Overview

< Step-by-step explanation of more than 100 video lessons on Abstract Algebra: Group Theory> This is an advanced level course of Introduction to Abstract Algebra with majors in Group Theory. Students who want to learn algebra at an advanced level, usually learn Introduction to Abstract Algebra: Group Theory. The course is offered for pure mathematics students in different universities around the world. However, the students who take the Introduction to Abstract Algebra: Group Theory course, are named super genius in group theory. Not so much difficult, but regular attention and interest can lead to the students in the right learning environment of mathematics. Many students around the world have their interest in learning Introduction to Abstract Algebra: Group Theory but they could't find any proper course or instructor.Abstract Algebra is comprised of one of the main topics which are also called Group theory. Group Theory or Group is actually the name of the fundamental four properties of mathematics that are frequently used in real analysis. We actually establish a strong background of Group Theory by defining different concepts. Proof of theorems and solutions of many examples is one of the interesting parts while studying Group Theory.This course is filmed on a whiteboard (8 hours) and Tablet (2 hours). The length of this course is 10 hours with more than 15 sections and 100 videos. Almost every content of Group Theory has been included in this course. The students have difficulties in understanding the theorem, especially in Group Theory. Theorems have been explained with proof and examples in this course. A number of examples and exercises make this course easy for every student, even those who are taking this course the first time. I assure all my students that they will enjoy this course. But however, if they have any difficulty then they can discuss it with me. I will answer your every question with a prompt response. One thing I will ask you is that you must see the contents sections and some free preview videos before enrolling in this course. CONTENTS OF THIS COURSEGroups and related examplesThe identity element is the only element that is idempotentCancellation law hold in a group GDefinition of Subgroups and related examplesH is a subgroup if ab^-1 is contained in HThe intersection of any collection of subgroups is a subgroupHuK is a subgroup if H is contained in Kor K is contained in HCyclic group and related examplesEvery subgroup of a cyclic group is cyclicDefinition of cosets and related examplesProve that the number of left or right cosets define the partition of a group GStatement and Proof of Lagrange's TheoremSymmetric groups and related examples and exercisesGroup of querternian and Klein's four groupNormalizers, centralizers, and center of a group G and related theorem and examplesQuotient or Factor groupsDerived groups and related many examplesNormal Subgroups, conjugacy classes, conjugate subgroups, and related examples and theoremsKernel of groupAutomorphism and inner automorphismP Group and related theorems and examplesRelations in groups like homomorphism and isomorphismThe centralizer is a subgroup of a group GThe normalizers is a subgroup of a group GThe Center of a group is a subgroup of a group GThe relation of conjugacy is an equivalence relationTheorem and examples on quotient groupsDouble cosets and related examplesDefinition of automorphismWhat is an inner automorphismEvery cyclic group is an abelian groupGroups of residue classes on a different modeExamples of D_4 and D_5 groupsExamples related to C_6 and V_4The first isomorphism theorem and its proofThe 2nd isomorphism theorem and its proofThe 3rd isomorphism theorem and its proofThe direct product of cyclic group

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