# JAM 2012 Exam Syllabus - MA (Mathematics)

## Syllabus: Joint Admission Test For M.Sc. 2012

## Mathematics (MA)

**Sequences, Series and Differential Calculus:** Sequences of real numbers.
Convergent sequences and series, absolute and conditional convergence. Rolle’s
Theorem, Mean value theorem. Taylor's theorem. Maxima and minima of functions of
a single variable. Functions of two and three variables. Limit, Continuity,
Partial derivatives, differentiability, maxima and minima.

**Integral Calculus:** Double and triple integrals, Areas, Volumes, and Surface
areas.

**Differential Equations:** Ordinary differential equations of the first order of
the form y'=f(x,y). Linear differential equations of second and higher order
with constant coefficients. Cauchy- Euler equation.

**Vector Calculus:** Gradient, divergence, curl and Laplacian. Green's, Stokes and
Gauss theorems and their applications.

**Group Theory:** Groups, subgroups and normal subgroups, Lagrange's Theorem for
finite groups, group homeomorphisms and basic concepts of quotient groups.

**Linear Algebra:** Vector spaces, Linear dependence of vectors, basis, dimension,
linear transformations and matrix representation with respect to an ordered
basis, rank and inverse of a matrix, determinant, solutions of systems of linear
equations, consistency conditions. Eigen values and eigenvectors.

**Real Analysis:** Open and closed sets, limit points, completeness of R, Uniform
convergence, Power series.

Courtesy: iitb.ac.in