spring 2018 MAT-2300 Algebra 1 - 10 ECTS
Admission requirements
Applicants from Nordic countries: Generell studiekompetanse eller realkompetanse + Matematikk R1 eller (S1+S2) og enten Matematikk (R1+R2) eller Fysikk (1+2) eller Kjemi (1+2) eller Biologi (1+2) eller Informasjonsteknologi( 1+2) eller Geologi (1+2) eller Teknologi og forskningslære (1+2).
International applicants: Higher Education Entrance Qualification and certified language requirements in English. It is a requirement that students have some prior knowledge of biology and ecology, chemistry and mathematics (Participants must have taken introductory level university courses, and achieved pass grades, in these subjects).
A list of the requirements for the Higher Education Entrance Qualification in Norway can be found on the Norwegian Agency for Quality Assurance in Education website - nokut.no
Recommended prerequisites is MAT-1004 Linear algebra or equal .
Application code is 9336.
Objectives of the course
The students should know, and be able to use, the following concepts in simple problems:- groups and subgroups
- cyclic groups
- normal subgroups
- permutation groups
- the structure theorem for finitely generated abelian groups
- homomorphisms and isomorphisms
- quotient groups
- rings and subrings
- integral domains
- quotient fields
- polynomials
- ideals
- fields and subfields
- field extensions
- algebraic extensions
- unique factorization domains
Recommended reading/syllabus
Syllabus for MAT-2300 Algebra 1, spring 2018
UiT The Arctic University of Norway, Department of Mathematics and Statistics
Textbook: John B. Fraleigh, "A First Course In Abstract Algebra", Seventh ed, Pearson Education 2003.
Syllabus:
Chap. 0, except Cardinality
Chap. I.2 - I.6
Chap. I.7, except Cayley Digraphs
Chap. II.8 - II.11
Chap. III.13 - III.14
Chap. III.15
Chap. IV.18 - IV.19
Chap. IV.20, except ax=b(mod m)
Chap. IV.21 - IV.22
Chap. IV.23, except 23.11 - 23.17
Chap. V.26 - V.27
Chap. VI.29 - VI.30
Chap. VI.31 (31.12-31.21; only understanding of algebraically closed fields, and some examples)
Chap. VI.33
Chap. IX.45 (45.1 - 45.18)
Error rendering component
- About the course
- Campus: Tromsø |
- ECTS: 10
- Course code: MAT-2300
- Responsible unit
- Institutt for matematikk og statistikk