Mathematics Mathematics for IIT JAM, CSIR NET, UGC NET
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Course content
Mathematics for IIT JAM, CSIR NET, UGC NET
Analysis7 subtopics
Set Theory4 docs
- Elementary Set Theory - CSIR-NET Mathematical SciencesReadLength: 13 pages
- Supremum, Infimum - Set Theory, CSIR-NET Mathematical SciencesReadLength: 6 pages
- Finite, Countable and Uncountable Sets - Set Theory, CSIR-NET Mathematical SciencesReadLength: 31 pages
- Real Number System as a Complete Ordered Field and Archimedean Property - CSIR-NET MathematicalReadLength: 8 pages
Sequences and Series5 docs
- Sequences and Their Algebra, Bolzano Weierstrass Theorem - CSIR-NET Mathematical SciencesReadLength: 15 pages
- Series - Sequences and Series, CSIR-NET Mathematical SciencesReadLength: 7 pages
- Convergence Tests - Sequences and Series, CSIR-NET Mathematical SciencesReadLength: 9 pages
- Liminf and Limsup for Bounded Sequences of Real Numbers - CSIR-NET Mathematical SciencesReadLength: 2 pages
- Heine Borel - Sequences and Series, CSIR-NET Mathematical SciencesReadLength: 2 pages
Continuity and Differentiability6 docs
- Continuity and Uniform Continuity - Continuity and Differentiability, CSIR-NET Mathematical SciencesReadLength: 8 pages
- Differentiability - Continuity and Differentiability, CSIR-NET Mathematical SciencesReadLength: 8 pages
- Rolle's Theorem and The Mean Value Theorem - CSIR-NET Mathematical SciencesReadLength: 6 pages
- Sequences and Series Del- CSIR-NET Mathematical ScienceReadLength: 10 pages
- Sequences and Series of Functions and Uniform Convergence (Part -1) - CSIR-NET Mathematical ScienceReadLength: 10 pages
- Sequences and Series of Functions and Uniform Convergence (Part -2) - CSIR-NET Mathematical ScienceReadLength: 10 pages
Integral Calculus2 docs
Real Analysis4 docs
- Monotonic Functions - Real Analysis, CSIR-NET Mathematical SciencesReadLength: 4 pages
- Types of Discontinuity - Real Analysis, CSIR-NET Mathematical SciencesReadLength: 1 pages
- Lebesgue Measure and Lebesgue Integral - Real Analysis, CSIR-NET Mathematical SciencesReadLength: 12 pages
- Functions of Bounded Variation - Real Analysis, CSIR-NET Mathematical SciencesReadLength: 5 pages
Differential Calculus5 docs
- Functions of Several Variables - Differential Calculus, CSIR-NET Mathematical SciencesReadLength: 7 pages
- Directional Derivative - Differential Calculus, CSIR-NET Mathematical SciencesReadLength: 10 pages
- Partial Derivative - Differential Calculus, CSIR-NET Mathematical SciencesReadLength: 11 pages
- Derivative as a Linear Transformation - Differential Calculus, CSIR-NET Mathematical SciencesReadLength: 3 pages
- Inverse and Implicit Function Theorems - Differential Calculus, CSIR-NET Mathematical SciencesReadLength: 4 pages
Linear Functional Analysis6 docs
- Metric Spaces (Part - 1) - Linear Functional Analysis, CSIR-NET Mathematical SciencesReadLength: 7 pages
- Metric Spaces (Part - 2) - Linear Functional Analysis, CSIR-NET Mathematical SciencesReadLength: 8 pages
- Compactness and connectedness (Part -1) - Linear Functional Analysis, CSIR-NET Mathematical SciencesReadLength: 5 pages
- Compactness and Connectedness (Part -2) - Linear Functional Analysis, CSIR-NET Mathematical SciencesReadLength: 6 pages
