This course is an introduction to mathematical algorithms, important tools for scientific computing. The course addresses basic notions such as floating point arithmetics, numerical differential calculus and characterization of algorithmic complexity.
I) Floating point arithmetics including IEEE standards, rounding errors and detailed examples on the numerical computation of the number pi. II) Algorithms for differential calculus including finite differences and applications to partial differential equations, truncation errors, numerical methods for ordinary differential equations and initial value problems III) Complexity of iterative deterministic algorithms including practical characterization of complexity, recursivity, classification of algorithms with respect to their complexity, and various examples (sorting algorithms, fast fourier transform, arithmetic algorithms, etc.) IV) Algorithmic strategies (greedy algorithms, divide and conquer, bactracking, branch-and-bound) - Artificial intelligence in game theory
The exam is divided into two parts. A first one consists of practical resolution of some numerical problems similar to the examples in the lecture notes. They are to be realized on computer and students will summarize their results on a brief report. The second part consists of an oral presentation of some theoretical concepts and demonstrations, as well as the design of an algorithmic startegy adapted to a given problem. If these two parts are passed (at least 10/20), the final grade is the arithmetic mean. Otherwise, the arithmetic mean is not considered as a sufficient criterion and both parts are carefully examined before fixing the grade. If the grade of one part is inferior to 7/20, the exam is failed in any case.
| Training | Study programme | Block | Credits | Mandatory |
|---|---|---|---|---|
| Bachelier en sciences mathématiques | Standard | 0 | 4 | |
| Bachelier en sciences mathématiques | Standard | 3 | 4 |