Spring 2022 - MATH 341 D100

Algebra III: Groups (3)

Class Number: 6506

Delivery Method: In Person

Overview

  • Course Times + Location:

    Mo, We, Fr 3:30 PM – 4:20 PM
    WMC 2810, Burnaby

  • Exam Times + Location:

    Apr 26, 2022
    3:30 PM – 6:30 PM
    WMC 3220, Burnaby

  • Instructor:

    Jonathan Jedwab
    jed@sfu.ca
    1 778 782-3337
  • Prerequisites:

    MATH 340 or 342 or 332, with a minimum grade of C-.

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:

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

Grading

  • Assignments 15%
  • Midterm 30%
  • Final Exam 55%

Materials

REQUIRED READING:

Contemporary Abstract Algebra
Joseph A. Gallian
9th Edition
ISBN: 9781305657960

RECOMMENDED READING:

Visual Group Theory
Nathan Carter
ISBN: 9780883857571

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.