- Normed linear Spaces - Linear Functional Analysis, CSIR-NET Mathematical SciencesReadLength: 9 pages
- Spaces of Continuous Functions as examples - CSIR-NET Mathematical SciencesReadLength: 8 pages
Linear Algebra2 subtopics
Vector Algebra4 docs
- Vector Spaces and Subspaces - Vector Algebra, CSIR-NET Mathematical SciencesReadLength: 1 pages
- Linear Dependence - Vector Algebra, CSIR-NET Mathematical SciencesReadLength: 4 pages
- Basis and Dimension - Vector Algebra, CSIR-NET Mathematical SciencesReadLength: 6 pages
- Algebra of Linear Transformations - Vector Algebra, CSIR-NET Mathematical SciencesReadLength: 5 pages
Matrix Algebra12 docs
- Algebra of Matrices (Determinant of a Matrix) - Matrix Algebra, CSIR-NET Mathematical SciencesReadLength: 3 pages
- Rank of Matrices - Matrix Algebra, CSIR-NET Mathematical SciencesReadLength: 1 pages
- Solving Linear Equations - Matrix Algebra, CSIR-NET Mathematical SciencesReadLength: 1 pages
- Eigenvalues and Eigenvectors (Part - 1)- Matrix Algebra, CSIR-NET Mathematical ScienceReadLength: 7 pages
- Eigenvalues and Eigenvectors (Part - 2) - Matrix Algebra, CSIR-NET Mathematical SciencesReadLength: 7 pages
- Cayley Hamilton Theorem - Matrix Algebra, CSIR-NET Mathematical SciencesReadLength: 6 pages
- Matrix Representation of Linear Transformations - Matrix Algebra, CSIR-NET Mathematical SciencesReadLength: 4 pages
- Change of Basis - Matrix Algebra, CSIR-NET Mathematical SciencesReadLength: 2 pages
- Canonical Forms : Diagonal Forms, Triangular Forms, Jordan Forms - CSIR-NET Mathematical SciencesReadLength: 5 pages
- Inner Product Spaces - Matrix Algebra, CSIR-NET Mathematical SciencesReadLength: 10 pages
- Orthonormal Basis - Matrix Algebra, CSIR-NET Mathematical SciencesReadLength: 3 pages
- Quadratic Forms (Reduction and Classification of Quadratic Forms) - CSIR-NET Mathematical SciencesReadLength: 13 pages
Complex Analysis17 docs
- Algebra of Complex Numbers - Complex Analysis, CSIR-NET Mathematical SciencesReadLength: 13 pages
- The Complex Plane - Complex Analysis, CSIR-NET Mathematical SciencesReadLength: 7 pages
- Power Series - Complex Analysis, CSIR-NET Mathematical SciencesReadLength: 1 pages
- Analytic Functions - Complex Analysis, CSIR-NET Mathematical SciencesReadLength: 3 pages
- Cauchy-Riemann Equations - Complex Analysis, CSIR-NET Mathematical SciencesReadLength: 7 pages
- Contour Integral, Cauchy’s Theorem, Cauchy’s Integral Formula - CSIR-NET Mathematical SciencesReadLength: 11 pages
- Liouville’s Theorem - Complex Analysis, CSIR-NET Mathematical SciencesReadLength: 2 pages
- Maximum Modulus Principle - Complex Analysis, CSIR-NET Mathematical SciencesReadLength: 7 pages
- Schwarz Lemma - Complex Analysis, CSIR-NET Mathematical SciencesReadLength: 4 pages
- Open Mapping Theorem - Complex Analysis, CSIR-NET Mathematical SciencesReadLength: 2 pages
- Taylor Series, Laurent Series - Complex Analysis, CSIR-NET Mathematical SciencesReadLength: 11 pages
- Calculus of Residues - Complex Analysis, CSIR-NET Mathematical SciencesReadLength: 7 pages
- Conformal Mappings - Complex Analysis, CSIR-NET Mathematical SciencesReadLength: 3 pages
- Mobius Transformations - Complex Analysis, CSIR-NET Mathematical SciencesReadLength: 7 pages
- Transcendental functions such as exponential, trigonometric and hyperbolic functions (Part - 1)ReadLength: 9 pages
