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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
Polynomials
Determinants
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
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
Some Important Groups of Infinite Order
Continuity
Invariant/Normal Subgroup
Groups within Groups
Basic Concepts and Definitions
Algebraic Extension of Fields
ED, PID & UFD
Ring of Polynomials
Basic Algebraic Structure
Some Important Structures
Subring and Ideals
Some Important Groups of Finite Order
Uniform Convergence (Sequence & Series of Function)
Conjugate Classes and Class Equation
Symmetric Group or Permutation Group
Sylow Theorems
Homomorphism and their Counting
Set and Relations
Differentiability
Reimann Integration & Bounded Variation and Improper Integral
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
Hypothesis Testing
Markov Chains
Inference - Parameter Estimation
Maximum Likelihood Estimation
Special Univariate Distributions
Elements of Bayesian Inference
Joint & Conditional Distributions
Miscellaneous
Probability