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Index

Set Theory

Sequences and Series

Continuity and Differentiability

Integral Calculus

Real Analysis

Differential Calculus

Linear Functional Analysis

Matrix Algebra

Vector Algebra

Complex Analysis

Group Theory

Algebra

Field Theory

Ring Theory

Topology

Ordinary Differential Equations (ODEs)

Partial Differential Equations (PDEs)

Numerical Analysis

Calculus of Variations

Linear Integral Equations

Classical Mechanics

Statistics

Probability and probability Distributions

All Exams > Mathematics > Mathematics for IIT JAM, GATE, CSIR NET, UGC NET > All Notes

All notes of Mathematics for IIT JAM, GATE, CSIR NET, UGC NET

Set Theory

Elementary Set Theory - CSIR-NET Mathematical Sciences

19 pages

Finite, Countable and Uncountable Sets - Set Theory, CSIR-NET Mathematical Sciences

29 pages

Supremum, Infimum - Set Theory, CSIR-NET Mathematical Sciences

6 pages

Real Number System as a Complete Ordered Field and Archimedean Property - CSIR-NET Mathematical

8 pages

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Sequences and Series

Series - Sequences and Series, CSIR-NET Mathematical Sciences

7 pages

Liminf and Limsup for Bounded Sequences of Real Numbers - CSIR-NET Mathematical Sciences

2 pages

Sequences and Their Algebra, Bolzano Weierstrass Theorem - CSIR-NET Mathematical Sciences

15 pages

Convergence Tests - Sequences and Series, CSIR-NET Mathematical Sciences

9 pages

Heine Borel - Sequences and Series, CSIR-NET Mathematical Sciences

2 pages

Continuity and Differentiability

Continuity and Uniform Continuity - Continuity and Differentiability, CSIR-NET Mathematical Sciences

8 pages

Differentiability - Continuity and Differentiability, CSIR-NET Mathematical Sciences

8 pages

Sequences and Series Del- CSIR-NET Mathematical Science

10 pages

Sequences and Series of Functions and Uniform Convergence - 1 - CSIR-NET Mathematical Science

10 pages

Sequences and Series of Functions and Uniform Convergence - 1 - CSIR-NET Mathematical Science

10 pages

Rolle's Theorem and The Mean Value Theorem - CSIR-NET Mathematical Sciences

6 pages

Integral Calculus

Riemann Sums and Riemann Integral - Integral Calculus, CSIR-NET Mathematical Sciences

11 pages

Improper Integrals - Integral Calculus, CSIR-NET Mathematical Sciences

8 pages

Real Analysis

Types of Discontinuity - Real Analysis, CSIR-NET Mathematical Sciences

1 page

Lebesgue Measure and Lebesgue Integral - Real Analysis, CSIR-NET Mathematical Sciences

12 pages

Monotonic Functions - Real Analysis, CSIR-NET Mathematical Sciences

7 pages

Functions of Bounded Variation - Real Analysis, CSIR-NET Mathematical Sciences

5 pages

Differential Calculus

Directional Derivative - Differential Calculus, CSIR-NET Mathematical Sciences

10 pages

Derivative as a Linear Transformation - Differential Calculus, CSIR-NET Mathematical Sciences

3 pages

Functions of Several Variables - Differential Calculus, CSIR-NET Mathematical Sciences

7 pages

Partial Derivative - Differential Calculus, CSIR-NET Mathematical Sciences

11 pages

Inverse and Implicit Function Theorems - Differential Calculus, CSIR-NET Mathematical Sciences

4 pages

Linear Functional Analysis

Metric Spaces - Linear Functional Analysis - 1

7 pages

Metric Spaces - Linear Functional Analysis - 2

8 pages

Compactness and connectedness: Linear Functional Analysis - 1

5 pages

Compactness and connectedness: Linear Functional Analysis - 2

6 pages

Normed linear Spaces - Linear Functional Analysis, CSIR-NET Mathematical Sciences

