ANALYSIS FROM AN ADVANCED STANDPOINT
Learning outcomes of the course unit
Knowledge and skill of learning
At the end of the learning activity the student should acquired knowledge and skills related to the essentials elements of the Mathematical Analysis through the examination of some selected results.
Ability to apply knowledge and understandingThrough the exercises done in the classroom, the student learns how to apply the theoretical knowledge acquired to solve concrete problems related to the topics discussed in the course.
Autonomy of judgement.
The student must be able to value the consistency and rightness of the results obtained by him or others.Communication skills.
The student should be able to communicate, in a clear and accurate way, mathematical contents related to the program, even outside of a purely applicative context. Classroom lessons and the dialogue with the teacher will improve the students's scientific vocabulary.
The student after completing the course will be able to independently develop mathematical analysis topics and to arrange different sources to get an effective synthesis.
Course contents summary
Complements of real and complex analysis
Complex numbers and the Foundamental Theorem of Algebra
The Fourier series with some classical examples.Elements of distribution theory.
The Stone-Weierstrass theorem.
Notes provided by the professor
The course includes 4 hours of frontal teaching per week. During frontal lessons, in traditional mode, the
Topics will be formally and rigorously presented. These topics will be accompanied by significant examples and appropriate exercises.
Assessment methods and criteria
Learning is verified through a written work in which the student develops a topic agreed with the teacher (which may be different from the ones discussed in the course), followed by a seminar in which the student exposes the agreed topic.
The exam is passed when the written work explains correctly the agreed topic and the student exposes it with language skills and master it in all its aspects.