UE M6-B - Mathematics II

Level of knowledge:

The prerequisites for the Probability course are light and do not directly involve measurement theory. This course will call on basic notions of matrix calculus and series and integral calculus.
The prerequisites for the Integration course concern the topology of Rn and the Euclidean vector spaces of Rn.

N1: beginner
N2: intermediate
N3: advanced
N4: expert

The knowledge expected at the end of the course


Acquire the fundamental elements of probability theory (C1,N1)


Understand the specificity of random modeling (C1,N1)


Master the practice of probability calculus: calculation of law, expectation, confidence interval (C1,N1)


Acquire the fundamentals of Lebesgue integral (C1,N2)


Acquire the fundamentals of Fourier analysis (C1,N3)


Acquire basic notions of Hilbert space (C1,N2)



Learning outcomes in terms of abilities, skills and attitudes expected at the end of the course


Master the essential notions of probability calculus: events, probabilities, random variables, probability law, conditional probability and independence (C1,N1).


Know how to construct simple random models and calculate the probabilistic elements needed to use these models (C1,N1).


Master the various notions of convergence used in probability in order to grasp two fundamental results, namely the strong law of large numbers and the central limit theorem, which have numerous and varied applicative consequences (C1,N1).


Introduction to Monte Carlo techniques and their implications for numerical simulation.


Understand the links between integration theory and probability theory, in particular for calculating expectations (C1,N1).


Know how to use the fundamental theorems of Lebesgue integration: Dominated convergence, Fubini and Change of variable (C1,N2). Calculate double and triple integrals.


Calculate Fourier transforms of standard functions and solve simple linear partial differential equations using this tool (C1,N3).


Use a scalar product and calculate an orthogonal projection. (C1,N2)