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NATIONAL INSTITUTE OF TECHNOLOGY KARNATAKA, SURATHAKAL -----------------------------------------------------------------------------------------------------------------solutions, similarity, symmetric matrices, diagonalization, Quadratic forms, Rotation of Co-ordinates, Orthogonal transformations. G. Hadley, Linear Algebra, Narosa 2000. G. Strang, Linear Algebra and its applications, Thomson Learning, 2003. MA205 MODERN COMPUTER ALGEBRA (3-0-0) 3 PREREQ: MA101/ MA151 Fundamental algorithms. Extended Euclidean algorithm and applications. Modular inverses, repeated squaring continued fractions and Diophantine approximation. Modular algorithms and interpolation Chinese Remainder Algorithm. Resultant and GCD computation. Applications to decoding BCH codes. Joachim Von Zur Gathen and Jurgen Gerhard, Modern Computer Algebra, Cambridge University Press, 1999. MA206 NUMBER THEORY AND CRYPTOGRAPHY (3-0-0) 3 PREREQ: MA101/ MA151 Elementary Number Theory. Congruences, applications to Factoring. Finite fields, Quadratic residues and reciprocity. Simple cryptosystems, public key cryptography, RSA, Discrete logs. Primality and Factoring, the rho method, Fermat factorization, continued fraction and Quadratic Sieve methods. N. Kobltiz, A course in Number Theory and Cryptography, Springer, 1994. MA207 NUMERICAL METHODS (3-0-0) 3 PREREQ: MA101/ MA151 Approximations and errors in computations. Interpolation and inverse interpolation. Numerical differentiation and numerical integration. Numerical solution of initial value problems in ordinary differential equations. Numerical solution of algebraic and transcendental equations. Solution of systems of equations by iterative methods. Eigen values and Eigen vectors. Difference equations. Linear and quadratic curve fitting using least square principle. S. S. Sastry : Introductory methods for numerical analysis, Prentice Hall. M. K. Jain, S. R. K. Iyengar and R. K. Jain : Numerical methods for Scientific and Engg. computations. Wiley Eastern. MA208 PROBABILITY THEORY AND APPLICATIONS (3-0-0) 3 PREREQ: MA101/ MA151 Introduction to probability, Sample space, Definitions of probability, Conditional probability, Bayes� theorem, Random variables, pmf, pdf, cdf, Marginal and Conditional Distributions, Mean and Variance, Covariance and Correlation, Probability distributions: Bernoulli, binomial, Poisson, uniform, exponential, normal, Gamma and use of statistical tables. P.L. Meyer, Introductory Probability and Statistical Applications, Oxford & IBH Publishing Co. S.M. Ross, Introduction to Probability and Statistics for Engineers and Scientists, John Wiley. MA209 THEORY OF COMPLEX VARIABLES (3-0-0) 3 PREREQ: MA101/ MA151 Functions of complex variables. Cauchy Riemann equations. Properties of analytic functions. Conformal mapping. Line integrals in complex plane. Cauchy's theorems. Power series. Residues. Evaluation of standard real integrals using contour integration. Erwin Kreyszig : Advanced Engg. Mathematics, Wiley Eastern. Lars V. Ahlfors : Complex Analysis , Mc Graw Hill Book Co. MA301 ADVANCED GRAPH THEORY (3-0-0) 3 PREREQ: MA203 Representations of Graphs, Trees, Enumeration, Spanning Trees, Planar and Dual Graphs, Detection of planarity, Geometric and Combinatorial Duals, Covering and Independence, Coloring, Structure of k-chromatic graphs, Perfect graphs, properties. D.B.West, Introduction to Graph Theory, PHI --------------------------------------------------------------------- NITK-Course Contents(UG)2010 Page 128 of 134
NATIONAL INSTITUTE OF TECHNOLOGY KARNATAKA, SURATHAKAL ------------------------------------------------------------------------------------------------------------------ MA302 DATA ANALYSIS, TIME SERIES ANALYSIS AND NON-PARAMETRIC METHODS (3-0-0) 3 PREREQ: MA208 Data analysis: Correlation and Regression of data, simple linear regression, Time series analysis: definitions, characteristic movements, measurement of trend, secular trend, seasonal movements, cyclical movements. Non � parametric methods, Wald � Wolfowitz test, sign test, Mann � Whitney U test, signed rank test, Kolmogorov � Smirnov tests, Kruskal � Wallis test. W.W. Hines and D.C. Montgomery, Probability and Statistics in Engineering and Management Science, John Wiley. J. Medhi, Statistical Methods, Wiley Eastern. MA303 INTEGRAL TRANSFORMS & APPLICATIONS (3–0–0) 3 PREREQ: MA101/ MA151 Laplace Transforms: solutions of boundary value problem using Laplace transforms, Applications of Laplace Transforms to the solutions of partial differential equations. Fourier Transforms: Fourier sine and cosine transforms, Applications of Fourier Transforms to the solutions of ordinary differential equations and partial differential equations. Hankel and Mellin and z – Transforms: solution of difference equations using z – transforms. I.N. Sneddon; Integral Transforms. P.P. Gupta; Integral Transforms, 1989, 2 nd Edition, Meerut Publishers. MA304 LINEAR PROGRAMMING AND APPLICATIONS (3–0–0) 3 PREREQ: MA204 Linear programming theory of simplex method, Duality dual sensitivity analysis. Integer linear programming Transportation problem, assignment problem, solution by the Hungarian method, transshipment model. Game theory � 2 persons zero sum game G. Hadley, Linear Programming, Narosa Publish, 1987. Hamdy A.Taha, Opertions Research, Fifth edition, Mc Millan Publishing company, 1992. Kanti Swarup, Gupta and Manmohan, Operations Research, Sultan Chand Publications, 1995,. MA305 NETWORK OPTIMIZATION (3–0–0) 3 PREREQ: MA203 Network Models, Minimal Spanning Tree, Shortest Route Problem (viewed as transshipment model), Matching and Covering Problems. Max-Flow Min-Cut Theorem, Capacitated Network Model and Network Simplex Method. PERT and CPM, Resource analysis in Network Scheduling: LP formulation, Precedence Planning Updating, Resource Allocation and Scheduling. C.H. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms & Complexity, PHI Hamdy Taha, Operations Research, McMillan MA306 OPERATIONS RESEARCH (3–0–0) 3 PREREQ: MA204 Introduction, Linear Programming, Duality Theory, Transportation and Assignment problem., Integer Programming: Branch and bound method for IPP, Dynamic Programming: Introduction to Non- linear programming. G. Hadley, Linear Programming, Narosa Publishers, 1987. Hamdy A. Taha, Operations Research, Fifth Edition Mc. Millan publishing company, 1992. Fredericks Hiller and G.J. Leibermann, Operations Research, Holden Day Inc., 1974. MA307 OPTIMIZATION TECHNIQUES AND STATISTICAL METHODS (3-0-0) 3 PREREQ: MA 208 Linear programming, simplex method, duality, transportation and assignment problems, Reliability, definitions, concept of hazard, bath-tub curve, system reliability for various configurations, data analysis: correlation and regression of data, simple linear regression, time series analysis: definitions, characteristic movements, measurement of trend, secular trend, seasonal movements, cyclical movements. H.A. Taha, Operations Research, Prentice Hall India J. Medhi, Statistical Methods, Wiley Eastern. --------------------------------------------------------------------- NITK-Course Contents(UG)2010 Page 129 of 134
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