MATH2008 home page
An Introduction to Modern Algebra
This page refers to the unit of study MATH2008 "Introduction to
Modern Algebra" as it was given in 2nd Semester 2003. This unit
of study was abolished in the change from 4 credit point units to
6 credit point units that was implemented in 2005.
The page was updated weekly throughout the semester,
as links were added for tutorial solutions and
lecture summaries. This material was also made
available for purchase from KopyStop.
The information sheet for Math2008 in 2003 is still available
here.
Please report any problems you have with this web site by email to
R.Howlett@maths.usyd.edu.au
Page contents
Course objectives
- To gain proficiency in dealing with abstract concepts, with emphasis on
clear explanations of such concepts to others.
- To understand the theory of inner product spaces,
including concepts such as the orthogonal projection
onto a subspace, and its use in finding the best polynomial model for a data set,
and finding the best approximation, by polynomials or by sines
and cosines, to a continuous function over an interval.
- To see how group theory can be used to study symmetry
in geometric and abstract contexts.
- To understand the basic group theoretic concepts
such as subgroup, coset and homomorphism, and their
elementary properties.
- To learn how to use the computer algebra package MAGMA
(to a small extent).
Assessment details
The examination is two hours in length and carries 85% of the assessment.
The other 15% is made up as follows: assignments 10%, tutorial participation 5%.
Tutors will record attendance and participation in the standard
tutorials; attendance at the computer tutorials will be monitored via
computer login records.
There will be two assignments: the first will be distributed near the
end of Week 4, and its due date will be the first Tuesday in Week 6.
The second will be due on the first Tuesday after the mid-semester
break – that is, at the start of Week 10. The questions will be
distributed two weeks before that.
Classes
Lectures are at 9:00 am Tuesdays
in Carslaw 175 and 9:00 am Thursdays in
Carslaw 275. Students should also attend one computer tutorial
and one standard tutorial each week, starting in the 2nd week of the
semester. Note that you will benefit more from the tutorials if you
attempt the questions beforehand.
The times and locations for computer tutorials are as follows:
Monday 10:00 am, 2:00 pm in Carslaw 610/611,
Tuesday 10:00 am in Carslaw 729/730.
The times and locations for standard tutorials are as follows:
Tuesday 11:00 am in Eastern Avenue 312, Thursday 10:00 am
and Friday 11:00 am in Carslaw 350.
Please attend the tutorial to which you have been timetabled. If
exceptional circumstances force you to miss your scheduled
tutorial class then you may attend another instead.
In the computer tutorials we shall be using the computer algebra package
MAGMA to investigate inner product spaces and to learn about
group theory. There will be problems for you to solve each week: these are
complementary to the problems in the standard tutorials and are designed
to help you understand the theory of lectures. You will be expected to
learn some basic MAGMA commands: the assignments may require the use of
MAGMA and there will be questions in the examination about the
use of MAGMA.
Consultations
The lecturer is A/Prof Bob Howlett, whose room is Carslaw 523.
Office hours: 12:00 – 2:00 Mondays and 1:00 – 2:00 Tuesdays.
(Possibly also available for consultation at other times: click
here
to see his timetable, to find the best times to try.)
Stewvac consultation times:
I shall be in my room between 2:30 and 3:30 on Wednesday
5th and Thursday 6th. But I shall be in every day between now
and the exam, and you are welcome to ask questions any time.
Books
The following are useful reference books.
- Carol Whitehead, A Guide to Abstract Algebra, MacMillan
Mathematical Guides, 1988.
- H Anton, Elementary Linear Algebra, Fifth Edition, Wiley, 1987.
- G Strang, Linear Algebra and its Applications, HBJ, 1988.
- J A Green, Sets and Groups, Routledge and Kegan Paul.
- J R Durbin, Modern Algebra, an Introduction, Second Edition, Wiley, 1985.
Tutorials and assignments
Tutorial and assignment solutions will be made available from Kopystop,
55 Mountain Street, Ultimo. They will also be
available for web download. Links will be provided here in due course.
Tutorials
Instructions relating to computer tutorials.
Assignments
Lecture summaries
Notes on each week's lecture material will also be available via
KopyStop and the internet.
The lecture summaries are available from KopyStop
in book form. Individual weekly summaries will not be sent to
KopyStop, but will remain available via the web. Any corrections
that are made to the KopyStop versions will be announced here.
Examination papers from previous years
The exam paper from 2000
(extended answer section only) is available for download.
The solutions to the 2000 exam are also available.
If you want to look at exam papers from other years, you can
download them from the library's website:
http://www.library.usyd.edu.au/exams/.
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