Simon Fraser University
Engaging the World

Course Outlines

Spring 2025 - MATH 740 G100

Galois Theory (3)

Class Number: 2755

Delivery Method: In Person

Overview

  • Course Times + Location:

    Jan 6 – Apr 9, 2025: Mon, Wed, Fri, 10:30–11:20 a.m.
    Burnaby

  • Exam Times + Location:

    Apr 11, 2025
    Fri, 12:00–3:00 p.m.
    Burnaby

Description

CALENDAR DESCRIPTION:

An introduction to the theory of fields, with emphasis on Galois theory. Students may not take a 700-division course if it is being offered in conjunction with a 400-division course which they have taken previously.

COURSE DETAILS:

I. Extension fields

  • Introduction
  • Degree of an extension
  • Finite and algebraic extensions
  • Algebraic Closures
II. Galois theory
  • Splitting fields and normal extensions
  • Separable extensions
  • Galois groups
  • The Galois correspondence
III. Background for applications
  • Symmetric functions and discriminants
  • Sylow theorems
IV. Applications and further topics
  • The fundamental theorem of algebra
  • Solvable extensions
  • Insolvability of the quintic
  • Geometric constructions

Grading

  • Assignments 15%
  • Midterm and/or Quizzes 25%
  • Final Exam 60%

NOTES:

THE INSTRUCTOR RESERVES THE RIGHT TO CHANGE ANY OF THE ABOVE INFORMATION.

Students in Math 740 will be required to complete additional homework and exam questions.

This course is delivered in person, on campus. Should public health guidelines recommend limits on in person gatherings, this course may include virtual meetings. As such, all students are recommended to have access to strong and reliable internet, the ability to scan documents (a phone app is acceptable) and access to a webcam and microphone (embedded in a computer is sufficient).

Materials

REQUIRED READING:

Galois Theory
David A. Cox,
Second edition, 2012
John Wiley & Sons, Inc.
ISBN: 978-1-118-07205-9

RECOMMENDED READING:

Abstract Algebra
David Dummit and Richard Foote
3/E, 2004
John Wiley and Sons
ISBN: 978-0471433347

A First Course in Abstract Algebra Rings, Groups, and Fields
Marlow Anderson and Todd Feil
3/E, 2005
Chapman and Hall/CRC Press
ISBN: 9781482245523

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

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.