Introduction, Systems of Linear Equations, Iterative Methods, Linear Least Squares, Eigenvalue Problems, Nonlinear Equations, Optimization; Coursework and Programming Projects.

For further information see the academic catalog: IAM561

Interpolation, Numerical Integration and Differentiation, Initial Value Problems for Ordinary Differential Equations, Boundary Value Problems for Ordinary Differential Equations, Partial Differential Equations, Fast Fourier Transform.

For further information see the academic catalog: IAM562

Fixed-income securities, basic portfolio optimization, binomial method for options; Ito process and its applications in stock market, Black-Scholes equation and its solution; random numbers, transformation of random numbers and generating normal variates, Monte Carlo integration, pricing options by Monte Carlo simulation, variance reduction techniques, quasi-random numbers and quasi-Monte Carlo simulation; introduction to finite difference methods, explicit and implicit finite difference schemes, Crank-Nicolson method, free-boundary value problems for American options.

For further information see the academic catalog: IAM749

Unconstrained optimization: line search methods, steepest descent, Newton and quasi Newton methods, the conjugate gradient method constrained optimization: equality and inequality constraints, linear constraints and duality, linear programming, the simplex method, Lagrange multiplier algorithms, interior point methods, penalty methods, large scale optimization.

For further information see the academic catalog: IAM566

This course is intended to all students at the Institute. After a short introduction to Matlab various algorithms, their complexity will be introduced and symbolic, numerical and stochastic algorithms will be followed. Students will be encouraged to carry out several projects in groups. Moreover, students in groups will complete a term project at the end of the semester.

For further information see the academic catalog: IAM565

The course consists of a detailed description of continuous and discrete dynamical systems. We shall combine the introduction to the general theory with the consideration of bifurcations and chaos, the most important subtopics. The analysis of appropriate mechanical, physical, economic and biological models is an essential part of almost every lecture of the course. To support the course numerical and computational toolbox will be used.

For further information see the academic catalog: IAM529

Basics of programming, introducing MATLAB, programming with MATLAB, basic algorithms and problem solving in Linear Algebra, Differential Equations, Optimization, and so an. Reporting and presenting problems and their solutions, introducing \(\LaTeX\) and/or Scientific Workplace, Typesetting text and mathematical formulae, graphing, making bibliography and index, packages and defining your own styles.

For further information see the academic catalog: IAM564