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