9 pages

Spaces of Continuous Functions as examples - CSIR-NET Mathematical Sciences

8 pages

Matrix Algebra

Rank of Matrices - Matrix Algebra, CSIR-NET Mathematical Sciences

1 page

Matrices & Determinants: Matrix Algebra - 1

13 pages

Solving Linear Equations - Matrix Algebra, CSIR-NET Mathematical Sciences

1 page

Matrices & Determinants: Matrix Algebra - 2

11 pages

Eigenvalues & Eigenvectors - 1

7 pages

Eigenvalues & Eigenvectors - 2

7 pages

Cayley Hamilton Theorem - Matrix Algebra, CSIR-NET Mathematical Sciences

6 pages

Matrix Representation of Linear Transformations - Matrix Algebra, CSIR-NET Mathematical Sciences

4 pages

Change of Basis - Matrix Algebra, CSIR-NET Mathematical Sciences

2 pages

Canonical Forms : Diagonal Forms, Triangular Forms, Jordan Forms - CSIR-NET Mathematical Sciences

5 pages

Inner Product Spaces - Matrix Algebra, CSIR-NET Mathematical Sciences

10 pages

Orthonormal Basis - Matrix Algebra, CSIR-NET Mathematical Sciences

3 pages

Quadratic Forms (Reduction and Classification of Quadratic Forms) - CSIR-NET Mathematical Sciences

13 pages

Vector Algebra

Vector Spaces and Subspaces - Vector Algebra, CSIR-NET Mathematical Sciences

2 pages

Basis and Dimension - Vector Algebra, CSIR-NET Mathematical Sciences

6 pages

Linear Dependence - Vector Algebra, CSIR-NET Mathematical Sciences

4 pages

Algebra of Linear Transformations - Vector Algebra, CSIR-NET Mathematical Sciences

5 pages

Complex Analysis

Algebra of Complex Numbers - Complex Analysis, CSIR-NET Mathematical Sciences

13 pages

Open Mapping Theorem - Complex Analysis, CSIR-NET Mathematical Sciences

2 pages

Power Series - Complex Analysis, CSIR-NET Mathematical Sciences

1 page

Analytic Functions - Complex Analysis, CSIR-NET Mathematical Sciences

3 pages

Cauchy-Riemann Equations - Complex Analysis, CSIR-NET Mathematical Sciences

7 pages

The Complex Plane - Complex Analysis, CSIR-NET Mathematical Sciences

7 pages

Contour Integral, Cauchy’s Theorem, Cauchy’s Integral Formula - CSIR-NET Mathematical Sciences

11 pages

Liouville’s Theorem - Complex Analysis, CSIR-NET Mathematical Sciences

2 pages

Maximum Modulus Principle - Complex Analysis, CSIR-NET Mathematical Sciences

7 pages

Schwarz Lemma - Complex Analysis, CSIR-NET Mathematical Sciences

4 pages

Taylor Series, Laurent Series - Complex Analysis, CSIR-NET Mathematical Sciences

11 pages

Calculus of Residues - Complex Analysis, CSIR-NET Mathematical Sciences

7 pages

Conformal Mappings - Complex Analysis, CSIR-NET Mathematical Sciences

3 pages

Mobius Transformations - Complex Analysis, CSIR-NET Mathematical Sciences

7 pages

Transcendental functions such as exponential, trigonometric and hyperbolic functions (Part - 1)

9 pages

Transcendental functions such as exponential, trigonometric and hyperbolic functions (Part - 2)

15 pages

Transcendental functions such as exponential, trigonometric and hyperbolic functions (Part - 3)

7 pages

Group Theory

Groups, Subgroups, Cyclic Groups and Permutation Groups - CSIR-NET Mathematical Sciences

8 pages

Normal Subgroups,Quotient Groups and Homomorphisms - Group Theory, CSIR-NET Mathematical Sciences

