Mathematical Sciences

Common Subject

Algebra

Fundamental Theory of Arithmetic

Group Theory

Ring Theory

Fields

Permutations & Combinations

Sylow Theorems

Subring and Ideals

Some Important Groups of Finite Order

ED, PID & UFD

Conjugate Classes and Class Equation

Algebraic Extension of Fields

Symmetric Group or Permutation Group

Basic Concepts and Definitions

Groups within Groups

Invariant/Normal Subgroup

Some Important Groups of Infinite Order

Homomorphism and their Counting

Uniform Convergence (Sequence & Series of Function)

Set and Relations

Differentiability

Some Important Structures

Reimann Integration & Bounded Variation and Improper Integral

Basic Algebraic Structure

Continuity

Ring of Polynomials

Partial Differential Equation

Origin of PDE

Linear PDE of Order One

Non-linear PDE of Order One

Linear PDE with Constant Coeff.

PDE Reducible to Equations

2nd Order Variable Coeff. PDE

PDE into Cononial/Normal Form

Monge’s Method

Heat, Wave & Laplace Equation

Classification & Formation of PDE

Classification of Second Order PDE

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