Algebra (2012/2013)

Course code
4S00022
Credits
6
Coordinator
Lidia Angeleri
Academic sector
MAT/02 - ALGEBRA
Language of instruction
Italian
Teaching is organised as follows:
Activity Credits Period Academic staff Timetable
Teoria 3 I semestre Lidia Angeleri
Esercitazioni 2 I semestre Lidia Angeleri
Esercitazioni 1 I semestre Francesca Mantese

Lesson timetable

I semestre
Activity Day Time Type Place Note
Teoria Tuesday 2:30 PM - 4:30 PM lesson Lecture Hall E  
Teoria Wednesday 4:30 PM - 6:30 PM lesson Lecture Hall E  
Esercitazioni Thursday 1:30 PM - 3:30 PM practice session 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. 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

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.

Reference books
Activity Author Title Publisher Year ISBN Note
Teoria S. Bosch Algebra Springer Unitext 2003 978-88-470-0221-0
Teoria I. N. Herstein Algebra Editori Riuniti 2003
Teaching aids
Title Format (Language, Size, Publication date)
filo rosso  pdfpdf (it, 533 KB, 09/01/13)
PRESENTAZIONE CORSO  pdfpdf (it, 195 KB, 02/10/12)
Primo appello  pdfpdf (it, 112 KB, 08/02/13)
Prova scritta del 9/7/2013  pdfpdf (it, 85 KB, 10/07/13)
Foglio 1  pdfpdf (it, 110 KB, 03/10/12)
Foglio 10  pdfpdf (it, 96 KB, 12/12/12)
Foglio 11(versione aggiornata)  pdfpdf (it, 93 KB, 19/12/12)
Foglio 12  pdfpdf (it, 72 KB, 10/01/13)
Foglio 13 (facoltativo)  pdfpdf (it, 56 KB, 23/01/13)
Foglio 2  pdfpdf (it, 66 KB, 15/10/12)
Foglio 3  pdfpdf (it, 99 KB, 23/10/12)
Foglio 4  pdfpdf (it, 105 KB, 24/10/12)
Foglio 5  pdfpdf (it, 93 KB, 31/10/12)
Foglio 6  pdfpdf (it, 95 KB, 07/11/12)
Foglio 7  pdfpdf (it, 109 KB, 14/11/12)
Foglio 8  pdfpdf (it, 55 KB, 21/11/12)
Foglio 9  pdfpdf (it, 68 KB, 28/11/12)