1 page

Sylow theorems - Group Theory, CSIR-NET Mathematical Sciences

5 pages

Homomorphism - Group Theory, CSIR-NET Mathematical Sciences

5 pages

Cayley’s theorem - Group Theory, CSIR-NET Mathematical Sciences

1 page

Class Equations - Group Theory, CSIR-NET Mathematical Sciences

10 pages

Algebra

Pigeonhole Principle - Algebra, CSIR-NET Mathematical Sciences

3 pages

Derangements - Algebra, CSIR-NET Mathematical Sciences

5 pages

Inclusion Exclusion Principle - Algebra, CSIR-NET Mathematical Sciences

8 pages

Fundamental Theorem of Arithmetic - Algebra, CSIR-NET Mathematical Sciences

3 pages

Divisibility in Z - Algebra, CSIR-NET Mathematical Sciences

6 pages

Congruences - Algebra, CSIR-NET Mathematical Sciences

17 pages

Chinese Remainder Theorem - Algebra, CSIR-NET Mathematical Sciences

9 pages

Euler’s function - Algebra, CSIR-NET Mathematical Sciences

5 pages

Primitive roots - Algebra, CSIR-NET Mathematical Sciences

5 pages

Permutations and combinations (Part - 1)- Algebra, CSIR-NET Mathematical Sciences

12 pages

Permutations and combinations (Part - 2)- Algebra, CSIR-NET Mathematical Sciences

12 pages

Field Theory

Finite Fields - Field Theory, CSIR-NET Mathematical Sciences

6 pages

Fields - Field Theory, CSIR-NET Mathematical Sciences

10 pages

Field Extensions and Galois Theory - Field Theory, CSIR-NET Mathematical Sciences

13 pages

Ring Theory

Rings, Ideals, Quotient Rings - Ring Theory, CSIR-NET Mathematical Sciences

4 pages

Prime and Maximal Ideals - Ring Theory, CSIR-NET Mathematical Sciences

7 pages

Unique Factorization Domain - Ring Theory, CSIR-NET Mathematical Sciences

6 pages

Principal Ideal Domain - Ring Theory, CSIR-NET Mathematical Sciences

2 pages

Euclidean Domain - Ring Theory, CSIR-NET Mathematical Sciences

1 page

Polynomial Rings and Irreducibility Criteria - Ring Theory, CSIR-NET Mathematical Sciences

10 pages

Topology

Basis Topology - Topology, CSIR-NET Mathematical Sciences

9 pages

Dense Sets - Topology, CSIR-NET Mathematical Sciences

2 pages

Subspace Topology - Topology, CSIR-NET Mathematical Sciences

1 page

Product Topology - Topology, CSIR-NET Mathematical Sciences

2 pages

Separation Axioms - Topology, CSIR-NET Mathematical Sciences

8 pages

Connectedness and Compactness (Part - 1) - Topology, CSIR-NET Mathematical Sciences

5 pages

Connectedness and Compactness (Part - 2) - Topology, CSIR-NET Mathematical Sciences

6 pages

Ordinary Differential Equations (ODEs)

Existence and Uniqueness of Solutions of Initial Value Problems for First Order ODEs - CSIR-NET Math

10 pages

Singular Solutions of First Order ODEs - 1

6 pages

Singular Solutions of First Order ODEs - 2

5 pages

System of First Order ODEs - 1

8 pages

System of First Order ODEs - 2

12 pages

General Theory of Homogeneous and Non-Homogeneous linear ODEs - CSIR-NET Mathematical Sciences

6 pages

Variation of Parameters - Ordinary Differential Equations, CSIR-NET Mathematical Sciences

6 pages

Sturm-Liouville Boundary Value Problem - CSIR-NET Mathematical Sciences

9 pages

Green’s Function - Ordinary Differential Equations, CSIR-NET Mathematical Sciences

15 pages

Partial Differential Equations (PDEs)

Lagrange and Charpit Methods for Solving First order PDEs - CSIR-NET Mathematical Sciences

5 pages

Cauchy Problem for First Order PDEs - Partial Differential Equations, CSIR-NET Mathematical Sciences

11 pages

Classification of Second Order PDEs - Partial Differential Equations, CSIR-NET Mathematical Sciences

4 pages

General Solution of Higher Order PDEs with Constant Coefficients - CSIR-NET Mathematical Sciences

6 pages

Method of Separation of Variables for Laplace Equation - CSIR-NET Mathematical Sciences

