Spring 2020 - MATH 441 D100

Commutative Algebra and Algebraic Geometry (3)

Class Number: 3740

Delivery Method: In Person

Overview

  • Course Times + Location:

    Tu 2:30 PM – 4:20 PM
    AQ 5018, Burnaby

    Th 2:30 PM – 3:20 PM
    AQ 5018, Burnaby

  • Exam Times + Location:

    Apr 21, 2020
    8:30 AM – 11:30 AM
    RCB 8100, Burnaby

  • Prerequisites:

    MATH 340.

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, the division algorithm, Groebner bases and the Hilbert basis theorem, elimination theory, Hilbert's Nullstellensatz, irreducible varieties, projective space, Bezout's theorem

Grading

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

Materials

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

RECOMMENDED READING:

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

Registrar Notes:

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

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS