Explore a comprehensive 20-hour playlist on Group Theory, covering essential topics for B.Sc., M.Sc., B.Tech, and competitive exams like IIT-JAM, CSIR NET, and GATE. Delve into discrete mathematics, semi-groups, monoids, Abelian groups, modular arithmetic, subgroups, cyclic groups, cosets, Lagrange's theorem, simple groups, quotient groups, homomorphisms, isomorphisms, automorphisms, permutation groups, finite integral domains, ring theory, vector spaces, and more. Learn through detailed explanations, examples, and theorems, gaining a solid foundation in abstract algebra and linear algebra concepts. Enhance your understanding of advanced mathematical structures and their properties, preparing you for higher-level mathematics and related fields.
Overview
Syllabus
Group Theory | Semi-Group , Monoid | Abelian Group | Discrete Mathematics.
Group Theory | Examples Of Group & Abelian Group | Discrete Mathematics.
Group Theory | Addition modulo and Multiplication modulo | Discrete Mathematics.
Group Theory | Properties Of Groups | Discrete Mathematics.
Group Theory | Subgroup | Subgroup Theorems | Discrete Mathematics.
Group Theory | Subgroup | Subgroup Examples | Discrete Mathematics.
Group Theory | Cyclic Group | Generator Of Cyclic Group | Discrete Mathematics.
Group Theory | Cyclic Group | Properties Of Cyclic Group | Discrete Mathematics.
Group Theory | Cosets | Cosets Examples | Abstract Algebra.
Group Theory | Cosets | Lagrange Theorem Group Theory | Abstract Algebra.
Group Theory | Normal Subgroup | Simple Group | Invariant Subgroup | Abstract Algebra.
Group Theory | Quotient Group | Quotient Group Examples | Abstract Algebra.
Group Theory | Quotient Group | Properties Of Quotient Group | Abstract Algebra.
Group Theory | Homomorphism | Homomorphism Examples | Abstract Algebra.
Group Theory | Homomorphism | Kernel Of Homomorphism | Abstract Algebra.
Group Theory | Homomorphism | Fundamental Theorem Of Homomorphism | Proof.
Group Theory | Isomorphism | Examples of Isomorphism.
Group Theory | Isomorphism | Isomorphism Theorem | Cayley's Theorem.
Group Theory | Automorphism | Automorphism Examples & Theorems | Abstract Algebra.
Group Theory | Permutation Group | Even & Odd Permutation | Order Of Permutation.
Group Theory | Symmetric Group S3 & S4 | Alternating Group A3 & A4 | Order Of Element.
Ring Theory | Commutative Ring | Ring With Unity | Definition/Examples/Properties.
Ring Theory | Zero Divisors | Boolean Ring | Cancellation Law / Example / Definitions.
Ring Theory | Integral Domain | Integral Domain Examples | Theorems / Definitions.
Field Theory | Definition & Example Of Field | Unit Element in Ring | Abstract Algebra.
Ring Theory | Finite Integral Domain is Field | Skew Field | Characteristic Of Ring.
Ring Theory | Examples Of Ring, Integral Domain & Field | Abstract Algebra.
Ring Theory | Subring | Theorems & Examples Of Subring | Abstract Algebra.
Ring Theory | Subfield | Prime Field | Theorems & Examples Of Subfield | Abstract Algebra.
Ideals Of Ring | Ring Theory | Simple Ring | Examples | Abstract Algebra.
Ideals Of Ring | Ring Theory | Simple Ring | Theorems | Abstract Algebra.
Vector Space | Definition Of Vector Space | Examples Of Vector Space | Linear Algebra.
Vector Space | Properties Of Vector Space | Linear Algebra.
Vector Subspace | Subspace Theorems & Examples | Linear Algebra.
Vector Subspace | Algebra Of Subspace Theorems | Linear Algebra.
Vector Subspace | Linearly Independent | Linearly Dependents Vectors | Linear Algebra.
Vector Subspace | Basis & Dimension | Examples Of Basis | Linear Algebra.
Vector Space | Linear Transformation | Examples Of Linear Transformation | Linear Algebra.
Rank Of Matrix | How to find Rank of Matrix | MATRICES | Linear Algebra.
System Of Linear Equations | Non Homogeneous Equation | Matrices.
System Of Linear Equations | Homogeneous Equation | Matrices.
Career Options | For B.Sc. & B.Tech. Students | By Dr.Gajendra Purohit.
Eigenvalues and Eigenvectors | Properties and Important Result | Matrices.
Eigenvalues and Eigenvectors | Eigen Values Examples | Eigen Vectors Examples.
Cayley Hamilton Theorem | Short Trick to Find Inverse of Matrices.
How To Choose The Right Career | Career Option After 12th | Career Counselling For Students.
Diagonalization of Matrix | Algebraic Multiplicity and Geometric Multiplicity | Matrices.
CSIR NET June 2020 Exam Update | CSIR NET & GATE Exam Strategy | Books & Cutoff.
Diagonalization | Eigenvalues, Eigenvectors with Concept of Diagonalization | Matrices.
Group Theory | Center Of A Group - Conjugate Elements | Concepts and Example.
Group Theory | Normalizer of Element - Normalizer of Subgroup | Concepts and Example.
Group Theory | Class Equation - Sn & Dn | Class Equation Proof.
Group Theory | Sylow Theorem | Sylow First Theorem - Proof and Example.
Group Theory | Special Properties Of Groups of Order 1 to 5.
Dihedral Group | Important Concepts Of Dihedral Group | Group Theory.
Group Theory | Special Properties Of Groups Of Order 6 To 7 - Concepts and Example By GP Sir.
Dihedral Group | Important Concepts Of Dihedral Group | Group Theory.
Group Theory | Special Properties Of Groups Of Order 8 - Concepts and Example By GP Sir.
Group Theory | Sylow Second Theorem | Sylow 2nd Theorem - Concept and Example.
Group Theory | Special Properties Of Groups Of Order 9 To 10 - Concepts and Example By GP Sir.
Group Theory | Sylow Third Theorem | Sylow 3rd Theorem - Concept and Example.
Inner Product | Inner Product Space - Concept & Properties of Inner Product | Liner Algebra.
Taught by
Gajendra Purohit
