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 magistrale in Mathematics - 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
| Modules | Credits | TAF | SSD |
|---|
| Modules | Credits | TAF | SSD |
|---|
| Modules | Credits | TAF | SSD |
|---|
1 module between the following1 module between the following 3 modules among the followingLegend | 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.
Algebraic Geometry - METHODS OF ALGEBRAIC GEOMETRY (2020/2021)
Teaching code
4S008272
Academic staff
Credits
3
Language
English
Scientific Disciplinary Sector (SSD)
MAT/03 - GEOMETRY
Period
II semestre dal Mar 1, 2021 al Jun 11, 2021.
To show the organization of the course that includes this module, follow this link: Course organization
Learning outcomes
The goal of the course is to introduce the basic notions and techniques of algebraic geometry including the relevant parts of commutative algebra, and create a platform from which the students can take off towards more advanced topics, both theoretical and applied, also in view of a master's thesis project.
Program
The first part of the course provides an introduction to commutative algebra, covering topics such as localization, spectrum of a ring and Noetherian property. The second part builds upon the first in order to study fundamental results about algebraic varieties over algebraically closed fields. The course will finish with some applications to cryptography. More precisely, regarding how the elliptic curve discrete logarithm problem provides examples for key agreement and digital signatures that are currently being used in cryptography.
| Author | Title | Publishing house | Year | ISBN | Notes |
|---|---|---|---|---|---|
| William Fulton | Algebraic Curves. An Introduction to Algebraic Geometry. | Addison-Wesley | 2008 | ||
| Sigfried Bosch | Algebraic Geometry and Commutative Algebra | Springer | 2013 | ||
| Douglas R. Stinson | Cryptography: Theory and Practice, Third Edition | Chapman and Hall/CRC | 2005 | 1584885084 | |
| Lawrence C. Washington | Elliptic Curves: Number Theory and Cryptography, Second Edition | Chapman and Hall/CRC | 2008 | 1420071467 |
Examination Methods
The exam consists of a written examination. The mark obtained in the written examination can be improved by the mark obtained by an optional oral examination. Only students who have passed the written exam will be admitted to the oral examination
