__IIT JAM Mathematics (MA) Exam Syllabus 2015/ IIT M.SC+Ph.D (Mathematics) Admission Entrance Test 2015__**: 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.**

__Sequence & Serial of Real Number__**: Limit, Continuity, differentiation, Rolle's Theorem, Mean Value Theorem, Taylor's Theorem, Maxima & Minima.**

__Functions of One Variable__

__JAM 2015 Mathematics Cut Off Marks__**: Limit, Continuity, partial derivative, differentiability, maxima & minima, Method of Lagrange multiplier, Homogeneous functions including Euler Theorem.**

__Function of Two real variable__**: 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.**

__Integral Calculus__

__JAM Mathematics 2015 Pattern/Written Test Syllabus__**: 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.**

__Differential Equations__**: Scalar & vectors fields, gradient divergence, curl & laplacian, Scalar line integral Green Strokes & Gauss Theorem & their applications.**

__Vector Calculus__

__IIT JAM 2015 Seats (Category Wise)__**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).**

__Group Theory :__**: 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.**

__Linear Algebra__

__IIT M.SC (Mathematics) Admission Entrance Test 2015__**: 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.**

__Real Analysis__Check - JAM 2015 Paper Pattern

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