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Mathematical Sciences
Common Subject
Complex Analysis
Preliminaries
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
Algebra
Fundamental Theory of Arithmetic
Group Theory
Ring Theory
Fields
Permutations & Combinations
Uniform Convergence (Sequence & Series of Function)
Some Important Structures
Basic Algebraic Structure
Ring of Polynomials
Continuity
Reimann Integration & Bounded Variation and Improper Integral
Differentiability
Set and Relations
Homomorphism and their Counting
Some Important Groups of Infinite Order
Invariant/Normal Subgroup
Groups within Groups
Basic Concepts and Definitions
Algebraic Extension of Fields
ED, PID & UFD
Subring and Ideals
Some Important Groups of Finite Order
Conjugate Classes and Class Equation
Symmetric Group or Permutation Group
Sylow Theorems
Ordinary Differential Equation
Introduction and Preliminaries
Uniqueness and Existence
System of Differential Equations
Trajectories
Sol. of 1st Order & Higher Degree
LDE with Constant Coefficients
Homogeneous Linear Equations
Method of Variation of Parameters
Ordinary Simultaneous DE
Linear Equations of Second Order
Picard’s Method & Existence
Simultaneous Equations
Partial Differential Equations
Riccati’s Equation
Power Series
Integration in Series
Legendre Polynomials
Legendre Functions of Second Kind
Orthogonal Sets of Functions
LDE Solution with Const. & Var. Coefficients
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
Classification & Formation of PDE
Classification of Second Order PDE
Heat, Wave & Laplace Equation
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
Maximum Likelihood Estimation
Probability
Markov Chains
Miscellaneous
Joint & Conditional Distributions
Elements of Bayesian Inference
Special Univariate Distributions
Inference - Parameter Estimation
Hypothesis Testing
