Integrated Ph d in Maths Preparation Tips

Can you tell me how to prepare for Entrance Test for Integrated Ph d in Maths as I need to prepare for the same?

[Arun Vats]

For admission to Integrated Ph.D. in Mathematics program one has to clear JAM (Joint Admission Test for Masters) as JAM qualified candidates are provided admission only.

Integrated Ph d in Maths Preparation Tips

Try and solve as many past year question papers as you can. It will give you a close into the kind of questions which are generally asked.

Solve mock test papers available online as it will help you strategies your time management techniques.

Refer IIT JAM books by various authors.

Make short notes to help in last minute revision.

Devote more time towards revising topics which have more weightage in comparison to others.

Never to start a new topic at the last minute of preparation, instead revise the topics you have already completed.

Most importantly keep yourself calm and don't panic.


IIT JAM 2015 Mathematics Syllabus

Sequences, Series and Differential Calculus : Sequences and Series of real numbers : Sequences and series of real numbers. Convergent and divergent sequences, bounded and monotone sequences, Convergence criteria for sequences of real numbers, Cauchy sequences, absolute and conditional convergence; Tests of convergence for series of positive terms – comparison test, ratio test, root test, Leibnitz test for convergence of alternating series.

Functions of one variable : mit, continuity, differentiation, Rolle’s Theorem, Mean value theorem. Taylor’s theorem. Maxima and minima.


Functions of two real variable : Limit, continuity, partial derivatives, differentiability, maxima and minima. Method of Lagrange multipliers, Homogeneous functions including Euler’s theorem.

Integral Calculus : Integration as the inverse process of differe ntiation, definite integrals and their properties, Fundamental theorem of integral calculus. Double and triple integrals, change of order of integration. Calculating surface areas and volumes using double integrals and pplications. Calculating volumes using triple integrals and applications.

Differential Equations : Ordinary differential equations of the first order of the form y’=f(x,y). Bernoulli’s equation, exact differential equations, integrating factor, Orthogonal trajectories, Homogeneous differential equations – separable solutions, Linear differential equations of second and higher order with constant coefficients, method of variation of parameters. Cauchy – Euler equation

Vector Calculus : Scalar and vector fields, gradient, divergence, curl and Lapla cian. Scalar line integrals and vector line integrals, scalar surface integrals and vector surface integrals, Green’s, Stokes and Gauss theorems and their applications.

Group Theory : Groups, subgroups, Abelian groups, non – abelian groups, cyclic groups, per mutation groups; Normal subgroups, Lagrange’s Theorem for finite groups, group homomorphisms and basic concepts of quotient groups ( only group theory ).


Linear Algebra : Vector spaces, Linear dependence of vectors, basis, dimension, linear transformations, matrix representation with respect to an ordered basis, Range space and null space, rank – nullity theorem; Rank and inverse of a matrix, determinant, solutions of systems of linear equations, consistency conditions. Eigenvalues and eigenvectors. Cayley – Hami lton theorem. Symmetric, skew – symmetric, hermitian, skew – hermitian, orthogonal and unitary matrices.

Real Analysis : Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets; completeness of R, Power series ( of real variable ) including Taylor’s and Maclaurin’s, domain of convergence, term – wise differentiation and integration of power series.