M.Sc Mathematics  (Miranda House, DU).
GATE 2018 Qualified
cleared IIT JAM in 2015
Participated in many ppts. competition and my ppt. at Dep

Rupal Aggarwal

In this course we will be learning group theory where we will understand different concepts and methods to approach a particular problem. Basic focus will be on questions related to CSIR NET and questions related to other exams will also be covered.

Crack CSIR NET by studying MATHEMATICS, PHYSICS, LIFE SCIENCE, CHEMISTRY, EARTH SCIENCE on one online platform. Everything you need to crack JRF.

CSIR-UGC NET

Hindi

(Hindi) Group Theory : CSIR-UGC NET

Fundamental Theory of Arithmetic

Algebra

Mathematical Sciences

NET Exams

Ace the toughest competitive and government exams in India 

Test Preparation

This is an insight into the coming series of lectures under the topic Group Theory.

Books Recommended :
• Dummit and Foote

• Contemporary Abstract Algebra by Joseph A. Gillian  ( most recommended)

• Michael Artin ( for extra knowledge)

Let's start the journey.

Introduction (in Hindi)

set theory and its definition, power  set and related questions

Set Theory 1 (in Hindi)

properties of set, laws on set, binary operation and it's examples

Set Theory 2 (in Hindi)

cartesian product, RELATION, identity, reflexive and irreflexive relation.

Set Theory 3 Relation (in Hindi)

Symmetric, asymmetric, anti symmetric and transitive RELATION, equivalence relation

Set Theory 4 (in Hindi)

Partition, Equivalence Classes, quotient set

Set Theory 5 ( Equivalence Classes)

Examples of Quotient Set and it's result, Fundamental Theorem of Equivalence Relation

Set Theory 6 ( Quotient Set)

modular function , it's  properties and application, Euler' s phi function and properties.

Preliminaries 1

Tau function, Groups ( Examples, properties )

Preliminaries 2 + Groups

Abelian Group (examples and Properties) , Order of a Group ( examples)

Abelian Group + Order of a group

Order of an Element, it's properties and important concepts and examples

Order Of an Element

Order Of an Element 2

Subgroups and types of Subgroups, examples, tests to prove a subset is a subgroup

Subgroups 1

Subgroups , points to prove that given set is not a Subgroups, examples of a Subgroups, set generated by an Element a is a subgroup of G

Subgroups 2

examples of Subgroups, results and properties

Subgroups 3

Properties of Subgroups, Equivalence relation on Subgroups, cosets defined using subgroups , Equivalence class on subgroups.

Subgroups 4

NOTE: only Z2 is the group with 1 generator and no other group of the form Zn has 1 generator.

Topics covered : Cyclic groups , definition, important examples.

Cyclic Groups 1

Fundamental Theorem of cyclic groups,  properties and examples

Cyclic Groups 2

important property of group structure and it's application. glimpse of ( definition of) homomorphism and isomorphism.

Cyclic Groups 3

Cyclic Groups properties and concepts, Lagrange's theorem and applications.

Cyclic Groups 4 + Lagrange's theorem

Lagrange's theorem  and about it's converse, Cauchy theorem and it's application

Lagrange's theorem

Group Zn

symmetric group, it's definitions, permutation group, composition of functions with respect to permutation group

Symmetric Group / Permutation Group

properties of permutations, cycle, length of cycle, order of cycle, transposition

Permutation Group 2

cyclic decomposition, counting of cycles, similar permutation, inverse of permutation, power of permutation

Permutation Group 3

even and odd permutation,  important theorem , inversion of permutation

Permutation Group 4

2 important concepts,  formation of An, properties

Permutation Group 5

discussion about group structure, it's order and nature (About Sn and An )

Permutation Group 6

about group S4 and A4, important result of A4, subgroups of A4

Permutation Group 7

External Direct Product, definition and properties, order of group and order of element

External Direct Product

Type  PKMATHS pankaj13 on YouTube to get Complete live Courses Subscribe on YouTube for free . 


Pankaj Kumar

In this course, the educator discusses an intuitive idea of Groups with Examples under Mathematical Sciences helpful for CSIR UGC NET Aspirants.

(Hindi) Groups (Properties and Examples): CSIR UGC NET

This course group theory for CSIR-UGC-NET/JRF with the concepts of Gallian and Dummit Foote has discussed beautifully.

Group Theory

Gajendra Purohit

In This Course Dr.Gajendra Purohit Will Cover Last Year Question Of Algebra With Mock Test. This Course Is Beneficial For CSIR NET Aspirants

(Hindi) Last Minute Revision of Algebra - CSIR UGC NET

B.Sc done from rajasthan University | M.Sc mathematics done from Parul University | IIT JAM 2018 cleared | NET JRF with AIR-150

Gaurav Kumar Agrawal

This course covers the Group theory of Abstract Algebra.

(Hindi) Abstract Algebra CSIR-UGC NET JRF Mathematics

mathematics is not only a sub.,
it is also a part of our life,
so every time of life do mathematics and learn mathematics

Ajay Kumar

We shall study subgroups and the various related results and Theorems in this course.  We also study cyclic groups and Theorems  in this course.

Lessons

30 lessons • 6h 47m

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Introduction (in Hindi)

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Set Theory 1 (in Hindi)

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Set Theory 2 (in Hindi)

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Set Theory 3 Relation (in Hindi)

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Set Theory 4 (in Hindi)

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Set Theory 5 ( Equivalence Classes)

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Set Theory 6 ( Quotient Set)

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Preliminaries 1

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Preliminaries 2 + Groups

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Abelian Group + Order of a group

+ See all lessons