Numerical Methods for CSE (401-0663-00L)
7 ECTS.
Fundamental algorithms in numerical mathematics, essential terms in numerical mathematics and the techniques used for the analysis of numerical algorithms.
Choosing the appropriate numerical method for concrete problems and correctly interpreting numerical results. Implementing numerical algorithms efficiently.
Content:
1. Direct Methods for linear systems of equations
2. Interpolation
3. Iterative Methods for non-linear systems of equations
4. Krylov methods for linear systems of equations
5. Eigensolvers
6. Least Squares Techniques
7. Filtering Algorithms
8. Approximation of Functions
9. Numerical Quadrature
10. Clustering Techniques
11. Single Step Methods for ODEs
12. Stiff Integrators
13. Structure Preserving Integrators
Probability and Statistics (401-0613-00L)
6 ECTS.
Basic concepts of probability and statistics with special emphasis on the topics needed in computer science. Laws of randomness and probabilistic thinking, intuition for stochastic modelling and simple and basic methods of statistics.
Probability: basic concepts (probability space, probability measure), independence, random variables, discrete and continuous distributions, conditional probability, expectation and variance, limit theorems
Statistics: parameter estimation, maximum likelihood and moment methods, tests, confidence intervals
Theoretical Computer Science (252-0057-00L)
8 ECTS.
Introduction to theoretical computer science, presenting the basic concepts and methods of computer science in its historical context. Computer science as an interdisciplinary science which, on the one hand, investigates the border between the possible and the impossible and the quantitative laws of information processing, and, on the other hand, designs, analyzes, verifies, and implements computer systems.
Main topics: alphabets, words, languages, measuring the information content of words, representation of algorithmic tasks. Finite automata, regular and context-free grammars. Turing machines and computability. Complexity theory and NP-completeness. Design of algorithms for hard problems.
Steven Battilana 