Algebra 2
About the course
The course is included in the study program Mathematical Sciences - master. It may be taken as a singular course and is also offered for inbound exchange students.
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.
Admission requirements
Bachelor of science degree in mathematics or equal.
Application code is 9371.
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.
Prerequisites
Anbefalte forkunnskaper
MAT-2300 Algebra 1
Credit reduction
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
Teaching methods
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.Recommended reading/syllabus
Du kan se og få tilgang til deler av pensum via Leganto.
Pensumliste for MAT-3300 Algebra 2 - Høst 2025Information 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
| Oral exam |
Grade: A–E, fail F |
To take an examination, the student must have passed the following coursework requirements
| Mandatory homework | Grade: Approved – not approved |
Everything you need to know about before, during, and after the exam; registration, absence, appeals, and diplomas: UiT Exams homepage