Simon Fraser University
Engaging the World

Course Outlines

Spring 2021 - MATH 740 G100

Galois Theory (3)

Class Number: 3887

Delivery Method: Remote

Overview

  • Course Times + Location:

    Jan 11 – Apr 16, 2021: Mon, Wed, Fri, 10:30–11:20 a.m.
    Burnaby

  • Exam Times + Location:

    Apr 26, 2021
    Mon, 3:30–6:30 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:

This course will be delivered online. You are expected to have access to a reliable internet connection. You will need a computer from which you can download course materials and activities and watch live and/or recorded lectures and participate in live tutorials or workshops.

You will need a camera to take photographs of your work. A phone is acceptable



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


COURSE DELIVERY

  •  Lecture: synchronous- lectures will be held at fixed times, on-line
  •  Midterm(s): synchronous; date: TBA
  •  Final exam: synchronous; date: TBA

Note: this is a cross-listed course with MATH 440

Grading

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

NOTES:

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

Materials

MATERIALS + SUPPLIES:

Required: 

  • Access to strong and reliable internet.
  • Ability to scan documents (phone app acceptable)
  • Access to webcam and microphone (embedded in computer sufficient)

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

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 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 2021

Teaching at SFU in spring 2021 will be conducted primarily through remote methods. There will be in-person course components in a few exceptional cases where this is fundamental to the educational goals of the course. Such course components will be clearly identified at registration, as will course components that will be “live” (synchronous) vs. at your own pace (asynchronous). Enrollment acknowledges 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. To ensure you can access all course materials, we recommend you have access to a computer with a microphone and camera, and the internet. In some cases your instructor may use Zoom or other means requiring a camera and microphone to invigilate exams. If proctoring software will be used, this will be confirmed in the first week of class.

Students with hidden or visible disabilities who believe they may need class or exam accommodations, including in the current context of remote learning, are encouraged to register with the SFU Centre for Accessible Learning (caladmin@sfu.ca or 778-782-3112).