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Analysis and probability

Presentation

Programme (detailed contents):

v  Multidimensional functions: continuity, differentiability, change of variables, one-parameter integrals, multiple integrals.

v  Probability spaces, conditional probability and independence, real and multidimensional random variables, limit theorems, statistical estimation.

 

Organisation:

 

v  Lectures with lecture notes containing self-evaluation tests.

v  Exercise sessions.

v  Computer session with Matlab.

 

 

Main difficulties for students:

v  Computations using all the prerequisite concepts. Understanding of the various notions of convergence for random variables.

Objectives

At the end of this module, the student will have understood and be able to explain (main concepts):

v  Multidimensional functions, differentiability and integration.

v  Probability spaces, random variables, introduction to statistics.

 

The student will be able to:

 

to handle multidimensional functions and random variables.

Needed prerequisite

First year mathematics, algebra and analysis of the first semester 2IMACS (I2MAMT11).

Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...

Additional information

Multidimensional functions, differentiability, integration, probability, statistics.