course contents - ug - National Institute of Technology Karnataka
course contents - ug - National Institute of Technology Karnataka
course contents - ug - National Institute of Technology Karnataka
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NATIONAL INSTITUTE OF TECHNOLOGY KARNATAKA, SURATHAKAL<br />
-----------------------------------------------------------------------------------------------------------------solutions,<br />
similarity, symmetric matrices, diagonalization, Quadratic forms, Rotation <strong>of</strong> Co-ordinates,<br />
Orthogonal transformations.<br />
G. Hadley, Linear Algebra, Narosa 2000.<br />
G. Strang, Linear Algebra and its applications, Thomson Learning, 2003.<br />
MA205 MODERN COMPUTER ALGEBRA (3-0-0) 3 PREREQ: MA101/ MA151<br />
Fundamental algorithms. Extended Euclidean algorithm and applications. Modular inverses, repeated<br />
squaring continued fractions and Diophantine approximation. Modular algorithms and interpolation<br />
Chinese Remainder Algorithm. Resultant and GCD computation. Applications to decoding BCH codes.<br />
Joachim Von Zur Gathen and Jurgen Gerhard,<br />
Modern Computer Algebra, Cambridge University Press, 1999.<br />
MA206 NUMBER THEORY AND CRYPTOGRAPHY (3-0-0) 3 PREREQ: MA101/ MA151<br />
Elementary Number Theory. Congruences, applications to Factoring. Finite fields, Quadratic residues<br />
and reciprocity. Simple cryptosystems, public key cryptography, RSA, Discrete logs. Primality and<br />
Factoring, the rho method, Fermat factorization, continued fraction and Quadratic Sieve methods.<br />
N. Kobltiz, A <strong>course</strong> in Number Theory and Cryptography, Springer, 1994.<br />
MA207 NUMERICAL METHODS (3-0-0) 3 PREREQ: MA101/ MA151<br />
Approximations and errors in computations. Interpolation and inverse interpolation. Numerical<br />
differentiation and numerical integration. Numerical solution <strong>of</strong> initial value problems in ordinary<br />
differential equations. Numerical solution <strong>of</strong> algebraic and transcendental equations. Solution <strong>of</strong> systems<br />
<strong>of</strong> equations by iterative methods. Eigen values and Eigen vectors. Difference equations. Linear and<br />
quadratic curve fitting using least square principle.<br />
S. S. Sastry : Introductory methods for numerical analysis, Prentice Hall.<br />
M. K. Jain, S. R. K. Iyengar and R. K. Jain : Numerical methods for Scientific and Engg. computations.<br />
Wiley Eastern.<br />
MA208 PROBABILITY THEORY AND APPLICATIONS (3-0-0) 3 PREREQ: MA101/ MA151<br />
Introduction to probability, Sample space, Definitions <strong>of</strong> probability, Conditional probability, Bayes�<br />
theorem, Random variables, pmf, pdf, cdf, Marginal and Conditional Distributions, Mean and Variance,<br />
Covariance and Correlation, Probability distributions: Bernoulli, binomial, Poisson, uniform,<br />
exponential, normal, Gamma and use <strong>of</strong> statistical tables.<br />
P.L. Meyer, Introductory Probability and Statistical Applications, Oxford & IBH Publishing Co.<br />
S.M. Ross, Introduction to Probability and Statistics for Engineers and Scientists, John Wiley.<br />
MA209 THEORY OF COMPLEX VARIABLES (3-0-0) 3 PREREQ: MA101/ MA151<br />
Functions <strong>of</strong> complex variables. Cauchy Riemann equations. Properties <strong>of</strong> analytic functions. Conformal<br />
mapping. Line integrals in complex plane. Cauchy's theorems. Power series. Residues. Evaluation <strong>of</strong><br />
standard real integrals using contour integration.<br />
Erwin Kreyszig : Advanced Engg. Mathematics, Wiley Eastern.<br />
Lars V. Ahlfors : Complex Analysis , Mc Graw Hill Book Co.<br />
MA301 ADVANCED GRAPH THEORY (3-0-0) 3 PREREQ: MA203<br />
Representations <strong>of</strong> Graphs, Trees, Enumeration, Spanning Trees, Planar and Dual Graphs, Detection <strong>of</strong><br />
planarity, Geometric and Combinatorial Duals, Covering and Independence, Coloring, Structure <strong>of</strong><br />
k-chromatic graphs, Perfect graphs, properties.<br />
D.B.West, Introduction to Graph Theory, PHI<br />
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