Mathematical and Computer Modeling - 3GUC0205

Goal(s)

• To understand the needs of numerical computing and its specificities; to know and understand the standard methods of numerical analysis (continuous optimization, differential equations, function estimation...)

• To know the basic concepts and tools of Probabilities; to be capable of using them to model stochastic problems.
  
  • To understand the foundations of algorithmic and data structures; to know how to perform a top-down analysis of problems and design modular solutions based on the main concepts of object oriented programming; to be capable of implementing one's own programs using a programming language (Java).

Content(s)

Numerical analysis:

• error control;
• discretization, derivative evaluations, Euler method for differential equations;
• continuous optimization (properties, gradien and Newton method);
• continuous optimization with constraints (KKT conditions).

Probabilities:

• discrete and continuous random variables;
• independence, conditionnal probabilities;
• pseudo-random number generation;
• expected value and variance.

Computer science:

• algorithmic formalism and the main concepts of object oriented programming;
• top-down analysis of problems;
• definition of an algorithmic language (variables, control structures);
• data structures (tables, lists) and algorithmic techniques (recursion, divide and conquer)
• simple complexity analysis
• object oriented programming (objects, classes, attributes, encapsulation) and a programming language (JAVA).

Mathematics
Basics of Computer Sciences