Lectures and tutorials are now given remotely using Zoom. See this page for further instructions.
The exam on May 29 will be a remote exam with Zoom-proctoring. See this Canvas room for further information.

(Se även svensk version.)

Course structure

This is a course on abstract algebra. The course is split into two parts:

Groups, period 3, lecturer: Johan Håstad
Contents: groups, permutations, symmetries, homomorphisms, group actions, Sylow theorems, ...
Rings, period 4, lecturer: David Rydh
Contents: rings, ideals, fields, PID, UFD, quadratic integers, ...

Tutorials: Oliver Gäfvert

Also see the lecture plan with lecture notes.

Prerequisities

SF1672 Linear algebra or equivalent and preferably SF1681 Linear algebra, advanced course.

Literature

We will use the following book:

Thomas W. Judson, Abstract Algebra: Theory and Applications, edition 2019 (the editions of the previous 2 years are almost identical)

This book is freely available online and also fairly inexpensive as a printed book (ca 200 SEK).

Additional material:

Supplementary notes: in particular concerning notation
An alternative proof by Navarro of the fundamental theorem of finite abelian groups and an alternative proof by Johan Håstad.

Course administration

Answers to administrative questions, for example course registration, application to examinations, re-examinations and similar, can be found at the web pages of the Student Office. You can contact the Student Office at studentoffice@math.kth.se.

Support for students with disabilities

Students with disabilities may have the right to certain compensatory support for example during examination. KTH has coordinators for students with disabilities, Funka, who deals with issues relating to functional disabilities. You should turn to Funka at funka@kth.se for information about support. Course specific details can be found here.

Examination

The examination is based on homework and a final written exam.

This year's homework sets.
Collection of earlier exams.

Homework sets

The course will have six sets of homework problems. These will be handed out at least one week before they are due and made available on the Canvas page of the course. There will be three sets of problems on the "group"-part of the course and three sets on the "ring"-part.

Each set is given a score in the range {0,1,2}. The two best scores from the group-part are added to the group-part of the final exam and similarly for the ring-part.

Given the abundance of material on the Internet it is hard to avoid that there are solutions to given or closely related problems somewhere in cyberspace. Please do not look for such solutions intentionally. If you happen to stumble across such solutions while searching for general information please include a reference in your solution set. Using solutions found on the Internet without proper reference is considered cheating and will be reported.

Degree of collaboration

You should write down your own solutions in your own words to each homework. The solutions are handed in electronically through Canvas and it is strongly recommended to submit a pdf-file obtained from a LaTeX source (see template).

You are allowed to discuss the problems with one or two other student(s). In such a case state the identity of your discussion partner(s) in your solution set. The partner(s) need not remain the same for different homework sets, but should be the same for all problems within a particular set.

Deadlines and late solutions

Deadlines in this course are strict. Under special circumstances extensions can be granted. Special circumstances include severe illness or an unexpected private crisis. It does not include high workload due to other parallel courses or planned activities outside KTH. If you feel you are entitled to such an extension please email Johan or David at your earliest possibility.

The final exam

The final exam will consist of 6 problem with three problems on each of the two parts. Each problem is worth 6 points. The points from the homework on a part is added to the score on the final exam of the same part. If the total on either part exceeds 18 it is decreased to 18. The requirements for the grades are as follows.

With at least 18 total points and at least 8 points on each part you are guaranteed an E.
With at least 21 total points and at least 9 points on each part you are guaranteed a D.
With at least 24 total points and at least 9 points on each part you are guaranteed a C.
With at least 27 total points and at least 10 points on each part you are guaranteed a B.
With at least 30 total points and at least 12 points on each part you are guaranteed an A.

If you have at least 8 points on each part but not a total of 18 you obtain the grade Fx, and the possibility to solve an additional problem set to get the grade E.

The exam on May 29, 2020 will be a remote exam with Zoom-proctoring. For more information, see the Canvas room for the exam.

SF1678 VT20-1 Grupper och ringar