Deepen some selected topics in mathematical analysis.
The analysis courses covered in the three-year degree.
Course unit content
The course aims to resume contents already covered by the student in the three-year degree, through different formulations and demonstrations that allow the grasp of aspects not previously explored in depth.
Construction of real numbers. Equivalent formulations of the completeness axiom.
A generalization of trigonometric functions: the p-sine and p-cosine functions.
The Stone Weierstrass theorem.
Power series and Fourier series. Dirichlet and Fejer nuclei.
Riemann and Lebesgue integral. Integral by Daniell.
W. Rudin: Principles of Mathematical Analysis, McGraw-Hill
W. Rudin: Real and Complex Analysis, Boringhieri
H. Brezis: Analisi funzionale, Liguori
PDF notes from the lessons
Assessment methods and criteria
Written test with questions on the program covered in the course and a seminar on a topic agreed upon with the student.