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Undergraduate course

Algebra

  • ECTS credits10
  • Teaching semesterSpring
  • Course codeMAT220
  • Number of semesters1
  • LanguageEnglish
  • Resources

Semester of Instruction

Spring

Objectives 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.

Required Previous Knowledge

None

Recommended Previous Knowledge

MAT121 Linear Algebra

Compulsory Assignments and Attendance

Excercises

Forms of Assessment

Written examination: 5 hours. Examination support materials: Non- programmable calculator, according to model listed in faculty regulations

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

Contact Information

advice@math.uib.no

Exam information