# Algebraic geometry

- Years2 years
- ECTS credits120

## Introduction

### Objectives and content

The Master programme in Algebraic Geometry gives a general background in mathematics, with special focus on algebraic geometry. This is an area where one uses techniques from algebra and topology, and often also complex analysis or number theory, to study geometric objects as curves, surfaces and higher dimensional manifolds that can be defined through polynomial equations. Some of the problems are centuries old, whereas others can for instance be related to problems in modern physics and other fields.

The programme provides training in abstract thinking and in analyzing mathematical problems where the method of solution is not known. During the programme, the students will develop skills needed for independent study of new fields and for communicating mathematics.

**Learning outcomes: **

A candidate who has completed his or her qualifications should have the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge

The candidate

- has a thorough knowledge of mathematics, particularly in algebraic geometry. The candidate can relate general and abstract concepts and methods to calculations and applications.
- has extensive experience in problem solving and a knowledge of strategies for combining different methods.
- has insight into the most important structures in the discipline such as algebraic curves and varieties, vector bundles, sheaves and cohomology. The candidate can explain and discuss the basic theory of these structures.

Skills

The candidate

- can assess and explain the choice of methods for solving mathematical problems and analyze complex mathematical structures.
- can conduct a research project in an independent and systematic way, including the development of mathematical proofs and perform independent mathematical reasoning and calculations.
- can write and produce mathematics at professional standards, and in an understandable and readable manner.

General competence

The candidate

- can analyze mathematical texts and simplify mathematical reasoning by outlining the structure and the most important elements.
- can use the knowledge mentioned above as a basis for a critical approach to the application of the discipline.
- can solve complex problems, even in cases where the choice of method is not obvious or where several different methods must be combined.
- demonstrates understanding and respect for scientific values such as openness, precision and reliability.

## What you Learn

### Learning Outcomes

A candidate who has completed his or her qualifications should have the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge

The candidate

¿ has a thorough knowledge of mathematics, particularly in algebraic geometry. The candidate can relate general and abstract concepts and methods to calculations and applications.

¿ has extensive experience in problem solving and a knowledge of strategies for combining different methods.

¿ has insight into the most important structures in the discipline such

as algebraic curves and varieties, vector bundles, sheaves and cohomology. The candidate

can explain and discuss the basic theory of these

structures.

Skills

The candidate

¿ can assess and explain the choice of methods for solving mathematical problems and analyze complex mathematical structures.

¿ can conduct a research project in an independent and systematic way, including the development of mathematical proofs and perform independent mathematical reasoning and calculations.

¿ can write and produce mathematics at professional standards, and in an understandable and readable manner.

General competence

The candidate

¿ can analyze mathematical texts and simplify mathematical reasoning by outlining the structure and the most important elements.

¿ can use the knowledge mentioned above as a basis for a critical approach to the application of the discipline.

¿ can solve complex problems, even in cases where the choice of method is not obvious or where several different methods must be combined.

¿ demonstrates understanding and respect for scientific values such as openness, precision and reliability.

## How to Apply

### Admission Requirements

This programme is avalible for citizens from within the European Union/EEA/EFTA.

Follow these links to find the general entry requirements and guidelines on how to apply:

- Citizens from within the European Union/EEA/EFTA (1 March)
- Nordic citizens and applicants residing in Norway (15 April)

### Semester

Autumn

### Admission Requirements

A bachelor's degree with the following mathematical knowledge or equivalent prerequisite knowledge: MAT111 - Calculus I, MAT112 - Calculus II, MAT121 - Linear Algebra, MAT211 - Real Analysis, MAT212 - Functions of Several Variables, MAT220 ¿ Algebra, MAT224 - Commutative Algebra, and

at least one of the courses MAT242 - Topology or MAT243 - Manifolds. We recommend that both MAT242 and MAT243 is completed before admission.

The minimum requirement is grade C or better (in the Norwegian grading system) in the courses that are required. If there are more applicants to a program than there are vacant places, applicants will be ranked according to grades in their application for admission. For international students residing abroad, the admission is extremely competitive.

It is important to document the content and learning outcomes of the central mathematics subjects, either with attached course descriptions or with links to web pages where course descriptions can be found.

## More information

### About the programme

### Contact

Please contact the study adviser for the program if you have any questions: Advice@math.uib.noAdvice@math.uib.no