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### Høst 2022

# MAT-3300 Algebra 2 - 10 stp

## The course is administrated by

Institutt for matematikk og statistikk

## Type of course

The course is included in the study program Mathematical Sciences - master. It may also be taken as a singular course and is also offered for inbound exchange students.

## Course overlap

MA-330 Algebra II 10 stp

## Course contents

The course is devoted to solutions of algebraic equations. It starts with field extensions, Galois theory and roots of polynomials in one variable. Abel¿s theorem on insolvability of the quintic is one of the highlights. Then the course focusses on polynomials in several variables, covering Gröbner basis as an effective computation tool. Finally, the general theory of zeros of polynomial ideals is expressed in the language of algebraic geometry.

## Application deadline

Applicants from countries within EU/EEA: June 1st for the autumn semester and December 1st for the spring semester. Exchange students and Fulbright students: 1 October for the spring semester and 15 April for the autumn semester.

## Admission requirements

Bachelor of science degree in mathematics or equal. Recommended prerequsites is MAT-2300 Algebra 1. Application code is 9371.

## Objective of the course

The candidate shall obtain solid knowledge in selected topics beyond Algebra 1:

- understand the theory of field extensions and algebraic numbers;
- be able to compute Galois groups of polynomials and construct the corresponding extensions
- Manage calculations with Gröbner bases by hand and with symbolic packages;
- Know basics of algebraic geometry, including the correspondence between varieties and prime ideals.

## Language of instruction

The language of instruction and the syllabus is English. Examination questions will be given in English, but may be answered either in English or a Scandinavian language.

## Teaching methods

Lectures: 40 h Coursework: 30 h