MTH5112

Linear Algebra I

Course Material 
Autumn 2012 
General information
Parameters
 Value: 15 credits
 Level: 5
 Semester: A
 Prerequisites: Level 4 mathematical background. MTH4103 Geometry I desirable.
Administrative information
 Lectures: Wed 11, Thu 12 and Thu 3 in Mason Lecture Theatre.
 Lecturer: Professor Robert Wilson, Room G51. For office hours, see my homepage.
 Exercise classes: Wed 12 (Geog 126): surnames AK.
Thu 11 (BR 302): surnames LP. Thu 2 (BR 302): surnames QZ.
Please try to attend the right session, unless you have an unavoidable timetable clash.
 Solutions to exercises to be handed in to the RED box in the BASEMENT of the MATHEMATICS building by 12 NOON on FRIDAY.
Course descriptions and syllabus
Your working week
Each module is designed to fill onequarter of a fulltime working week.
That is, you are expected to work roughly ten hours a week on each module.
Only four hours are timetabled. The rest is your responsibility. It should include,
at the very least:

reading your lecture notes and/or the textbook,
 doing exercises,
preferably on your own, and
 going over the feedback
provided on your attempts, to see where you can improve.
Lectures, notes, and books
Lectures
What is the purpose of lectures, if the notes are available online? Experience has shown
that it is actually quite difficult to learn mathematics by reading notes or books,
even if you are conscientious about doing the exercises (which most people
are not).
If you are studying music, it is much better to hear it in real time, rather
than read the score. A mathematical proof is like a piece of music:
there is really no substitute for seeing it develop in real time.
Some people seem to have read the above as a rhetorical question, and deduced that
I will not be putting lecture notes online. But that is not what I actually wrote.
It was intended as a real question,
with some answers.
Notes
The following notes are scanned from the sheets
actually projected in the lectures.
Old notes from a previous lecturer on this module. I am following these notes
quite closely, with the same numbering system, so they should provide a convenient backup.
Exercises, tutorials, and feedback
Exercises and tutorials
These should be regarded as compulsory. Mathematics is not about
learning facts ("knowwhat"), it is about learning methods ("knowhow").
Methods and techniques cannot be learnt without practice.
As Confucius (551479BCE) said:
"I hear and I forget;
I see and I remember;
I do and I understand."
Mathematics is about doing, not about hearing or seeing.
Exercise sheets
Each week's set of exercises
is structured so that there are:
(a) practice questions, which you can get help on
in tutorials,
(b) one feedback question, to be handed in and marked for feedback, for
which help is not generally available in tutorials, since this defeats the purpose of feedback,
(c) extra questions for those who want to deepen their learning.
Marked work will normally be returned for feedback in the tutorials in the week after handing in.
Feedback
A worryingly large proportion of people are not collecting their marked work
for feedback. What is the point of handing work in if you make no effort
to learn from your mistakes?
10% of the assessment for this course is based on the midterm test, which takes place
towards the end of week 7.
The test will (in principle) cover all of the material from the first six weeks  roughly Chapters 14.
90% of the assessment is on the final exam in May/June.
Note: this does not mean that the weekly exercises are optional!
They are still compulsory, and anyone not making a genuine attempt at them
may be excluded from the course, including from the exam.
 Past exams can be found on the library website.
 Last year's midterm test paper. You are strongly
advised not to use this to guide your revision. There is a
tendency (which I cannot understand)
to think that if you can do last year's exam then
you can do this year's: but this implication is demonstrably false.
A number of people have sent me emails asking (in effect) what is going to be on the test. Of course, I will not answer such questions. A question like "Will there be definitions?" is
irrelevant, because you need to know the definitions anyway, in order to understand the questions that are being asked.
A question like "Will there be proofs?" is meaningless,
because mathematics is proof.
A question like "Do we need to know ... ?" can never be answered truthfully
by anything other than "I don't know". In life, as in exams,
it is not possible to
predict in advance what knowledge might or might not be useful to you.
Midterm test
Model solutions
I will not provide model solutions to past examination papers,
because they encourage poor quality learning. If you wish to use
past exam papers as an aid to your revision, you may bring your
solutions to one of my office hours, and I will
give you feedback on them as far as time allows.
Revision and exams
In order to get the best nourishment out of a
diet of mathematics, treat it as you would
a good meal:
 Take small bites.
 Chew your food thoroughly before you
swallow it.
 A balanced diet is good for you: just as you
need protein, fats and carbohydrates, vitamins
and minerals, so you need definitions, theorems
and proofs, examples and applications. Do not
neglect any of these, or you will suffer from
deficiency diseases.
Advice on revision:
 Don't do as some do, and cram as much
food as you can into your mouth just before
the exam, and regurgitate it over your exam paper.
(The examiner does not like to be faced with
a pile of vomit.)
 Instead, learn the recipes, and prepare
your own dishes as you go.
 Try out the recipes several times in advance:
a professional chef practices not just until he
gets it right, but until he cannot get it wrong.
Advice on exams:
 Ideally, an exam tests how well you can prepare
the mathematical dishes yourself, not just whether
you can recognise the dishes prepared by the examiner.
 You should present your dishes to the general
customer, not to the head chef. To put it another
way, the head chef will assess its effect on the
customer, rather than assessing whether you know
in theory how to make a souffle.
Other course material

Some thoughts on the overall aims of the course,
my teaching strategy, and study skills,
are collected here.

The recommended course text is
S J Leon: Linear Algebra with Applications. 7th Ed. (Pearson)

Further reading:
R W Kaye and R A Wilson: Linear algebra. (Oxford University Press)
Web Resources
Frequently asked questions
 Can we have more examples?
The module consists almost entirely of examples as it is.
 Can we have model solutions to last year's exam?
No. This only encourages a bad approach to learning.
 Will there be proofs in the exam?
Yes. Proof is what mathematics is all about.
 How many of the coursework marks count towards the final mark?
None. The `continuous assessment' part of the assessment is based entirely
on the midterm test, which counts 10%.
 What will the midterm test cover?
Anything from the first six
weeks of lectures, that is approximately Chapters 14.
 Why is there no revision lecture?
Revision is for you to do,
not me. I cannot do your revision for you.
 What is the format of the exam?
In accordance with new guidelines, there will be no choice on the exam.
The precise number and length of questions may vary, but there are likely to
be six questions, distributed among the major topics covered in the course
roughly according to the number of lectures.
Robert A. Wilson
Created 11 September 2012
Updated 11 March 2013