Course description 5

15. Methods of Optimizations

General outline ,basic definitions, linear programming, maximize and minimize problems. Decision making under uncertainty and decision making with multiple objectives. Linear programming and related topics, the simplex algorithm. One-variable case, descent methods, analysis of quadratic objective functions, quadratic-fitting algorithms, nelder-meade algorithm and simulated annealing, constrained minimization.

16. Discrete Mathematics ,

Short description. Digital logic, set theory, proposition logic, conditional statements , valid andinvalid arguments ,graphics, predicate logic, the logic of quantified statements, two classical theorems, algorithms, sequences, mathematical induction, sets, set theory and axion system. Relation function, chain and ring, tree, binomial theorem, Euler graph and Homulton graph.

17. Numerical Analysis

Short . description ,mathematical preliminaries, Taylor’s Theorm, orders of convergence ,computer arithmetic, floating-point numbers and errors, stable and unstable computations conditioning. Solution of nonlinear equations, bisection (Interval Halving Method, Newton’s Method, Secant Method), fixed points. and functional iteration,computing roots of polynomials. Homotopy and continuation methods. Solving systems of linear equations, matrix algebra, LU and Cholesky factorizations, pivoting and constructing an algorithm,norms and the analysis of errors, neumann Series and iterative refinement,analysis of roundoff error in the Gaussian algorithm. Selected topics in numerical linear algebra, QR-algorithm of francis for the eigenvalue problem,approximating functions, Hermite interpolation, spline interpolation,Taylor series,interpolatlon in higher dimensions,continued fractions, adaptive approximation, Gaussian quadrature, Romberg integration,Bernoulli polynomials and the Euler-Maclaurin formula,numeriral solution ot ordinary differential equations. Runge-Kutta methods, multistep methods,boundary-value problems,linear differential equations.

18.Data structure

Short description, programming languages, object oriented programming, basic concepts and experiences. Advanced concepts and techniques, multi-threaded programming, basic mathematical techniques, recurrence equations, algorithm analysis. Fundamental algorithms and data structures, lists, queues, stacks, search and sorting, binary trees. Advanced algorithms and data structures, specialized tree data structures, tree search, graphs, search, order.