Mathematics III - Abstract algebra
7.5 credits cr.
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In this course, you will study the algebraic structures groups, rings, fields and vector spaces, and learn to use methods in abstract algebra to solve mathematical and applied problems.
This course is one of the requirements for eligibility to our Master's Programme in Mathematics.
The course covers:
- Group theory: sub groups, cosets, Lagrange's theorem, homomorphisms, normal subgroups and quotient groups, permutation groups, simple groups.
- Rings and fields: matrix rings, quaternions, ideals and homomorphisms, quotient rings, polynomial rings, principal ideal rings, Euclidean rings and unique factorization.
- Fields and vector spaces: finite-dimensional vector spaces, algebraic field extensions, finite fields.
The course consists of one element.
Instruction is given in the form of lectures and exercises. When the course is given as a distance course instruction is digital, e.g., recorded videos and/or live sessions over Zoom.
The course is assessed through written and oral examination.
Assessment when the course is given as a distance course
Even when the course is given as a distance course, the exam is on campus. If you cannot come to Stockholm for the exam, you may be able to arrange to take the exam elsewhere, e.g. at another university or (if you are not in Sweden) at a Swedish embassy or consulate.
A list of examiners can be found on
ScheduleThe schedule will be available no later than one month before the start of the course. We do not recommend print-outs as changes can occur. At the start of the course, your department will advise where you can find your schedule during the course.
Note that the course literature can be changed up to two months before the start of the course.
Dummit & Foote: Abstract Algebra. John Wiley & Sons Inc.