Description

Abstract Algebra (A Crash Course in Group Theory)Abstract Algebra (A Crash Course in Group Theory) is an advance level course of pure mathematics. The students who wants to learn algebra at advance level, they usually learn Abstract Algebra. This course is offered for the pure mathematics students in different universities around the world. However, the students who take this course, they are named super genius. Not so much difficult, but a regular attention and interest can lead to the students in a right learning environment of mathematics. Many students around the world have their interest in learning abstract algebra but they could’t find any proper course or instructor.Abstract Algebra is comprises by one of the main topic which is also called Group theory. Group Theory or Group is actually the name of fundamental four properties of mathematics which are frequently used in real analysis. We actually establish a strong background of Group Theory by defining different concepts. Proof of theorems and solution of many examples is one of the interesting part while studying Group Theory.This course is filmed on 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 have been included in this course. The students have difficulties in understanding the theorem specially in Group Theory. Theorems have been explained with proof and examples in this course. Number of examples and exercises makes this course easy for every students, even who is taking this course first time. I assure to all my students that they will enjoy this course. But however, if they have any difficulty then they can discuss with me. I will answer your every question with a prompt response. One thing I will ask you that you must see the contents sections and some free preview videos before enrolling in this course. CONTENTS OF THIS COURSEGroups and related examplesIdentity element is the only elements which is idempotentCancellation law hold in a group GDefinition of Subgroups and related examplesH is subgroup if ab^-1 is contained in HIntersection of any collection of subgroups is subgroupHuK is subgroup if H is contained in K or 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 group like homomorphism and isomorphismThe centralizers is a subgroup of a group GThe normalizers is a subgroup of a group GCenter 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 different modeExamples of D_4 and D_5 groupsExamples related C_6 and V_4The first isomorphism theorem and its proofThe 2nd isomorphism theorem and its proofThe 3rd isomorphism theorem and its proofDirect product of cyclic groupMoreover the contents of ring and field has also included and the courses is updating on each month. I add new contents and examples ad exercises and much more the complete understanding of students. If someone from students ask me for particular contents or lectures I will publish that lecture. However there is question answer section on each video. If you have difficulties then you can ask me as many questions as many you want to ask. I will appreciate those students who will ask me the questions and by naturally my students learn more who ask me the questions. Hope you will join my courses and please stay healthy