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Università degli Studi di Parma Università degli Studi di Parma
Second cycle degree course in
Mathematics
Università degli Studi di Parma
Department of Mathematical, Physical and Computer Sciences

ANALYSIS FROM AN ADVANCED STANDPOINT
cod. 1007153

Academic year 2024/25
1° year of course - Second semester
Professor
Marino BELLONI
Academic discipline
Analisi matematica (MAT/05)
Field
Formazione teorica avanzata
Type of training activity
Characterising
48 hours
of face-to-face activities
6 credits
hub:
course unit
in ITALIAN
lectures timetable
exam calls
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Learning objectives

Deepen some selected topics in mathematical analysis.

Prerequisites

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.

Full programme

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.

Bibliography

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

Teaching methods

Frontal 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.

Other information

- - -

2030 agenda goals for sustainable development

- - -

Contacts

Toll-free number

800 904 084

Segreteria studenti

E. segreteria.scienze@unipr.it
T. +39 0521 905116

Quality assurance office

Education manager
dott.ssa Giulia Bonamartini
T. +39 0521 906968
Office E. smfi.didattica@unipr.it
Manager E.giulia.bonamartini@unipr.it

President of the degree course

Prof. Luca Lorenzi
E. luca.lorenzi@unipr.it

Faculty advisor

Prof. Luca Lorenzi
E. luca.lorenzi@unipr.it

Career guidance delegate

Prof. Francesco Morandin
E. francesco.morandin@unipr.it

Tutor Professors

Prof.ssa Alessandra Aimi
E. alessandra.aimi@unipr.it

Prof. Luca Lorenzi
E. luca.lorenzi@unipr.it

Prof. Adriano Tomassini
E. adriano.tomassini@unipr.it

 

Erasmus delegates

Prof. Leonardo Biliotti
E. leonardo.biliotti@unipr.it

Quality assurance manager

Prof.ssa Alessandra Aimi
E. alessandra.aimi@unipr.it

Internships

Prof. Costantino Medori
E. costantino.medori@unipr.it

Tutor students

Dott.ssa Fabiola Ricci
E. fabiola.ricci1@studenti.unipr.it