Can you give me syllabus for Mathematics Subject of Maharashtra State Eligibility Test for Lectureship examination ?

Here I am giving you syllabus for Mathematics Subject of Maharashtra State Eligibility Test for Lectureship examination in PDF file attached with it so you can get it easily.

1. Basic Concepts of Real and Complex Analysis : Sequences and series, Continuity, Uniform
continuity, Differentiabilty, Mean Value Theorem, Sequences and series of functions, Uniform
convergence, Riemann integral - definition and simple properties. Algebra of complex numbers,
Analytic functions, Cauchy’s Theorem and integral formula, Power series, Taylor’s and Laurent’s
series, Residues, Contour integration.

2. Basic Concepts of Linear Algebra : Space of n-vectors, Linear dependence, Basis, Linear
transformation, Algebra of matrices, Rank of a matrix, Determinants, Linear equations, Quadratic
forms, Characteristic roots and vectors.

3. Basic Concepts of Probability : Sample space, Discrete probability, Simple theorems on
probability, Independence of events, Bayes Theorem, Discrete and continuous random variables,
Binomial, Poisson and Normal distributions; Expectation and moments, Independence of random
variables, Chebyshev’s inequality.

4. Linear Programming Basic Concepts : Convex sets, Linear Programming Problem (LPP).
Examples of LPP. Hyperplane, open and closed Half-spaces. Feasible, basic feasible and
optimal solutions. Extreme point and graphical method.

5. Real Analysis : Finite, countable and uncountable sets, Bounded and unbounded sets,
Archimedean property, ordered field, completeness of R, Extended real number system, limsup
and liminf of a sequence, the epsilon-delta definition of continuty and convergence, the algebra
of continuous functions, monotonic functions, types of discontinuties, infinite limits and limits
at infinity, functions of bounded variation. elements of metric spaces.

6. Complex Analysis : Riemann Sphere and Stereographic projection. Lines, circles, crossratio.
Mobius transformations, Analytic functions, Cauchy-Riemann equations, line integrals, Cauchy’s
theorem, Morera’s theorem, Liouville’s theorem, integral formula, zero-sets of analytic functions,
exponential, sine and cosine functions, Power siries representation, Classification of singularities,
Conformal mapping.

7. Algebra : Group, subgroups, Normal subgroups, Quotient Groups, Homomorphisms, Cyclic
Groups, Permutation Groups, Cayley’s Theorm, Rings, Ideals, Integral Domains, Fields,
Polynomial Rings.

8. Linear Algebra : Vector spaces, subspaces, quotient spaces, Linear indepenence, Bases,
Dimension. The algebra of linear Transformations, kernal, range, isomorphism, Matrix
Representation of a linear transormation, change of bases, Linear functionals, dual space,
projection, determinant function, eigenvalues and eigen vectorsCayley-Hamilton
Theorem,Invariant Sub-spaces, Canonical Forms : diagonal form, Triangular form, Jordan
Form. Inner product spaces.

Attached Files

University of Pune SLET mathematics syllabus.pdf (39.2 KB, 129 views)