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.
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
Recommended Previous Knowledge
MAT121 Linear Algebra
Compulsory Assignments and Attendance
Forms of Assessment
Written examination: 5 hours. Examination support materials: Non- programmable calculator, according to model listed in faculty regulations
The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.
For written exams, please note that the start time may change from 09:00 to 15:00 or vice versa until 14 days prior to the exam. The exam location will be published 14 days prior to the exam.
Type of assessment: Written examination
- 23.05.2018, 09:00
- 5 hours
- Withdrawal deadline