MIDDLE
EAST TECHNICAL UNIVERSITY DEPARTMENT OF MATHEMATICS
MATH
463 Introduction to Group Theory
2010-2011
FALL Semester Web Page
Instructor
Gülin ERCAN
Office
Hours
To Be Announced
Lecture
Hours
Tuesday
13:40-15:30 (M-102)
Thursday
10:40-11:30 (M-102)
Computer
Algorithms with GAP
Erkan Murat TÜRKAN & Fuat ERDEM
Office
Hours
To Be Announced
Lab Sessions
Thursday
15:40-16:30 (*)
*Lab sessions will be held on 7.10.2010, 28.10.2010, 18.10.2010,
9.11.2010, 30.11.2010
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. We intend to teach the use
of the computer package GAP during 5 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
There
will be one midterm (%25) and one final examinations (%35). We will assign one
theoretical and one computational homework (%40) altogether. 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.