MSc in Applied Mathematics



MSc Applied Mathematics is a two year (four semester) academic programme.



Minimum Eligibility

12 years of schooling + a 3 or 4 year Bachelor’s degree (with Mathematics as a subject for at least two years) from an institution recognized by the government of any of the SAARC countries, with the following minimum eligibility marks criteria:

 

  1. For candidates from the annual system: 55% and above

  2. For candidates from the semester system (percentage): 60% and above

  3. For candidates from the GPA semester system, the formula for determining percentage is as follows:

        CGPA obtained X 100 / Maximum GPA obtainable.

    Such candidates are required to have a minimum of 65% marks or above.


Format of the Entrance Test Paper

The duration of the Entrance Test will be 3 hours and the question paper will consist of 100 multiple choice questions in two parts.

 

PART A : will have 40 questions on Basic Mathematics.

PART B : will have 60 questions on Undergraduate Level Mathematics.


Calculators will not be allowed. However, Log Tables may be used.


The combined syllabus for both Part A and Part B is as follows:

Calculus and Analysis:Limit, continuity, uniform continuity and differentiability; Bolzano Weierstrass theorem; mean value theorems; tangents and normal; maxima and minima; theorems of integral calculus; sequences and series of functions; uniform convergence; power series; Riemann sums; Riemann integration; definite and improper integrals; partial derivatives and Leibnitz theorem; total derivatives; Fourier series; functions of several variables; multiple integrals; line; surface and volume integrals; theorems of Green; Stokes and Gauss; curl; divergence and gradient of vectors.

 

Algebra: Basic theory of matrices and determinants; groups and their elementary properties; subgroups, normal subgroups, cyclic groups, permutation groups; Lagrange's theorem; quotient groups; homomorphism of groups; isomorphism and correspondence theorems; rings; integral domains and fields; ring homomorphism and ideals; vector space, vector subspace, linear independence of vectors, basis and dimension of a vector space.

 

Differential equations:General and particular solutions of ordinary differential equations (ODEs); formation of ODE; order, degree and classification of ODEs; integrating factor and linear equations; first order and higher degree linear differential equations with constant coefficients; variation of parameter; equation reducible to linear form; linear and quasi-linear first order partial differential equations (PDEs); Lagrange and Charpits methods for first order PDE; general solutions of higher order PDEs with constant coefficients.

 

Numerical Analysis: Computer arithmetic; machine computation; bisection, secant; Newton-Raphson and fixed point iteration methods for algebraic and transcendental equations; systems of linear equations: Gauss elimination, LU decomposition, Gauss Jacobi and Gauss Siedal methods, condition number; Finite difference operators; Newton and Lagrange interpolation; least square approximation; numerical differentiation; Trapezoidal and Simpsons integration methods.

 

Probability and Statistics:Mean, median, mode and standard deviation; conditional probability; independent events; total probability and Baye’s theorem; random variables; expectation, moments generating functions; density and distribution functions, conditional expectation.


Linear Programming: Linear programming problem and its formulation; graphical method, simplex method, artificial starting solution, sensitivity analysis, duality and post-optimality analysis.



Negative Marks for Wrong Answers

If the answer given to any of the Multiple Choice Questions is wrong, ¼ of the marks assigned to that question will be deducted.



MSc Applied Mathematics Entrance Test Paper for the year 2015.

 

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