Algebra (2016/2017)

Course code
4S00022
Name of lecturers
Lidia Angeleri, Francesco Mattiello
Coordinator
Lidia Angeleri
Number of ECTS credits allocated
6
Academic sector
MAT/02 - ALGEBRA
Language of instruction
Italian
Location
VERONA
Period
I sem. dal Oct 3, 2016 al Jan 31, 2017.

Lesson timetable

I sem.
Day Time Type Place Note
Wednesday 8:30 AM - 10:30 AM practice session Lecture Hall F from Oct 12, 2016  to Jan 31, 2017
Wednesday 3:30 PM - 5:30 PM lesson Lecture Hall E  
Thursday 1:30 PM - 3:30 PM lesson Lecture Hall E  

Learning outcomes

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 groups. 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

Reference books
Author Title Publisher Year ISBN Note
S. Bosch Algebra Springer Unitext 2003 978-88-470-0221-0
I. N. Herstein Algebra Editori Riuniti 2003

Assessment methods and criteria

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

Documents

STUDENT MODULE EVALUATION - 2016/2017