Laurea in Matematica Applicata

Algebra (2011/2012)

Course code 4S00022   Credits 6   Coordinator Lidia Angeleri Disciplinary sector MAT/02 - Algebra Teaching language Italian

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Teaching is organised as follows:

Lecture timetable

Educational objectives

The course provides an introduction to modern algebra. After presenting and discussing the main algebraic structures (groups, rings, fields), the focus is on Galois theory. Also some applications are discussed, in particular results on solvability of polynomial equations by radicals.

Syllabus

Groups. Subgroups, cosets, quotient group. Cyclic groups. The symmetric group. Solvable groups. Rings. Ideals. Homomorphisms. Principal ideal domains. Unique factorization domains. Euclidean rings. The ring of polynomials. Fields. Algebraic field extensions. The splitting field of a polynomial. Normal extensions. Separable extensions. Galois theory. Theorem of Abel-Ruffini.

Prerequisites: Linear Algebra

Exam methods

The exam consists of a written examination. The mark obtained in the written examination can be improved by the mark obtained for the homework and/or by an optional oral examination. Only students who have passed the written exam will be admitted to the oral examination.

Teaching aids
Activity	Title	Format (Language, Size, Publication date)
Teoria	Filo rosso	pdf (it, 532.581 KB, 1/9/12)
Teoria	Presentazione corso	pdf (it, 185.381 KB, 10/2/11)
Teoria	Prove scritte appelli 1 e 2	pdf (it, 97.148 KB, 2/22/12)
Teoria	Prove scritte appelli 1 e 2 - soluzioni	pdf (it, 5,700.96 KB, 2/22/12)

Statistics on students' past performance (Art. 2 del D.M. 31/10/2007, n. 544)

Data from AA 2011/2012 based on 51 students. I valori in percentuale sono arrotondati al numero intero più vicino.