autumn 2024
MAT-3300 Algebra 2 - 10 ECTS

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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.

Admission requirements

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

Course overlap

If you pass the examination in this course, you will get an reduction in credits (as stated below), if you previously have passed the following courses:

MA-330 Algebra II 10 ects

Course content

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.

Recommended prerequisites

MAT-2300 Algebra 1

Objectives 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 and examination

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: Approx 40 h. Coursework: Approx 30 h.

Information to incoming exchange students

This course is open for inbound exchange student who meets the admission requirements. Please see the "Admission requirements" section.

Do you have questions about this module? Please check the following website to contact the course coordinator for exchange students at the faculty: https://en.uit.no/education/art?p_document_id=510412

Examination

Examination: Grade scale:
Oral exam A–E, fail F

Coursework requirements:

To take an examination, the student must have passed the following coursework requirements:
Mandatory homework Approved – not approved
UiT Exams homepage

Re-sit examination

Students with valid grounds for absence will be offered a postponed examination early in the following semester.
  • About the course
  • Campus: Tromsø |
  • ECTS: 10
  • Course code: MAT-3300
  • Earlier years and semesters for this topic