Abstract Group Theory

About Course

Abstract Group Theory.

This course will introduce abstract groups. We will start with definitions, basic properties, and constructions and cover many important theorems in basic group theory, such as Lagrange’s theorem, Cauchy’s theorem, and Sylow’s theorems. A major emphasis of the course will be to present numerous worked-out examples and problems. A part of the lecture every week will be devoted to explicit calculations.

INTENDED AUDIENCE: BSc, MSc students studying mathematics.

Course Content

Introduction to Abstract Group Theory

Lecture 45 – Problems 10

00:00
Lecture 32 – Alternating groups

00:00
Lecture 31 – Odd and even permutations II

00:00
Lecture 30 – Odd and even permutations I

00:00
Lecture 29 – Symmetric groups IV

21:42
Lecture 28 – Symmetric groups III

19:42
Lecture 27 – Symmetric Groups II

27:38
Lecture 26 – Symmetric groups I

00:00
Lecture 25 – Problems 6

00:00
Lecture 24 – Cauchy’s theorem

00:00
Lecture 33 – Group actions

00:00
Lecture 34 – Examples of group actions

00:00
Lecture 35 – Orbits and stabilizers

00:00
Lecture 44 – Problems 9

00:00
Lecture 43 – Sylow Theorem III

00:00
Lecture 42 – Sylow Theorem II

00:00
Lecture 41 – Sylow Theorem I

00:00
Lecture 40 – Group actions on subsets

00:00
Lecture 39 – Problems 8 and Class equation

00:00
Lecture 38 – Problems 7

00:00
Lecture 37 – Cayley’s theorem

00:00
Lecture 36 – Counting formula

00:00
Lecture 23 – Third isomorphism theorem

00:00
Lecture 22 – Examples and Second isomorphism theorem

00:00
Lecture 09 – Types of groups

00:00
Lecture 08 – Subgroups

00:00
Lecture 07 – Problems 3

00:00
Lecture 06 – Problems 2

00:00
Lecture 05 – Problems 1

00:00
Lecture 04 – “Basic properties of groups and multiplication tables”

00:00
Lecture 03 – “More examples of groups”

00:00
Lecture 02 – “Definition of a group and examples”

00:00
Lecture 01 – “Motivational examples of groups”

00:00
Lecture 10 – Group homomorphisms and examples

00:00
Lecture 11 – Properties of homomorphisms

00:00
Lecture 12 – Group isomorphisms

00:00
Lecture 21 – First isomorphism theorem

00:00
Lecture 20 – Examples of quotient groups

00:00
Lecture 19 – Quotient groups

00:00
Lecture 18 – Problems 5

00:00
Lecture 17 – S_3 revisited

00:00
Lecture 16 – Cosets and Lagrange’s theorem

00:00
Lecture 15 – Problems 4

00:00
Lecture 14 – Equivalence relations

00:00
Lecture 13 – Normal subgroups

00:00
INTRODUCTION TO ABSTRACT GROUP THEORY

00:00

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eim001

8 months ago

Great course!

About Course

Abstract Group Theory.

What Will You Learn?

Course Content

Introduction to Abstract Group Theory

Lecture 45 – Problems 10

Lecture 32 – Alternating groups

Lecture 31 – Odd and even permutations II

Lecture 30 – Odd and even permutations I

Lecture 29 – Symmetric groups IV

Lecture 28 – Symmetric groups III

Lecture 27 – Symmetric Groups II

Lecture 26 – Symmetric groups I

Lecture 25 – Problems 6

Lecture 24 – Cauchy’s theorem

Lecture 33 – Group actions

Lecture 34 – Examples of group actions

Lecture 35 – Orbits and stabilizers

Lecture 44 – Problems 9

Lecture 43 – Sylow Theorem III

Lecture 42 – Sylow Theorem II

Lecture 41 – Sylow Theorem I

Lecture 40 – Group actions on subsets

Lecture 39 – Problems 8 and Class equation

Lecture 38 – Problems 7

Lecture 37 – Cayley’s theorem

Lecture 36 – Counting formula

Lecture 23 – Third isomorphism theorem

Lecture 22 – Examples and Second isomorphism theorem

Lecture 09 – Types of groups

Lecture 08 – Subgroups

Lecture 07 – Problems 3

Lecture 06 – Problems 2

Lecture 05 – Problems 1

Lecture 04 – “Basic properties of groups and multiplication tables”

Lecture 03 – “More examples of groups”

Lecture 02 – “Definition of a group and examples”

Lecture 01 – “Motivational examples of groups”

Lecture 10 – Group homomorphisms and examples

Lecture 11 – Properties of homomorphisms

Lecture 12 – Group isomorphisms

Lecture 21 – First isomorphism theorem

Lecture 20 – Examples of quotient groups

Lecture 19 – Quotient groups

Lecture 18 – Problems 5

Lecture 17 – S_3 revisited

Lecture 16 – Cosets and Lagrange’s theorem

Lecture 15 – Problems 4

Lecture 14 – Equivalence relations

Lecture 13 – Normal subgroups

INTRODUCTION TO ABSTRACT GROUP THEORY

Student Ratings & Reviews