MIDDLE
EAST TECHNICAL UNIVERSITY DEPARTMENT OF MATHEMATICS
MATH
463 Introduction to Group Theory
2009-2010
FALL Semester Web Page
Instructor
Gülin ERCAN
Office
Hours
Wednesday
11:40-12:30
Thursday
11:40-12:30
Computer
Algorithms with GAP
Erkan Murat TÜRKAN
Office
Hours
To Be Announced
Textbooks
There will be no textbook to purchase. We list some books
below according to topic:
·
General Group Theory
o
J. Rotman, An
Introduction to Theory of Groups
o
J. Rose, A Course
on Group Theory
·
GAP and Computational Group Theory
o
Information about
GAP is obtained from its web site http://www.gap-system.org/
o
From this site
you can download GAP free of charge to your own computer.
o
From this page click
on 'GAP support', then 'manual', then 'tutorial' to get a tutorial
o
From the same
page as before click on 'About GAP', then 'examples', then 'Rubik's cube' to
get a useful example
o
A.M. Cohen et al,
Some tapas of computer algebra, Springer 1999, ISBN 3540634800 (chapter 8,
projects 5 and 6).
o
D.F. Holt, B.
Eick, E.A. O’Brien, Handbook of computational group theory, Chapman &
Hall/CRC, c2005
o
J. Neubueser, An
elementary introduction to coset table methods in computational group theory,
pp. 1-45 in Groups - St. Andrews 1981 (C,M, Campbell and E.F. Robertson, eds),
Cambridge UP.
o
C.C. Sims,
Computation with finitely presented groups, Cambridge University Press 1994,
ISBN 0521432138
Course
Content
This semester there will be two parallel courses, one
addressing the theoretical side of finite groups, the other dealing with
computer algorithms in group theory using the computer system GAP. The
theoretical side will be taught on 2 days each week and on the third class day
each week (on Tuesday evenings at 5.40 pm) we intend to teach the use of the
computer package GAP during 10 sessions in the computer lab, teaching both the
use of the GAP commands and language, and simultaneously the theory behind the
algorithms which are used. No prior programming experience is necessary. We
will start by learning the basics of the language which GAP uses, and go on to
learn how to do computations with groups given as permutation groups, by
presentations, and as matrix groups. As part of this we will learn how the
algorithms we use work, and thereby gain some insight into their limitations.
On the theoretical side we will start with Group Actions and continue with
Sylow Theorems, Composition Series, Semidirect Product, Wreath Product,
Solvable Groups and Nilpotent Groups.
Course Assessment
We
will assign a set of homework problems roughly every 2 weeks, giving a total of
six homework assignments (%75) altogether. At the end of the semester we will
assign you a Take Home examination (%30). You do not have to obtain correct
solutions to these questions, only make genuine attempts. We believe that it is
extremely difficult to obtain a sound and permanently-lasting command of the
material presented without doing some work which actively involves the student.
Expectations of written work
Most
of the time in the conventional homework problems, to satisfy our criterion of
making a genuine attempt you will need to write down explanations for the
calculations and arguments you make. Where explanations need to be given, these
should be written out in sentences i.e. with verbs, capital letters at the
beginning, periods at the end, etc. and not in an abbreviated form.
Some of the homework will be computer exercises in GAP. An essential part of
what you hand in for these exercises will be a transcript of a GAP session, but
it will help if you insert explanatory comments. We do prefer to see a hard
copy of what you have done.
We encourage you to
form study groups. However everything to be handed in must be written up in
your own words. If two students hand in identical assignments, they will both
receive no credit.