Introduction to Abstract Algebra: Group Theory

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Introduction to Abstract Algebra: Group Theory, Learn group theory or abstract algebra in pure mathematics with examples and solved exercises.

This is an advanced level course of Introduction to Abstract Algebra with majors in Group Theory. The 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 COURSE

  • Groups and related examples
  • The identity element is the only element that is idempotent
  • Cancellation law hold in a group G
  • Definition of Subgroups and related examples
  • H is a subgroup if ab^-1 is contained in H
  • The intersection of any collection of subgroups is a subgroup
  • HuK is a subgroup if H is contained in Kor K is contained in H
  • Cyclic group and related examples
  • Every subgroup of a cyclic group is cyclic
  • Definition of cosets and related examples
  • Prove that the number of left or right cosets define the partition of a group G
  • Statement and Proof of Lagrange’s Theorem
  • Symmetric groups and related examples and exercises
  • Group of querternian and Klein’s four group
  • Normalizers, centralizers, and center of a group G and related theorem and examples
  • Quotient or Factor groups
  • Derived groups and related many examples
  • Normal Subgroups, conjugacy classes, conjugate subgroups, and related examples and theorems
  • Kernel of group
  • Automorphism and inner automorphism
  • P Group and related theorems and examples
  • Relations in groups like homomorphism and isomorphism
  • The centralizer is a subgroup of a group G
  • The normalizers is a subgroup of a group G
  • The Center of a group is a subgroup of a group G
  • The relation of conjugacy is an equivalence relation
  • Theorem and examples on quotient groups
  • Double cosets and related examples
  • Definition of automorphism
  • What is an inner automorphism
  • Every cyclic group is an abelian group
  • Groups of residue classes on a different mode
  • Examples of D_4 and D_5 groups
  • Examples related to C_6 and V_4
  • The first isomorphism theorem and its proof
  • The 2nd isomorphism theorem and its proof
  • The 3rd isomorphism theorem and its proof
  • The direct product of cyclic group
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