTION:

A study of ideals and varieties. Topics include affine varieties, ideals, Groebner bases, 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. Students who have taken this course as MATH 439 Special Topics may not complete this course for further credit.

COURSE DETAILS:

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:

Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra
David A. Cox, John Little, Donal O’Shea
Springer, 4th Edition

Also available as an e-book from Springer, which can be found here:
https://link.springer.com/book/10.1007%2F978-3-319-16721-3
ISBN: 9783319167206

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

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity web site 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

TEACHING AT SFU IN SPRING 2022

Teaching at SFU in spring 2022 will involve primarily in-person instruction, with safety plans in place.  Some courses will still be offered through remote methods, and if so, this will be clearly identified in the schedule of classes.  You will also know at enrollment whether remote course components will be “live” (synchronous) or at your own pace (asynchronous).

Enrolling in a course acknowledges that you are able to attend in whatever format is required.  You should not enroll in a course that is in-person if you are not able to return to campus, and should be aware that remote study may entail different modes of learning, interaction with your instructor, and ways of getting feedback on your work than may be the case for in-person classes.

Students with hidden or visible disabilities who may need class or exam accommodations, including in the context of remote learning, are advised to register with the SFU Centre for Accessible Learning (caladmin@sfu.ca or 778-782-3112) as early as possible in order to prepare for the spring 2022 term.