Studying at the University of Verona
Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.
Study Plan
This information is intended exclusively for students already enrolled in this course.If you are a new student interested in enrolling, you can find information about the course of study on the course page:
Laurea in Matematica applicata - Enrollment from 2025/2026The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.
Please select your Study Plan based on your enrollment year.
1° Year
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2° Year activated in the A.Y. 2017/2018
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3° Year activated in the A.Y. 2018/2019
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Legend | Type of training activity (TTA)
TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.
Algebra (2017/2018)
Teaching code
4S00022
Credits
9
Language
Italian
Also offered in courses:
- Algebra of the course Bachelor's degree in Applied Mathematics
Scientific Disciplinary Sector (SSD)
MAT/02 - ALGEBRA
The teaching is organized as follows:
Elementi di algebra
Teoria di Galois
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.
Program
Elements of Algebra:
Groups, subgroups, cosets, quotient groups. Solvable groups. Sylow's theorems. 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. Finite fields. Constructions with ruler and compass.
Galois Theory:
Separable extensions. Galois theory. Theorem of Abel-Ruffini.
Prerequisites: Linear Algebra
Bibliography
| Activity | Author | Title | Publishing house | Year | ISBN | Notes |
|---|---|---|---|---|---|---|
| Elementi di algebra | S. Bosch | Algebra | Springer Unitext | 2003 | 978-88-470-0221-0 | |
| Elementi di algebra | I. N. Herstein | Algebra | Editori Riuniti | 2003 |
Examination 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.
