SF2729 Groups and Rings, 7,5 hp
Course Web Page
News
- 25/5
- The re-examination in August will be on August 19, 8.00-12.00.
- 18/5
- The final exam will take place in room D2, May 26 at
8.00-12.00.
- 21/4
- Graded homework will be returned in class on May 6.
- 1/4
- The second set of homework is now posted. It is due on April 20.
- 23/3
- The second part of the course has started. The recommended exercises are in the notes of the lectrure number 8.
- 19/3
- There will be an extra mid-term exam on Saturday, April 17,
due to the circumstances on Monday, March 15. Sign up for this
exam by email no later than Sunday, April 11.
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Contents
Course description
As James Newman once said, algebra is "a branch of mathematics
in which one does something to something and then compares the results
with the result of doing the same thing to something else, or
something else to the same thing".
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, fields. These
operations unify and distinguish objects at the same time. Adding
matrices work similarly 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 just their elements, we have to relate their operations as
well. For this reason group and ring homomophisms are defined. These
are functions between groups or rings that "respect" their
operation. This type of function are 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.
This course is divided in two parts:
- Group Theory
- Rings and Modules
Read more here:
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