10 pages

Method of Separation of Variables for Heat Equation - CSIR-NET Mathematical Sciences

4 pages

Method of Separation of Variables for Wave Equation - CSIR-NET Mathematical Sciences

1 page

Numerical Analysis

Numerical Solutions of Algebraic Equations - CSIR-NET Mathematical Sciences

4 pages

Rate of Convergence - Numerical Analysis, CSIR-NET Mathematical Sciences

3 pages

Finite Differences - Numerical Analysis, CSIR-NET Mathematical Sciences

6 pages

Solution of Systems of Linear Algebraic Equations Using Gauss-Seidel Method - CSIR-NET Maths

10 pages

Solution of Systems of Linear Algebraic Equations Using Gauss Elimination - CSIR-NET Maths

6 pages

Lagrange and Apline Interpolation - Numerical Analysis, CSIR-NET Mathematical Sciences

8 pages

Numerical Differentiation and Integration - Numerical Analysis, CSIR-NET Mathematical Sciences

10 pages

Numerical Solutions of ODEs using Picard Method - Numerical Analysis, CSIR-NET Mathematical Sciences

2 pages

Numerical Solutions of ODEs using Euler - Numerical Analysis, CSIR-NET Mathematical Sciences

2 pages

Numerical solutions of ODEs using modified Euler method - CSIR-NET Mathematical Sciences

1 page

Numerical Solutions of ODEs using Runge-Kutta Method - CSIR-NET Mathematical Sciences

3 pages

Calculus of Variations

Variation of a functional - Calculus of Variations, CSIR-NET Mathematical Sciences

8 pages

Euler Lagrange Equation - Calculus of Variations, CSIR-NET Mathematical Sciences

4 pages

Necessary and Sufficient Conditions for Extrema - CSIR-NET Mathematical Sciences

6 pages

Variational Methods for Boundary Value Problems in ODE"s and PDE"s - CSIR-NET Mathematical Sciences

12 pages

Linear Integral Equations

Linear Integral Equation of the First and Second Kind of Fredholm and Volterra Type (Part - 1)

5 pages

Linear Integral Equation of the First and Second Kind of Fredholm and Volterra Type (Part - 2)

9 pages

Characteristic Numbers and Eigenfunctions - Linear Integral Equations, CSIR-NET Mathematical Science

4 pages

Classical Mechanics

Generalized Coordinates - Classical Mechanics, CSIR-NET Mathematical Sciences

4 pages

Two-dimensional motion of rigid bodies - Classical Mechanics, CSIR-NET Mathematical Sciences

6 pages

Lagrange’s Equations - Classical Mechanics, CSIR-NET Mathematical Sciences

4 pages

Hamilton’s canonical equations - Classical Mechanics, CSIR-NET Mathematical Sciences

2 pages

Hamilton’s principle - Classical Mechanics, CSIR-NET Mathematical Sciences

3 pages

Principle of least action - Classical Mechanics, CSIR-NET Mathematical Sciences

1 page

Euler’s dynamical equations for the motion of a rigid body about an axis - CSIR-NET Mathematical Sci

7 pages

Theory of small oscillations - Classical Mechanics, CSIR-NET Mathematical Sciences

8 pages

Statistics

Descriptive statistics - Statistics, CSIR-NET Mathematical Sciences

3 pages

Exploratory data analysis:Introduction and Univariate non-graphical EDA

17 pages

Univariate Graphical EDA - Statistics, CSIR-NET Mathematical Sciences

13 pages

Multivariate non-graphical EDA - Statistics, CSIR-NET Mathematical Sciences

5 pages

Multivariate graphical EDA - Statistics, CSIR-NET Mathematical Sciences

4 pages

Probability and probability Distributions

Systematic sampling - 1, CSIR-NET Mathematical Sciences

5 pages

Systematic sampling - 2, CSIR-NET Mathematical Sciences

4 pages

Sample space - Probability and probability Distributions, CSIR-NET Mathematical Sciences

2 pages

Independent events - Probability and probability Distributions, CSIR-NET Mathematical Sciences

4 pages

Discrete probability - Probability and probability Distributions, CSIR-NET Mathematical Sciences

