MODULE
2LA (Linear Algebra)
This module is compulsory
for all MAM200W students, as well as for MAM204H students who are doing the
course as the minimum mathematics co-requisite for MAM246W and PHY213H.
Content:
This course introduces you to the vast subject of
Linear Algebra. Linear Algebra is one of the fundamental tools of more advanced
mathematics. It encompasses the study of Matrices, Vector Spaces, Linear
Transformations and the many applications of these notions. As we go along, we
will also look briefly at some basic mathematical tools (such as sets, methods
of proof, relations and functions) that you will need in this and other modules. (We have incorporated the 10 lecture section
on Foundations mentioned in the faculty handbook into the Linear Algebra
module this year.)
Notes and textbooks:
You will receive two sets of notes for this module: a
short set of notes entitled Nuts and bolts for MAM200W (this is the
material on foundations) and a more substantial set of notes on Linear
Algebra. Notes will be issued
early on in the term. These will be paid for by your levy for this course. The notes will not be used slavishly, but
rather like a textbook. This means that some material appearing in the notes
may be omitted, and additional material and examples presented in lectures. If
you miss a lecture, the onus is on you to find out what you have missed.
There is no prescribed textbook, but your lecturer may
mention some useful books for you to consult. You will find books on linear
algebra classified under the code DS512.5 in the university library.
Timetable:
2LA is lectured
in 5th period every Monday and Thursday and on the following Wednesdays:
23 February; 9 March, 6 April, 13 April, 11 May, 25
May.
Lecturers:
Dr Jurie Conradie
(Room M325, tel. 650 3199, e-mail: jurie@maths.uct.ac.za) and
Prof George Janelidze (Room M413.1, tel. 650 4065, e-mail:
janelidg@maths.uct.ac.za).
Tutorials:
You must attend one tutorial (lasting for one period)
per week. Tutorials are held on Thursday and Friday afternoons. You will be
assigned to a tutorial based on the information filled in on your enrolment
form. You will work in groups during the tutorial period. The tutorials form an
integral part of the course and satisfactory
tutorial attendance is a DP requirement.
Exercises:
There is a set of exercises at the end of every
section of the lecture notes. These exercises complement the problems you will
be given in the tutorials. It is important that you work through them in your
own time. The lecturer will from time to time give you an indication of which
exercises you should be able to do at that time.
Class Tests:
Both class tests take place from 18h00 to 19h30. The
venues will be announced later.
·
Test 1: Wednesday 30 March.
·
Test 2: Monday 9 May.
Please advise us in writing of any clashes with other
tests as soon as possible, but not later than Monday 28 February. No changes to
test times can be made after this date due to the difficulty in securing test
venues.
As far as the testing of theory in this course goes,
we will expect you to understand all the proofs that have been covered in the
course of the lectures. We will test your understanding by means of “comprehension
questions”. In this type of question we give you a proof and ask you to answer
questions about the proof, or to fill in gaps in the proof. Proofs will take on more significance than it
did in your first-year course because the theory becomes more important in this
module. We will also expect you to be able to create your own proofs of simple
facts and results. There will be examples of both these kinds of questions in
the exercises and tutorials.
Class Record, DP’s, Examinations:
Your class record for this module is the average of
your marks for the two class tests. Your final mark for the module is
calculated in one of two ways; either the class record counts 20% and the final
examination 80% or the class record counts 40% and the final examination 60 %,
whichever is to your advantage. It pays to have a good class record; you then
have a substantial part of your final mark in the bank, as it were.
A DP is awarded for the course as a whole and not for
each module. To obtain a DP for MAM200W you must obtain an average of at least
30% for the class records of the modules you have selected.
The final examination for this module (a two-hour
paper) is written in June.
Computing and computer
access:
Calculations in Linear Algebra, especially those
involving large matrices, may become quite tedious. MATLAB is an easy to use
computer program designed to do such calculations (and many other things as
well!) quickly and efficiently. The program MATLAB is available on the Scilab server.
You are encouraged to make use of it; some of the exercises will have an
indication that they are more easily done using MATLAB. You will find brief
instructions on how to start using MATLAB elsewhere on the 2LA website.
In addition, you may want to make use of the Linear Algebra Toolkit, which you can
find at
http://www.math.odu.edu/~bogacki/lat/
This online program allows you to follow certain basic
operation with matrices step by step on the screen.
Website:
If you are reading this, you
have already managed to gain access to the Linear Algebra website! We'll make
extensive use of it and regard it as our primary way of communicating with you
outside of lectures. Important notices about the module will appear here. Answers to exercises, some solutions to
tutorial questions and solutions to class tests will be posted here. From time
to time, other information and possibly even some self-tests will also appear
here. You are expected to check this site regularly as we'll assume that you
have read all notices appearing here.