Algebra

Language of Instruction

English

Pre-requirements

None

Learning Outcomes

After completed course, the students shall be able to:

• Do basic arguments with groups, rings, and fields.
• Give definitions and notions related to groups, rings, fields, and homomorphisms
  and isomorphisms of these. In particular permutations, group actions, factor groups
  and factor rings, integral domains, quotient fields, polynomial rings, ideals, prime ideals,
  maximal ideals, and field extensions.
• Perform basic calculations involving the above mentioned notions, both in concrete
  cases and in more general and abstract cases.
• Describe the main ideas in proofs involving the notions above, like for instance the
  impossibility of trisecting the angle and doubling the cube.

Contact Information

advice@math.uib.no

Course offered (semester)

Spring

Language of Instruction

English

Aim and Content

The course covers basic theory of groups and permutations, normal subgroups, group homeomorphisms and factor groups, group actions and Sylow Theory. In addition, the course includes the basic theory of rings and fields, polynomial rings, ideals and factor rings. Studies also include field extensions, finite fields and unique factorisation domains. In the latter, the focus is on groups of utomorphisms of fields, including the Galois theory necessary to show the insolvability of the general quintic by radicals.

Learning Outcomes

After completed course, the students shall be able to:

• Do basic arguments with groups, rings, and fields.
• Give definitions and notions related to groups, rings, fields, and homomorphisms
  and isomorphisms of these. In particular permutations, group actions, factor groups
  and factor rings, integral domains, quotient fields, polynomial rings, ideals, prime ideals,
  maximal ideals, and field extensions.
• Perform basic calculations involving the above mentioned notions, both in concrete
  cases and in more general and abstract cases.
• Describe the main ideas in proofs involving the notions above, like for instance the
  impossibility of trisecting the angle and doubling the cube.

Pre-requirements

None

Recommended previous knowledge

MAT121 Linear Algebra

Assessment methods

Written examination: 5 hours

Grading Scale

The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.

Contact Information

advice@math.uib.no