Chapters

Fundamental Theory of Arithmetic

Group Theory

Fields

Permutations & Combinations

Invariant/Normal Subgroup

Sylow Theorems

Symmetric Group or Permutation Group

Conjugate Classes and Class Equation

Subring and Ideals

ED, PID & UFD

Algebraic Extension of Fields

Basic Concepts and Definitions

Groups within Groups

Uniform Convergence (Sequence & Series of Function)

Some Important Groups of Infinite Order

Homomorphism and their Counting

Differentiability

Reimann Integration & Bounded Variation and Improper Integral

Continuity

Ring of Polynomials

Some Important Structures

Courses
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1
Fundamental Theory of Arithmetic
Practice

Lessons

Conformal Map & Rouche's Theorem with Problem Solving

1 hr 23 mins

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Complex Integration: Theorems, Results, and Problem Solving

1 hr 24 mins

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Integral Equation & Laplace Theorem with Problem Solving

1 hr 25 mins

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2
Group Theory
Notes

Available on android app

Practice

Lessons

Introduction of Group Theory: Sets, Relation & Equivalence class

2 hrs

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Congruence relation on Z, Binary operations & Group

2 hrs 3 mins

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Important Results, Subgroup, Special Types of Group & Dihedral Group

2 hrs

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Permutation Group & Order of Group

2 hrs 4 mins

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Order of Group, Abelian Group & Cyclic Group

2 hrs 1 min

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Group of Possible Order & Group Theory: Problem Solving

1 hr 59 mins

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Subgroup: Cyclic Group, Non Cyclic Group & Problem Solving

2 hrs

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Center of the Group Z(G) & Problem Solving

2 hrs

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Centralizer of an Element, Coset, Improper & Proper Normal Subgroup

1 hr 55 mins

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Symmetric Group & Group Theory: Problem Solving

1 hr 59 mins

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3
Fields
Practice

Lessons

Field, Minimal Polynomial, Kronecker Theorem, and Types of extension

1 hr 27 mins

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Permutations & Combinations

Lessons

Modern Algebra: Permutation, Combination & Problem Solving

1 hr 25 mins

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Number & Sum of Divisors, Principles of Pigeonhole, and Inclusion & Exclusion

1 hr 35 mins

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Permutation & Transposition and Rearrangement & Congruence

1 hr 38 mins

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Invariant/Normal Subgroup

Lessons

Invariant/Normal Subgroups - Part I

1 hr 45 mins

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Invariant/Normal Subgroups - Part II

1 hr 44 mins

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Invariant/Normal Subgroups - Part III

1 hr 42 mins

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Sylow Theorems

Lessons

Sylow's I, II & III Theorem & Problem Solving

1 hr 29 mins

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Symmetric Group or Permutation Group

Lessons

Symmetric Group/Permutation Group - Part I

1 hr 57 mins

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Groups Theory

1 hr 58 mins

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Symmetric Group/Permutation Group - Part II

2 hrs 6 mins

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Conjugate Classes and Class Equation

Lessons

Conjugate Classes and Class Equations Part I

2 hrs 11 mins

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Conjugate Classes and Class Equations Part II

2 hrs 3 mins

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Class Equations: Introduction

2 hrs 5 mins

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Conjugate Element & Class Equation Part III

2 hrs 10 mins

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Subring and Ideals

Lessons

Subring, Ideal & Gaussian Ring, and Problem Solving

1 hr 24 mins

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Polynomial Ring and Problem Solving

1 hr 25 mins

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ED, PID & UFD

Lessons

PID: Introduction, Theorems, Properties, and Theorem of Number Theory

1 hr 58 mins

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GCD, LCM, UFD, and Euclidean Domain

1 hr 33 mins

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ED Theorem, Polynomial & Quotient Ring, and Homomorphism

2 hrs 3 mins

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Irreducibility of Polynomial: Introduction, Test ,and UFD

2 hrs 4 mins

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Irreducibility of Polynomial: Introduction, Test Co Maximal, and Extension of Field

2 hrs 17 mins

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Algebraic Extension of Fields

Lessons

Modern Algebra: Problem Solving - I

2 hrs 3 mins

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Ring Theory, Commutative Ring, Zero Division, Integral Domain & Skew Field

2 hrs 10 mins

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Quadratic Field, PID, Norm on an Integral Domain & Primitive Polynomial

2 hrs 6 mins

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Algebraic Elements & Extension, Splitting Field, and Separable Extension

2 hrs 5 mins

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Modern Algebra: Problem Solving - II

2 hrs 5 mins

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12
Basic Concepts and Definitions

Lessons

Sets, Relation & its Types, and Abstract Algebra

1 hr 44 mins

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13
Groups within Groups

Lessons

Groups Within Group

2 hrs 13 mins

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14
Uniform Convergence (Sequence & Series of Function)

Lessons

Sequence, Uniform Convergence & Consequence of Uniform Convergence

2 hrs 2 mins

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15
Some Important Groups of Infinite Order

Lessons

Finite & Infinite Groups, and Subgroups

1 hr 53 mins

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Homomorphism and their Counting

Lessons

Normal Subgroups, Quotient & Factor Group, and Theorems on Homo-morphisms

1 hr 41 mins

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Homomorphism & their Counting - Part I

1 hr 43 mins

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Homomorphism & their Counting - Part II

1 hr 43 mins

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Differentiability

Lessons

Function: Lipschitz, Differentiability, and Problem Solving

1 hr 30 mins

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18
Reimann Integration & Bounded Variation and Improper Integral

Lessons

Differentiability: Introduction, Cauchy Mean Value Theorem & PYQs

1 hr 33 mins

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19
Continuity

Lessons

Real Analysis: D'alembert Ratio test & Problem Solving

1 hr 32 mins

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Real Analysis: Cauchy nth Root & Integral Test, Definitions, and Series

1 hr 31 mins

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20
Ring of Polynomials

Lessons

Degree of a Polynomial, GCD & LCM of Polynomial, and Polynomial Ring

1 hr 22 mins

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21
Some Important Structures

Lessons

Maximal & Prime Ideals, and Some important structures: Problem solving

1 hr 32 mins

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