Mathematical Sciences

Linear Algebra

Linear Equations

Matrices and Determinants

Vector Spaces

Linear Transformations

Diagonalizability & Canonical Forms

Inner Product Spaces

Operators on Inner Product Spaces

Bilinear Forms



Elementary Canonical Forms

Rational and Jordan Forms

Complex Analysis


Elementary Functions

Analytic Functions

Singularites of Analytic Functions

Limit, Continuity & Differentiability

Sequence and Series in Complex

Complex Integration

Laurent Series & Residue Theorem

Entire and Meromorphic Functions

Important Theorems & Applications

Max. and Min. Modulus Principle and Schwarz Lemma

Argument and Rouche’s Theorem

Calculus of Residues

Conformal Mapping

Bilinear Transformation & Mapping

Applications of Cauchy's Theorem

Harmonic Functions

Riemann Mapping Theorem

Analytic Continuation

Special Functions:The Exponential

Taylor and Laurent Expansion

Stereographic Projection & Point Set Topology

Fundamental Concepts of Complex Analysis


Fundamental Theory of Arithmetic

Group Theory

Ring Theory


Permutations & Combinations


Algebraic Extension of Fields

Set and Relations

Basic Algebraic Structure

Groups within Groups

Some Important Groups of Finite Order

Symmetric Group or Permutation Group

Some Important Groups of Infinite Order

Conjugate Classes and Class Equation

Invariant/Normal Subgroup

Homomorphism and their Counting

Sylow Theorems



Uniform Convergence (Sequence & Series of Function)

Reimann Integration & Bounded Variation and Improper Integral

Basic Concepts and Definitions

Some Important Structures

Subring and Ideals

Ring of Polynomials

Ordinary Differential Equation

Introduction and Preliminaries

First Order First Degree Differential Equation

General Theory of Linear Differential Equation of Higher Order

Solution of Linear Differential Equations with Constant and Variable Coefficients

Uniqueness and Existence

System of Differential Equations

Boundary Value Problems

Equtn of the 1st Order but Not of The 1st Degree

Equations of First Order & Degree


Sol. of 1st Order & Higher Degree

LDE with Constant Coefficients

Homogeneous Linear Equations

Method of Variation of Parameters

Ordinary Simultaneous DE

Exact Differential Equations

Equations of Special Forms

Linear Equations of Second Order

Picard’s Method & Existence

Simultaneous Equations

Partial Differential Equations

Riccati’s Equation

Chebyshev Polynomials

Beta and Gamma Functions

Power Series

Integration in Series

Legendre Polynomials

Legendre Functions of Second Kind

Bessel Functions

Orthogonal Sets of Functions

LDE Solution with Const. & Var. Coefficients


Sets & Number System

Series & Convergence

Theorem's in Analysis

Notions of Continuity

Integration Theory

Multivariable Calculus

Metric Spaces & Functions