Academics

Course Outline

Mathematics-I ( 07B11MA101 )

Partial differentiation., Taylors series, Maxima and minima, Jacobians, Double integrals, Equations to a line, plane, curve and surfaces, Line and surface integrals, Gradient, divergence and curl. Normal and tangent to a surface, Gauss and Stokes theorems, Differential Equations with constant coefficients, Laplace Transform, Algebra of matrices, Determinants, Gauss elimination method, Rank, Eigenvalues and vectors, Quadratic forms.

Mathematics -II ( 07B21MA102 )

Second order linear differential equations, Convergence of series, Solution in series, Bessel and Legendre functions, Chebyshev  polynomials, Partial differential equations, Equations of vibrating string, One dimensional wave and heat conduction equations, Functions of a complex variable, Analytic functions, Cauchy-Riemann equations, Conformal mapping, Poles and singularities, Complex Integration, Taylor’s and Laurent’s series,  Cauchy residue theorem and applications.

Discrete Mathematics ( 07B21MA103 )

Basics of set theory, Mathematical induction. Relations, Equivalence relation, partial ordered relation, algorithms and functions. Big O notation, Proposition, Basic logical operators, Propositional functions and quantifiers, Graphs and related definitions, Eulerian and Hamiltonian graphs, Trees, Graph colorings. Algebraic expressions and Polish notation, Shortest path.Algebraic Systems. Languages, Finite State Automata and Machines. Grammars, Lattice and Boolean algebra.

Probability and Statistics ( 07B31MA104 )

Classification of data, Measures of central tendency and dispersion. Sample space and events, Axioms of probability, Conditional probability, Baye’s theorem, Independent events, Random Variable, Discrete and continuous distributions,  Mean and variance of a random variable, Binomial, normal and Poisson distributions, Elementary sampling theory, distribution of means, Statistical decision theory, Test of hypothesis and significance, Chi-square test, Curve fitting by the method of least squares, Correlation and regression, Covariance, Time Series Analysis and Moving Averages.

Probability Theory and Random Processes ( 07B41MA105 )

Probability, Sample space, Baye’s Theorem. One dimensional random variable (discrete and continuous), Bivariate random variables, joint, marginal, and conditional distributions, Covariance and correlation. Characteristic functions, probability distributions, Reliability and hazard rate function. Random processes, Stationary  processes. Autocorrelation function, Random walk and Weiner process, Ergodic process, Power spectral density function. Gaussian processes, Poisson processes, Markov chain .

Numerical  Methods ( 07B31MA106 )

Solution of linear systems of equations - Direct and iterative methods, Eigenvalues and Eigenvectors, Jacobi and Householder methods, Interpolation and Approximation, Numerical differentiation, Numerical integration, Gauss quadrature. Solution of a single and a system of non-linear equations, Initial and boundary value problems in ODE, Numerical solutions of partial differential equations by finite difference method, Method of weighted residuals (MWR). 

Biostatistics ( 07B41MA107 )

Multiple linear regressions, Prediction and estimation, Non parametric tests for the analysis of non-normal data. Classification and clustering of data from different sources, Stochastic processes and applications of Markov Chains in Bio-informatics, The applications of Markov Chains in modeling the DNA sequence, Simple random walk, Brownian motion.