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Høst 2019
MAT3300 Algebra 2  10 stp
The course is administrated by
Faculty of Science and Technology
Type of course
The course is included in the study program Mathematics  master. It may also be taken independent of study program upon approval of the Department of mathematics and statistics.
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 Nordic countries: 1 June for the autumn semester and 1 December for the spring semester. Applicants from outside the Nordic countries: 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 MAT2300 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
Coursework: 30 h
Assessment
One oral exam counting 100%.
Assessment scale: Letter grades AF.
Coursework requirements
A passing grade is required on the mandatory homework sets for permission to take the exam.
Course overlap
MA330 Algebra II 10 stp
Lectures Autumn 2019 First attendance: Mon 19th Aug, 10:15, Room A152, Realfagbygget 

Lectures 
prof. Cordian Benedikt Riener 
Coursework 
prof. Cordian Benedikt Riener 