- Transcendental functions such as exponential, trigonometric and hyperbolic functions (Part - 2)ReadLength: 15 pages
- Transcendental functions such as exponential, trigonometric and hyperbolic functions (Part - 3)ReadLength: 7 pages
Algebra11 subtopics
Algebra11 docs
- Pigeon-Hole Principle - Algebra, CSIR-NET Mathematical SciencesReadLength: 3 pages
- Inclusion Exclusion Principle - Algebra, CSIR-NET Mathematical SciencesReadLength: 8 pages
- Derangements - Algebra, CSIR-NET Mathematical SciencesReadLength: 5 pages
- Fundamental Theorem of Arithmetic - Algebra, CSIR-NET Mathematical SciencesReadLength: 3 pages
- Divisibility in Z - Algebra, CSIR-NET Mathematical SciencesReadLength: 6 pages
- Congruences - Algebra, CSIR-NET Mathematical SciencesReadLength: 17 pages
- Chinese Remainder Theorem - Algebra, CSIR-NET Mathematical SciencesReadLength: 9 pages
- Euler’s function - Algebra, CSIR-NET Mathematical SciencesReadLength: 5 pages
- Primitive roots - Algebra, CSIR-NET Mathematical SciencesReadLength: 5 pages
- Permutations and combinations (Part - 1)- Algebra, CSIR-NET Mathematical SciencesReadLength: 12 pages
- Permutations and combinations (Part - 2)- Algebra, CSIR-NET Mathematical SciencesReadLength: 12 pages
Group Theory6 docs
- Groups, Subgroups, Cyclic Groups and Permutation Groups - CSIR-NET Mathematical SciencesReadLength: 8 pages
- Normal Subgroups,Quotient Groups and Homomorphisms - Group Theory, CSIR-NET Mathematical SciencesReadLength: 1 pages
- Homomorphism - Group Theory, CSIR-NET Mathematical SciencesReadLength: 5 pages
- Cayley’s theorem - Group Theory, CSIR-NET Mathematical SciencesReadLength: 1 pages
- Class Equations - Group Theory, CSIR-NET Mathematical SciencesReadLength: 10 pages
- Sylow theorems - Group Theory, CSIR-NET Mathematical SciencesReadLength: 5 pages
Ring Theory6 docs
- Rings, Ideals, Quotient Rings - Ring Theory, CSIR-NET Mathematical SciencesReadLength: 4 pages
- Prime and Maximal Ideals - Ring Theory, CSIR-NET Mathematical SciencesReadLength: 7 pages
- Unique Factorization Domain - Ring Theory, CSIR-NET Mathematical SciencesReadLength: 6 pages
- Principal Ideal Domain - Ring Theory, CSIR-NET Mathematical SciencesReadLength: 2 pages
- Euclidean Domain - Ring Theory, CSIR-NET Mathematical SciencesReadLength: 1 pages
- Polynomial Rings and Irreducibility Criteria - Ring Theory, CSIR-NET Mathematical SciencesReadLength: 10 pages
Field Theory3 docs
Topology7 docs
- Basis Topology - Topology, CSIR-NET Mathematical SciencesReadLength: 9 pages
- Dense Sets - Topology, CSIR-NET Mathematical SciencesReadLength: 2 pages
- Subspace Topology - Topology, CSIR-NET Mathematical SciencesReadLength: 1 pages
- Product Topology - Topology, CSIR-NET Mathematical SciencesReadLength: 2 pages
- Separation Axioms - Topology, CSIR-NET Mathematical SciencesReadLength: 8 pages
- Connectedness and Compactness (Part - 1) - Topology, CSIR-NET Mathematical SciencesReadLength: 5 pages
- Connectedness and Compactness (Part - 2) - Topology, CSIR-NET Mathematical SciencesReadLength: 6 pages
Ordinary Differential Equations (ODEs)9 docs
- Existence and Uniqueness of Solutions of Initial Value Problems for First Order ODEs - CSIR-NET MathReadLength: 10 pages
- Singular Solutions of First Order ODEs (Part - 1) - CSIR-NET CSIR-NET Mathematical SciencesReadLength: 6 pages
