Overview

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:

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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.

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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

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COURSE DELIVERY

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

Grading

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: