SF2729 Groups and Rings, 7,5 hp
Course Web Page - Spring 2011
News
- 19/8
- Now the second final exam
with solutions is
available here at the web page.
- 30/5
- The final exam has been graded and the exams are available
at the student expedition. The grades given were A: 8, B: 3,
C: 2, D: 4, E: 1, Fx: 1 and F: 9.
- 27/5
- Now the final exam
with solutions is
available here at the web page.
- 23/5
- The second homework assignment has been graded. Contact Carel Faber
by phone (7415) or e-mail (faber at kth) or pass by his office
to find out about your grade (and the number of credits on
problem 1 of part II of the exam).
- 10/5
- A complete list of recommended exercises can be found
here.
- 31/3
- The second homework assignment is now available here.
- 16/3
- Now the midterm
exam with solutions is
available here at the web page.
- 14/3
- There are a few spare seats for the midterm exam in room E33
tomorrow. The students who signed up for the exam have received
emails about where to go. Bring valid photo ID and be aware of the
regulations for written exams at KTH.
- 8/3
-
Recall that today is the deadline for signing up for the
optional midterm exam on March 15. Sign up by email.
- 24/2
- The homework has been graded and the result was excellent!
(See statistics.) The
homework will be returned tomorrow morning at the exercise
session, where we can also discuss different solutions.
Recall that you will have to sign up for the midterm exam on
March 15, no later than on March 8. Sign up by email.
- 15/2
- Today is the deadline for the first homework assignment. I
plan to use this as input for the course registration, so if you
plan to take the course, but will not deliver any homework
today, please let me know by email.
-
27/1
- The textbook has now arrived at the bookstore.
-
25/1
- The course started yesterday with the first lecture, and
lecture notes are available here at the web page. The first set
of homework problems
was distributed.
The bookstore has now the correct information about the
textbook and they promise it will arrive really soon.
The first exercise session will take place on Thursday morning,
8.15-10.00, in E36.
-
20/12
- The first course will start with the first lecture on January
24, 15-17 in D42. The text book will be A First Course in Abstract
Algebra, 7th Edition by John B. Fraleigh as last year.
- 19/8
- The course will start in January 2011 and the web page will be
updated in December. Until then you can look at last year's web
page. If you have questions about the course, please
let us know by
email.
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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 works 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 homomorphisms are defined. These
are functions between groups or rings that "respect" their
operation. 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.
This course is divided in two parts:
- Group Theory
- Rings, Fields and Vector Spaces
Read more here:
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