BASICS OF HIGHER ALGEBRA

BASICS OF HIGHER ALGEBRA

_
iten
Code
90694
ACADEMIC YEAR
2019/2020
CREDITS
7 credits during the 1st year of 9011 Mathematics (LM-40) GENOVA

7 credits during the 3nd year of 8760 Mathematics (L-35) GENOVA

SCIENTIFIC DISCIPLINARY SECTOR
MAT/02
LANGUAGE
Italian (English on demand)
TEACHING LOCATION
GENOVA (Mathematics)
semester
2° Semester
Teaching materials

OVERVIEW

Language: English

AIMS AND CONTENT

LEARNING OUTCOMES

The goal of the course is the study of system of polynomial equations via Galois theory and using  Groebner bases. 

Teaching methods

Teaching style: In presence+computational sections with the use of symbolic computation packages.

SYLLABUS/CONTENT

I - Rings, ideals and modules. Noetherian rings and the Hilbert basis theorem. Polynomials: The ring K [x_1, ..., x_n] of polynomials with coefficientsin a field. Grobner Bases  and the Buchberger algorithm. Systems of polynomial equations and elimination theory.

II - Review of field extensions. Splitting fields of polynomials with coefficients in a field of characteristic 0, normal extensions and their basic properties. Fundamental Theorem of Galois theory. The Galois group of a polynomial. Applications: cyclotomic fields, solvability by radicals of algebraic equations.

RECOMMENDED READING/BIBLIOGRAPHY

Computational Commutative Algebra, Kreuzer, Robbiano, Springer, 2004.

TEACHERS AND EXAM BOARD

Ricevimento: To be decided later on when the general timetable will be fixed. 

Exam Board

ALDO CONCA (President)

MATTEO VARBARO

FRANCESCO VENEZIANO

MARIA EVELINA ROSSI

ALESSANDRO DE STEFANI

EMANUELA DE NEGRI

ANNA MARIA BIGATTI

LESSONS

Teaching methods

Teaching style: In presence+computational sections with the use of symbolic computation packages.

LESSONS START

The class will start according to the academic calendar.

ORARI

L'orario di tutti gli insegnamenti è consultabile su EasyAcademy.

Vedi anche:

BASICS OF HIGHER ALGEBRA

EXAMS

Exam description

Oral and computer algebra  project