Abstract algebra is the area of mathematics that investigates algebraic structures. By defining certain operations on sets, one can construct more sophisticated objects: groups, rings, and fields. These operations unify and distinguish objects at the same time: adding matrices is similar to adding integers, while matrix multiplication is quite different from multiplication modulo n. Because structures like groups or rings are richer than sets, we cannot compare them using only their elements; we have to relate their operations as well. For this reason group and ring homomorphisms are defined. These are functions between groups or rings that "respect" their operations. This type of function is used not only to relate these objects, but also to build new ones, quotients for example.
Although at this point it may seem like the study of these new and strange objects is little more than an exercise in a mathematical fantasy world, the basic results and ideas of abstract algebra have permeated and are at the foundation of nearly every branch of mathematics.
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Spring 2026: P4 (3.8 hp), P3 (3.7 hp)
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Master of Science in Engineering and in Education, year 4, MAKE
Master of Science in Engineering and in Education, year 5, MAKE
Master of Science in Engineering and in Education, year 5, TEDA
Master of Science in Engineering and in Education, year 4, MAFY
Master of Science in Engineering and in Education, year 4, TEDA
Master of Science in Engineering and in Education, year 5, MAFY
Master's Programme, Applied and Computational Mathematics, year 1
Degree Programme in Engineering Mathematics, year 2
Please note: all information from the Course syllabus is available on this page in an accessible format.
Course syllabus SF1678 (Autumn 2019–)Group theory: groups, permutations, homomorphisms, group actions, Lagrange's theorem, Sylow's theorems, structure of abelian groups.
Ring theory: rings, ideals, fields and field extensions, factorization, principal ideal domains, polynomial rings, rings of integers.
After completing the course a student should be able to:
in order to
Completed basic course SF1672 Linear Algebra or SF1624 Algebra and Geometry.
Announced no later than 4 weeks before the start of the course on the course web page.
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
If the course is discontinued, students may request to be examined during the following two academic years.
The examiner decides, in consultation with KTHs Coordinator of students with disabilities (Funka), about any customized examination for students with documented, lasting disability. The examiner may allow another form of examination for re-examination of individual students.