- Singular Solutions of First Order ODEs (Part - 2) - CSIR-NET CSIR-NET Mathematical SciencesReadLength: 5 pages
- System of First Order ODEs (Part - 1) - CSIR-NET Mathematical SciencesReadLength: 8 pages
- System of First Order ODEs (Part - 2) - CSIR-NET Mathematical SciencesReadLength: 12 pages
- General Theory of Homogenous and Non-Homogeneous linear ODEs - CSIR-NET Mathematical SciencesReadLength: 6 pages
- Variation of Parameters - Ordinary Differential Equations, CSIR-NET Mathematical SciencesReadLength: 6 pages
- Sturm-Liouville Boundary Value Problem - CSIR-NET Mathematical SciencesReadLength: 9 pages
- Green’s Function - Ordinary Differential Equations, CSIR-NET Mathematical SciencesReadLength: 15 pages
Partial Differential Equations (PDEs)7 docs
- Lagrange and Charpit Methods for Solving First order PDEs - CSIR-NET Mathematical SciencesReadLength: 5 pages
- Cauchy Problem for First Order PDEs - Partial Differential Equations, CSIR-NET Mathematical SciencesReadLength: 11 pages
- Classification of Second Order PDEs - Partial Differential Equations, CSIR-NET Mathematical SciencesReadLength: 4 pages
- General Solution of Higher Order PDEs with Constant Coefficients - CSIR-NET Mathematical SciencesReadLength: 6 pages
- Method of Separation of Variables for Laplace Equation - CSIR-NET Mathematical SciencesReadLength: 10 pages
- Method of Separation of Variables for Heat Equation - CSIR-NET Mathematical SciencesReadLength: 4 pages
- Method of Separation of Variables for Wave Equation - CSIR-NET Mathematical SciencesReadLength: 1 pages
Numerical Analysis11 docs
- Numerical Solutions of Algebraic Equations - CSIR-NET Mathematical SciencesReadLength: 4 pages
- Rate of Convergence - Numerical Analysis, CSIR-NET Mathematical SciencesReadLength: 3 pages
- Solution of Systems of Linear Algebraic Equations Using Gauss Elimination - CSIR-NET MathsReadLength: 6 pages
- Solution of Systems of Linear Algebraic Equations Using Gauss-Seidel Method - CSIR-NET MathsReadLength: 10 pages
- Finite Differences - Numerical Analysis, CSIR-NET Mathematical SciencesReadLength: 6 pages
- Lagrange and Apline Interpolation - Numerical Analysis, CSIR-NET Mathematical SciencesReadLength: 8 pages
- Numerical Differentiation and Integration - Numerical Analysis, CSIR-NET Mathematical SciencesReadLength: 10 pages
- Numerical Solutions of ODEs using Picard Method - Numerical Analysis, CSIR-NET Mathematical SciencesReadLength: 2 pages
- Numerical Solutions of ODEs using Euler - Numerical Analysis, CSIR-NET Mathematical SciencesReadLength: 2 pages
- Numerical solutions of ODEs using modified Euler method - CSIR-NET Mathematical SciencesReadLength: 1 pages
- Numerical Solutions of ODEs using Runge-Kutta Method - CSIR-NET Mathematical SciencesReadLength: 3 pages
Calculus of Variations4 docs
- Variation of a functional - Calculus of Variations, CSIR-NET Mathematical SciencesReadLength: 8 pages
- Euler Lagrange Equation - Calculus of Variations, CSIR-NET Mathematical SciencesReadLength: 4 pages
- Necessary and Sufficient Conditions for Extrema - CSIR-NET Mathematical SciencesReadLength: 6 pages
- Variational Methods for Boundary Value Problems in ODE"s and PDE"s - CSIR-NET Mathematical SciencesReadLength: 12 pages
Linear Integral Equations3 docs
