Organisation : Indian Institute Of Technology
Exam Name : Joint Admission Test JAM
Announcement : Joint Admission Test JAM Mathematical Statistics (MS) Syllabus
Website : https://jam.iitg.ac.in/
Joint Admission Test JAM Syllabus
JAM 2023 is a Computer Based Test (CBT) to be conducted in SEVEN different subjects: Biotechnology (BT), Chemistry (CY), Economics (EN), Geology (GG), Mathematical Statistics (MS), Mathematics (MA), Physics (PH).
Related / Similar Syllabus : GATE Humanities & Social Sciences (XH) Syllabus 2023
JAM Mathematical Statistics (MS) Syllabus
Sequences and Series of real numbers:
** Sequences of real numbers, their convergence, and limits. Cauchy sequences and their convergence. Monotonic sequences and their limits. Limits of standard sequences. Infinite series and its convergence, and divergence.
** Convergence of series with non-negative terms. Tests for convergence and divergence of a series. Comparison test, limit comparison test, D’Alembert’s ratio test, Cauchy’s root test, Cauchy’s condensation test and integral test.
** Absolute convergence of series. Leibnitz’s test for the convergence of alternating series. Conditional convergence. Convergence of power series and radius of convergence.
Differential Calculus of one and two real variables:
** Limits of functions of one real variable. Continuity anddifferentiability of functions of one real variable. Properties of continuous and differentiable functions of one real variable. Rolle’s theorem and Lagrange’s mean value theorems. Higher order derivatives, Lebnitz’s rule and its applications. Taylor’s theorem with Lagrange’s and Cauchy’s form of remainders. Taylor’s and
** Maclaurin’s series of standard functions. Indeterminate forms and L’ Hospital’s rule. Maxima and minima of functions of one real variable, critical points, local maxima and minima, global maxima and minima, and point of inflection. Limits of functions of two real variables.
** Continuity and differentiability of functions of two real variables. Properties of continuous and differentiable functions of two real variables. Partial differentiation and total differentiation. Lebnitz’s rule for successive differentiation. Maxima and minima of functions of two real variables. Critical points, Hessian matrix, and saddle points. Constrained optimization techniques (with Lagrange multiplier).
** Fundamental theorems of integral calculus (single integral). Lebnitz’s rule and its applications. Differentiation under integral sign. Improper integrals.
** Beta and Gamma integrals: properties and relationship between them. Double integrals. Change of order of integration. Transformation of variables. Applications of definite integrals. Arc lengths, areas and volumes
Matrices and Determinants:
** Vector spaces with real field. Subspaces and sum of subspaces. Span of a set. Linear dependence and independence.
** Dimension and basis. Algebra of matrices. Standard matrices (Symmetric and Skew Symmetric matrices, Hermitian and Skew Hermitian matrices, Orthogonal and Unitary matrices, Idempotent and Nilpotent matrices).
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