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 7823337

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
 Terminology and Notation
 Subgroup Tests
 Examples of Subgroups
 Properties of Cyclic Groups
 Classification of Subgroups of Cyclic Groups
 Definition and Notation
 Cycle Notation
 Properties of Permutations
 Motivation
 Definition and Examples
 Cayley's Theorem
 Properties of Isomorphisms
 Automorphisms
 Properties of Cosets
 Lagranges Theorem and Consequences
 An Application of Cosets to Permutation Groups [OrbitStabilizer Theorem]
 The Rotation Group of a Cube
 Normal Subgroups
 Factor Groups
 Applications of Factor Groups [including Cauchy's Theorem]
 Definition and Examples
 Properties of Homomorphisms
 The First Isomorphism Theorem
 Conjugacy Classes
 The Class Equation
 The Sylow Theorems
 Applications of Sylow theorems
 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/s1001.html
TEACHING AT SFU IN SPRING 2022
Teaching at SFU in spring 2022 will involve primarily inperson 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 inperson 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 inperson 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 7787823112) as early as possible in order to prepare for the spring 2022 term.