- Linear Integral Equation of the First and Second Kind of Fredholm and Volterra Type (Part - 1)ReadLength: 5 pages
- Linear Integral Equation of the First and Second Kind of Fredholm and Volterra Type (Part - 2)ReadLength: 9 pages
- Characteristic Numbers and Eigenfunctions - Linear Integral Equations, CSIR-NET Mathematical ScienceReadLength: 4 pages
Classical Mechanics8 docs
- Generalized Coordinates - Classical Mechanics, CSIR-NET Mathematical SciencesReadLength: 4 pages
- Lagrange’s Equations - Classical Mechanics, CSIR-NET Mathematical SciencesReadLength: 4 pages
- Hamilton’s canonical equations - Classical Mechanics, CSIR-NET Mathematical SciencesReadLength: 2 pages
- Hamilton’s principle - Classical Mechanics, CSIR-NET Mathematical SciencesReadLength: 3 pages
- Principle of least action - Classical Mechanics, CSIR-NET Mathematical SciencesReadLength: 1 pages
- Two-dimensional motion of rigid bodies - Classical Mechanics, CSIR-NET Mathematical SciencesReadLength: 5 pages
- Euler’s dynamical equations for the motion of a rigid body about an axis - CSIR-NET Mathematical SciReadLength: 7 pages
- Theory of small oscillations - Classical Mechanics, CSIR-NET Mathematical SciencesReadLength: 8 pages
Statistics5 docs
- Descriptive statistics - Statistics, CSIR-NET Mathematical SciencesReadLength: 3 pages
- Exploratory data analysis:Introduction and Univariate non-graphical EDAReadLength: 17 pages
- Univariate Graphical EDA - Statistics, CSIR-NET Mathematical SciencesReadLength: 13 pages
- Multivariate graphical EDA - Statistics, CSIR-NET Mathematical SciencesReadLength: 4 pages
- Multivariate non-graphical EDA - Statistics, CSIR-NET Mathematical SciencesReadLength: 5 pages
Probability and probability Distributions52 docs
- Sample space - Probability and probability Distributions, CSIR-NET Mathematical SciencesReadLength: 2 pages
- Discrete probability - Probability and probability Distributions, CSIR-NET Mathematical SciencesReadLength: 1 pages
- Independent events - Probability and probability Distributions, CSIR-NET Mathematical SciencesReadLength: 4 pages
- Univariate and Multivariate Random variables - (Part - 1), CSIR-NET Mathematical SciencesReadLength: 6 pages
- Univariate and Multivariate Random variables - (Part - 2), CSIR-NET Mathematical SciencesReadLength: 2 pages
- Univariate and Multivariate distribution functions, CSIR-NET Mathematical SciencesReadLength: 15 pages
- Expectation and moments - Probability and probability Distributions, CSIR-NET Mathematical SciencesReadLength: 4 pages
- Independent random variables, CSIR-NET Mathematical SciencesReadLength: 1 pages
- Marginal and conditional distributions, CSIR-NET Mathematical SciencesReadLength: 1 pages
- Characteristic functions - Probability and probability Distributions, CSIR-NET Mathematical SciencesReadLength: 1 pages
- Probability inequalities (chebyshev, Markov, Jensen), CSIR-NET Mathematical SciencesReadLength: 4 pages
- Modes of convergence - Probability and probability Distributions, CSIR-NET Mathematical SciencesReadLength: 7 pages
- Weak and strong laws of large numbers, CSIR-NET Mathematical SciencesReadLength: 5 pages
- Central Limit theorems (i.i.d. case), CSIR-NET Mathematical SciencesReadLength: 3 pages
- Markov chains with finite and countable state space, CSIR-NET Mathematical SciencesReadLength: 7 pages
