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

Real Analysis

Sets and Number System

Point Set Topology

Series and Convergence

Function and its Property

Sequence and Series of Function

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

Descriptive Statistics

Introduction Meaning and Scope

Frequency Distributions

Measures of Central Tendency

Measures of Dispersion

Skewness and Kurtosis

Theory of Probability

Random Variables

Mathematical Expectation

Discrete Distributions

Continuous Distributions

Curve Fitting

Correlation and Regression

Theory of Attributes

Sampling and Large Sample Tests

Chi-Square Distribution

t,F and z distributions

Theory of Estimation

Statistical Inference-II


Special Univariate Distributions

Joint & Conditional Distributions

Inference - Parameter Estimation

Maximum Likelihood Estimation

Hypothesis Testing

Elements of Bayesian Inference

Markov Chains


General Aptitude

General Aptitude