Spring 2021 - MATH 341 D100

Algebra III: Groups (3)

Class Number: 3535

Delivery Method: Remote

Overview

  • Course Times + Location:

    Mo, We, Fr 3:30 PM – 4:20 PM
    REMOTE LEARNING, Burnaby

  • Exam Times + Location:

    Apr 20, 2021
    8:30 AM – 11:30 AM
    REMOTE LEARNING, Burnaby

  • Prerequisites:

    MATH 340 or 342 or 332.

Description

CALENDAR DESCRIPTION:

Finite groups and subgroups. Cyclic groups and permutation groups. Cosets, normal subgroups and factor groups. Homomorphisms and isomorphisms. Fundamental theorem of finite abelian groups. Sylow theorems. Students with credit for MATH 339 may not take this course for further credit.

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:


Groups:

  •     Definition and examples of Groups
  •     Elementary Properties of Groups

Finite Groups: Subgroups:

  •     Terminology and Notation
  •     Subgroup Tests
  •     Examples of Subgroups

Cyclic Groups:

  •     Properties of Cyclic Groups
  •     Classification of Subgroups of Cyclic Groups

Permutation Groups:

  •     Definition and Notation
  •     Cycle Notation
  •     Properties of Permutations
  
Isomorphisms:

  •     Motivation
  •     Definition and Examples
  •     Cayley's Theorem
  •     Properties of Isomorphisms
  •     Automorphisms

Cosets and Lagranges Theorem:

  •     Properties of Cosets
  •     Lagranges Theorem and Consequences
  •     An Application of Cosets to Permutation Groups [Orbit-Stabilizer Theorem]
  •     The Rotation Group of a Cube

Normal Subgroups and Factor Group:

  •     Normal Subgroups
  •     Factor Groups
  •     Applications of Factor Groups [including Cauchy's Theorem]
    

Group Homomorphisms:

  •     Definition and Examples
  •     Properties of Homomorphisms
  •     The First Isomorphism Theorem

Sylow Theorems:

  •     Conjugacy Classes
  •     The Class Equation
  •     The Sylow Theorems
  •     Applications of Sylow theorems

Other topics:
  •     The Fundamental Theorem of Finite Abelian Groups
  •     Simple Groups
  •     Composition Series
  •     Solvable Groups

  •     Indirect Products


COURSE DELIVERY

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

Grading

  • Class participation (polls) 10%
  • Assignments 10%
  • Small Midterm 15%
  • Big Midterm 25%
  • Final 40%

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:

A First Course in Abstract Algebra: Rings, Groups, and Fields
3rd Edition
Marlow Anderson, Todd Feil
ISBN: 9781482245523

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).