- Classification of states, CSIR-NET Mathematical SciencesReadLength: 5 pages
- Limiting behaviour of n-step transition probabilities, CSIR-NET Mathematical SciencesReadLength: 10 pages
- Stationary distribution, CSIR-NET Mathematical SciencesReadLength: 4 pages
- Poisson and birth-and-death processes, CSIR-NET Mathematical SciencesReadLength: 14 pages
- Sampling distributions, CSIR-NET Mathematical SciencesReadLength: 4 pages
- Standard errors , CSIR-NET Mathematical SciencesReadLength: 1 pages
- Distribution of order statistics and range, CSIR-NET Mathematical SciencesReadLength: 2 pages
- Methods of estimation, properties of estimators, CSIR-NET Mathematical SciencesReadLength: 4 pages
- Confidence intervals, CSIR-NET Mathematical SciencesReadLength: 2 pages
- Tests of hypotheses: most powerful and uniformly most powerful tests, likelihood ratio testsReadLength: 1 pages
- Chi-square test of goodness of fit, CSIR-NET Mathematical SciencesReadLength: 9 pages
- Large sample tests, CSIR-NET Mathematical SciencesReadLength: 1 pages
- Rank correlation, CSIR-NET Mathematical SciencesReadLength: 2 pages
- Test for independence, CSIR-NET Mathematical SciencesReadLength: 3 pages
- Elementary Bayesian inference (Part -1), CSIR-NET Mathematical SciencesReadLength: 15 pages
- Elementary Bayesian inference (Part -2), CSIR-NET Mathematical SciencesReadLength: 17 pages
- Best linear unbiased estimators, CSIR-NET Mathematical SciencesReadLength: 2 pages
- Tests for linear hypotheses, CSIR-NET Mathematical SciencesReadLength: 5 pages
- Analysis of variance and covariance, CSIR-NET Mathematical SciencesReadLength: 24 pages
- Fixed, random and mixed effects models, CSIR-NET Mathematical SciencesReadLength: 3 pages
- Simple and multiple linear regression, Logistic regression, CSIR-NET Mathematical SciencesReadLength: 6 pages
- Multivariate normal distribution, CSIR-NET Mathematical SciencesReadLength: 6 pages
- Wishart distribution and their properties, CSIR-NET Mathematical SciencesReadLength: 2 pages
- Distribution of quadratic forms, CSIR-NET Mathematical SciencesReadLength: 6 pages
- Partial correlation, CSIR-NET Mathematical SciencesReadLength: 6 pages
- Multiple Correlation, CSIR-NET Mathematical SciencesReadLength: 2 pages
- Principal component analysis and Factor Analysis, CSIR-NET Mathematical SciencesReadLength: 11 pages
- Discriminant Analysis, CSIR-NET Mathematical SciencesReadLength: 9 pages
- Cluster Analysis, CSIR-NET Mathematical SciencesReadLength: 9 pages
- Canonical correlation (Part - 1), CSIR-NET Mathematical SciencesReadLength: 20 pages
- Canonical correlation (Part - 2), CSIR-NET Mathematical SciencesReadLength: 16 pages
- Simple random sampling, CSIR-NET Mathematical SciencesReadLength: 3 pages
- Stratified sampling, CSIR-NET Mathematical SciencesReadLength: 2 pages
- Systematic sampling (Part - 1), CSIR-NET Mathematical SciencesReadLength: 5 pages
- Systematic sampling (Part - 2), CSIR-NET Mathematical SciencesReadLength: 4 pages
- Probability proportional to size sampling (Part - 1), CSIR-NET Mathematical SciencesReadLength: 8 pages
- Probability proportional to size sampling (Part - 2), CSIR-NET Mathematical SciencesReadLength: 1 pages
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