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## Sunday, April 17, 2011

### Thapar University Syllabus Entrance Exam MSc Mathematics & Computing

MSc PROGRAMMES

Syllabus for MSc (Mathematics and Computing) Entrance Examination
Paper will consists of 75 objective type questions. Each question will carry 1 mark and 1/4th mark will be deducted for wrong/blank answers.

Syllabus
Algebra: Set theory, Relations, Mapping and its applications, Permutations and combinations, Types of matrices, Rank and inverse of a matrix, Linear independence and linear dependence, Solution of system of linear equations, Eigen values and Eigen vectors of a matrix, Cayley Hamilton theorem.
Calculus: Limits, Continuity and Differentiability, Rolle’s and Mean value theorems, Successive differentiation, Partial differentiation, Maxima and Minima of function of one and two variables, Maclaurin’s and Taylor’s theorem for functions of one and two variables, Definite integral and its applications, Beta and gamma function, Double integral and its applications, Laplace and inverse Laplace transform and their properties, Convolution theorem.
Differential Equation: Ordinary differential equations of first order and their solutions, Linear differential equations of higher order with constant coefficients, Classification of partial differential equations, Partial differential equations of first order, Lagrange’s solution, Charpit’s method.
Analysis: Riemann integral, Integrability of continuous and monotonic functions, Mean value theorems of integral calculus, Infinite series and their convergence, Demoivre’s theorem and its applications, Functions of complex variables, Analytic function, C-R equations.
Abstract Algebra: Groups, Subgroups and their properties, Lagrange’s theorem, Rings, Subrings, Integral domain and Field, Vector spaces, Subspaces and their properties, Inner product spaces, Orthogonal vectors.
Numerical Analysis: Solution of non linear equations using iterative methods, Interpolation for equally and unequally spaced data, Trapezoidal and Simpson’s rules for integration.
Statistics, Probability and Linear Programming: Measures of central tendency, Dispersion, Skewness and kurtosis, Correlation and regression, Basic concepts of probability, Conditional probability, Baye’s theorem, Discrete and continuous distributions ( Binomial , Poisson and Normal), Fundamentals of linear programming problems, Graphical solution, Simplex method and its variants.
Computing Fundamentals: Organization of a computer, Central processing unit(CPU), Input/Output devices, Computer memory, Memory organization, Back-up devices, Representation of character, integers and fractions, Binary and hexadecimal representation, Binary arithmetic: addition, subtraction, division and multiplication, Floating point representation of numbers, Normalized floating point representation.

For details visit: http://www.thapar.edu/