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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

SUPERIOR ALGEBRA 2
cod. 1010206

Academic year 2023/24
1° year of course - Second semester
Professor
- Andrea APPEL
Academic discipline
Algebra (MAT/02)
Field
Attività formative affini o integrative
Type of training activity
Related/supplementary
48 hours
of face-to-face activities
6 credits
hub:
course unit
in - - -
lectures timetable
exam calls
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Learning objectives

The students will learn the basic definitions, problems, and techniques in Representation Theory.

Prerequisites


Algebra (groups, rings, fields); Linear Algebra.
The course “Algebra Superiore 1” is NOT a prerequisite.

Course unit content


Representation Theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory.
The course is meant as an introduction to Representation Theory. In the first part, we will discuss the basics of the theory and introduce the fundamental problems. In the second part, we will study in detail the representation theory of finite groups, in particular symmetric groups, with their character theory.

Full programme

- - -

Bibliography

[E] P. Etingof et al., Introduction to representation theory.
[FH] W. Fulton, J. Harris, Representation Theory. A first course.

Both books are freely available online.

Teaching methods


The topics of the course will be discussed during the lectures, together with examples, applications, and exercises. Attendance is highly recommended.

Assessment methods and criteria

At the end of the course there will be an exam at the board, where the student will be asked to solve an exercise and discuss, explain, and prove one of the main results of the course.

Other information


The courses of “Algebra Superiore 1” and “Algebra Superiore 2” are completely independent. However, they are complementary. The attendance of both courses may be beneficial, and it is strongly recommended.