Mathematics

ADRIANO PISANTE

General targets: to acquire basic knowledge in measure and integration theory, spaces L^p, Fourier series.

Specific targets: to acquire the ability to use the definitions and theorems contained in the course.

Knowledge and understanding: the student will have acquired the basic notions and results related to the Theory of Abstract Measure, to the construction of the Lebesgue Measure, to the Theory of Integration, to the spaces L^p, to the spaces of Hilbert, to the Fourier series.

Apply knowledge and understanding: the student will be able to understand the concept of measurement and integral in abstract spaces, to integrate discontinuous functions, to operate with different notions of convergence in L^p, to use the Fourier series in L^2.

Critical and judgmental skills: the student will have the basis to deal with some problems of pure and applied mathematics, related to the Theory of Measurement, the spaces L^p, the spaces of Hilbert, the Fourier series.

Communication skills: the student will be able to expose the course contents in a clear and understandable way, both in the written and oral part.

Learning skills: the knowledge acquired will allow study, individual or taught in a master-level course, relating to more specialized aspects concerning the Theory of Measurement, the spaces L ^ p, the spaces of Hilbert, the Fourier series.