IIT JAM Mathematics Syllabus:The syllabus for the IIT JAM Mathematics exam is divided into various topics. Below is the detailed topic-wise syllabus along with the marks weightage:
1. Mathematical Statistics:- Estimation: Unbiasedness, consistency, efficiency, sufficiency, method of moments, maximum likelihood estimation.
- Testing of Hypotheses: Neyman-Pearson lemma, likelihood ratio tests, chi-square tests.
- Confidence Intervals.
- Analysis of Variance.
- Regression Analysis: Linear regression, Least squares estimation, multiple regression, analysis of residuals.
- Sampling Distributions: Chi-square, t, F distributions.
- Large Sample Theory: Consistency, efficiency, Central Limit Theorem.
- Multivariate Normal Distribution.
- Stochastic Processes: Poisson process, renewal theory, Markov chains.
Marks Weightage:- Estimation: 3-4 marks
- Testing of Hypotheses: 3-4 marks
- Confidence Intervals: 2-3 marks
- Analysis of Variance: 2-3 marks
- Regression Analysis: 3-4 marks
- Sampling Distributions: 2-3 marks
- Large Sample Theory: 2-3 marks
- Multivariate Normal Distribution: 2-3 marks
- Stochastic Processes: 3-4 marks
2. Calculus:- Real Numbers.
- Sequences and Series: Convergence, limits, tests for convergence, power series.
- Functions of One Variable: Continuity, differentiability, mean value theorem, Taylor's theorem, maxima and minima.
- Functions of Two Real Variables: Limits, continuity, partial derivatives, directional derivatives, maxima and minima.
- Integral Calculus: Riemann integration, improper integrals.
- Multiple Integrals: Double and triple integrals, change of variables, surface and volume integrals.
- Vector Calculus: Scalar and vector fields, line integrals, surface integrals, divergence and curl, Green's theorem, Stokes' theorem, Gauss' theorem.
Marks Weightage:- Real Numbers: 1-2 marks
- Sequences and Series: 2-3 marks
- Functions of One Variable: 2-3 marks
- Functions of Two Real Variables: 2-3 marks
- Integral Calculus: 2-3 marks
- Multiple Integrals: 3-4 marks
- Vector Calculus: 3-4 marks
3. Linear Algebra:- Vector Spaces: Linear dependence, basis, dimension, linear transformations, rank and nullity.
- Matrices: Rank, inverse, eigenvalues and eigenvectors, diagonalization.
- Determinants: Properties, cofactor expansion, eigenvalues of matrices.
- Systems of Linear Equations: Consistency, rank, inverse, Gauss-Jordan method, solution of homogeneous and non-homogeneous systems.
- Inner Product Spaces: Inner product, norm, orthogonality, Gram-Schmidt process.
- Eigenvalues and Eigenvectors: Cayley-Hamilton theorem, diagonalization, similarity transformation.
Marks Weightage:- Vector Spaces: 3-4 marks
- Matrices: 3-4 marks
- Determinants: 2-3 marks
- Systems of Linear Equations: 2-3 marks
- Inner Product Spaces: 2-3 marks
- Eigenvalues and Eigenvectors: 3-4 marks
4. Real Analysis:- Sequences and Series of Real Numbers: Convergence, limits, Cauchy sequences, tests for convergence.
- Continuity: Continuous functions, intermediate value theorem, uniform continuity.
- Differentiation: Derivatives, mean value theorem, Taylor's theorem, L'Hôpital's rule, maxima and minima.
- Riemann Integration: Riemann sums, definite and indefinite integrals, fundamental theorem of calculus.
- Metric Spaces: Open and closed sets, completeness, compactness, connectedness.
Marks Weightage:- Sequences and Series of Real Numbers: 2-3 marks
- Continuity: 2-3 marks
- Differentiation: 3-4 marks
- Riemann Integration: 2-3 marks
- Metric Spaces: 2-3 marks
5. Complex Analysis:- Analytic Functions: Complex numbers, complex plane, complex functions, Cauchy-Riemann equations, harmonic functions.
- Contour Integration: Line integrals, Cauchy's theorem, Cauchy's integral formula, Liouville's theorem, maximum modulus principle.
- Taylor and Laurent Series: Convergence, singularities, residues, residue theorem, contour integration.
- Conformal Mappings: Möbius transformations, bilinear transformations.
Marks Weightage:- Analytic Functions: 2-3 marks
- Contour Integration: 3-4 marks
- Taylor and Laurent Series: 2-3 marks
- Conformal Mappings: 2-3 marks
6. Ordinary Differential Equations:- First Order Differential Equations: Existence and uniqueness, separable equations, linear first-order equations, exact equations, integrating factors.
- Second Order Linear Differential Equations: Homogeneous and non-homogeneous equations, solutions using power series, method of Frobenius.
- Higher Order Linear Differential Equations: Homogeneous and non-homogeneous equations, solutions using power series, method of Frobenius.
- Systems of Linear Differential Equations: Homogeneous and non-homogeneous systems, solutions using matrix methods.
Marks Weightage:- First Order Differential Equations: 2-3 marks
- Second Order Linear Differential Equations: 3-4 marks
- Higher Order Linear Differential Equations: 2-3 marks
- Systems of Linear Differential Equations: 2-3 marks
7. Partial Differential Equations:- Classification of Second Order Partial Differential Equations: Linear and quasi-linear equations, method of characteristics.
- Solutions of First Order Linear and Quasi-Linear Partial Differential Equations: Method of characteristics, Cauchy problem.
- Second Order Linear Homogeneous Equations: Classification, separation of variables, Fourier series solutions.
- Higher Order Linear Homogeneous Equations: Classification, separation of variables, Fourier series solutions.
Marks Weightage:- Classification of Second Order Partial Differential Equations: 2-3 marks
- Solutions of First Order Linear and Quasi-Linear Partial Differential Equations: 2-3 marks
- Second Order Linear Homogeneous Equations: 3-4 marks
- Higher Order Linear Homogeneous Equations: 2-3 marks
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This course is helpful for the following exams: IIT JAM, Mathematics