1 page

Univariate and Multivariate distribution functions, CSIR-NET Mathematical Sciences

15 pages

Expectation and moments - Probability and probability Distributions, CSIR-NET Mathematical Sciences

4 pages

Independent random variables, CSIR-NET Mathematical Sciences

1 page

Marginal and conditional distributions, CSIR-NET Mathematical Sciences

1 page

Characteristic functions - Probability and probability Distributions, CSIR-NET Mathematical Sciences

1 page

Probability inequalities (chebyshev, Markov, Jensen), CSIR-NET Mathematical Sciences

4 pages

Modes of convergence - Probability and probability Distributions, CSIR-NET Mathematical Sciences

7 pages

Weak and strong laws of large numbers, CSIR-NET Mathematical Sciences

5 pages

Central Limit theorems (i.i.d. case), CSIR-NET Mathematical Sciences

3 pages

Markov chains with finite and countable state space, CSIR-NET Mathematical Sciences

7 pages

Classification of states, CSIR-NET Mathematical Sciences

5 pages

Limiting behaviour of n-step transition probabilities, CSIR-NET Mathematical Sciences

10 pages

Stationary distribution, CSIR-NET Mathematical Sciences

4 pages

Poisson and birth-and-death processes, CSIR-NET Mathematical Sciences

14 pages

Sampling distributions, CSIR-NET Mathematical Sciences

4 pages

Standard errors , CSIR-NET Mathematical Sciences

1 page

Distribution of order statistics and range, CSIR-NET Mathematical Sciences

2 pages

Methods of estimation, properties of estimators, CSIR-NET Mathematical Sciences

4 pages

Confidence intervals, CSIR-NET Mathematical Sciences

2 pages

Tests of hypotheses: most powerful and uniformly most powerful tests, likelihood ratio tests

1 page

Chi-square test of goodness of fit, CSIR-NET Mathematical Sciences

9 pages

Large sample tests, CSIR-NET Mathematical Sciences

1 page

Rank correlation, CSIR-NET Mathematical Sciences

2 pages

Test for independence, CSIR-NET Mathematical Sciences

3 pages

Elementary Bayesian inference - 1, CSIR-NET Mathematical Sciences

15 pages

Elementary Bayesian inference - 2, CSIR-NET Mathematical Sciences

17 pages

Best linear unbiased estimators, CSIR-NET Mathematical Sciences

2 pages

Tests for linear hypotheses, CSIR-NET Mathematical Sciences

5 pages

Analysis of variance and covariance, CSIR-NET Mathematical Sciences

24 pages

Fixed, random and mixed effects models, CSIR-NET Mathematical Sciences

3 pages

Simple and multiple linear regression, Logistic regression, CSIR-NET Mathematical Sciences

6 pages

Multivariate normal distribution, CSIR-NET Mathematical Sciences

6 pages

Wishart distribution and their properties, CSIR-NET Mathematical Sciences

2 pages

Distribution of quadratic forms, CSIR-NET Mathematical Sciences

6 pages

Partial correlation, CSIR-NET Mathematical Sciences

6 pages

Multiple Correlation, CSIR-NET Mathematical Sciences

2 pages

Principal component analysis and Factor Analysis, CSIR-NET Mathematical Sciences

11 pages

Discriminant Analysis, CSIR-NET Mathematical Sciences

9 pages

Cluster Analysis, CSIR-NET Mathematical Sciences

9 pages

Canonical correlation - 1, CSIR-NET Mathematical Sciences

20 pages

Canonical correlation - 2, CSIR-NET Mathematical Sciences

16 pages

Simple random sampling, CSIR-NET Mathematical Sciences

3 pages

Stratified sampling, CSIR-NET Mathematical Sciences

2 pages

Probability proportional to size sampling - 1, CSIR-NET Mathematical Sciences

8 pages

Probability proportional to size sampling - 2, CSIR-NET Mathematical Sciences

1 page

Multivariate Distributions

40 pages

Random Variables and Probability Distributions

17 pages

Mathematics for IIT JAM, GATE, CSIR NET, UGC NET

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