Spring 2022 - MATH 341 D100
Algebra III: Groups (3)
Class Number: 6506
Delivery Method: In Person
Overview
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Course Times + Location:
Jan 10 – Apr 11, 2022: Mon, Wed, Fri, 3:30–4:20 p.m.
Burnaby -
Exam Times + Location:
Apr 26, 2022
Tue, 3:30–6:30 p.m.
Burnaby
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Instructor:
Jonathan Jedwab
jed@sfu.ca
1 778 782-3337
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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 [Orbit-Stabilizer 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/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.