IIT JAM Mathematics (MA) Exam Syllabus 2015/ IIT M.SC+Ph.D (Mathematics) Admission Entrance Test 2015
Sequence & Serial of Real Number : Sequence & serial of real number, Convergent & Divergent, Sequence, bounded & monotone sequence, Convergence criteria for sequence of real number, Cauchy Sequence, absolute & conditional convergence, test of convergence for series of positive terms comparison test, ratio test, root test, Leibnitz test for test of alternative series.
Functions of One Variable : Limit, Continuity, differentiation, Rolle's Theorem, Mean Value Theorem, Taylor's Theorem, Maxima & Minima.
JAM 2015 Mathematics Cut Off Marks
Function of Two real variable : Limit, Continuity, partial derivative, differentiability, maxima & minima, Method of Lagrange multiplier, Homogeneous functions including Euler Theorem.
Integral Calculus : Integration as the Inverse Process of differentiation, definite integral & their properties, Fundamental theorem of Integral Calculus. Double & triple integral, change of order of integration. Calculating Surface area & volume using double integrals & applications, Calculating volume using triple integral & applications.
JAM Mathematics 2015 Pattern/Written Test Syllabus
Differential Equations : Ordinary Differential Equation of the first order of the form y=f(x,y). Bernoulli's Equation, exact differential equation, integrating factor, Orthogonal trajectories, Homogeneous Differential Equation-saparable solutions, Linear Differential equation of second & higher order with constant coefficient, methods of variation of parameters. Cauchy-Euler Equation.
Vector Calculus : Scalar & vectors fields, gradient divergence, curl & laplacian, Scalar line integral Green Strokes & Gauss Theorem & their applications.
IIT JAM 2015 Seats (Category Wise)
Group Theory : Groups, subgroups, Abelian Groups, non Abelian Groups, Cyclic groups, permutation groups, Normal Subgroups, Lagrange's Theorem of finite groups, group homomorphisms & basic concept of quotient groups (only group theory).
Linear Algebra : Vector spaces, Linear dependence of vectors, basis, dimensions, linear transformations, matrix representation with respect to an ordered basis, Range space & null space, rank nullity theorem, Rank & Inverse of a matrix, determinant, solutions of system of linear equation, consistency conditions. Eigenvalues & Eigenvectors. Cayley-Hamilton Theorem, Symmetric, Skew Symmetric, Hermitian, Skew-Hermitian, Orthogonal & Unitary Matrices.
IIT M.SC (Mathematics) Admission Entrance Test 2015
Real Analysis : Interior Points, limit points, open sets, closed sets, compact sets, completeness of R, Power Series (of Real variables) including Taylor's & Maclaurin's, Domain of convergence, team wise differentiation & integration of power series.
Check - JAM 2015 Paper Pattern
Sequence & Serial of Real Number : Sequence & serial of real number, Convergent & Divergent, Sequence, bounded & monotone sequence, Convergence criteria for sequence of real number, Cauchy Sequence, absolute & conditional convergence, test of convergence for series of positive terms comparison test, ratio test, root test, Leibnitz test for test of alternative series.
Functions of One Variable : Limit, Continuity, differentiation, Rolle's Theorem, Mean Value Theorem, Taylor's Theorem, Maxima & Minima.
JAM 2015 Mathematics Cut Off Marks
Function of Two real variable : Limit, Continuity, partial derivative, differentiability, maxima & minima, Method of Lagrange multiplier, Homogeneous functions including Euler Theorem.
JAM Mathematics 2015 Pattern/Written Test Syllabus
Differential Equations : Ordinary Differential Equation of the first order of the form y=f(x,y). Bernoulli's Equation, exact differential equation, integrating factor, Orthogonal trajectories, Homogeneous Differential Equation-saparable solutions, Linear Differential equation of second & higher order with constant coefficient, methods of variation of parameters. Cauchy-Euler Equation.
Vector Calculus : Scalar & vectors fields, gradient divergence, curl & laplacian, Scalar line integral Green Strokes & Gauss Theorem & their applications.
IIT JAM 2015 Seats (Category Wise)
Group Theory : Groups, subgroups, Abelian Groups, non Abelian Groups, Cyclic groups, permutation groups, Normal Subgroups, Lagrange's Theorem of finite groups, group homomorphisms & basic concept of quotient groups (only group theory).
Linear Algebra : Vector spaces, Linear dependence of vectors, basis, dimensions, linear transformations, matrix representation with respect to an ordered basis, Range space & null space, rank nullity theorem, Rank & Inverse of a matrix, determinant, solutions of system of linear equation, consistency conditions. Eigenvalues & Eigenvectors. Cayley-Hamilton Theorem, Symmetric, Skew Symmetric, Hermitian, Skew-Hermitian, Orthogonal & Unitary Matrices.
IIT M.SC (Mathematics) Admission Entrance Test 2015
Real Analysis : Interior Points, limit points, open sets, closed sets, compact sets, completeness of R, Power Series (of Real variables) including Taylor's & Maclaurin's, Domain of convergence, team wise differentiation & integration of power series.
Check - JAM 2015 Paper Pattern
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