Linear Algebra I

Course Material Autumn 2012
Important notice
The format of this year's exam will be:
8 questions, roughly distributed over the majority of the syllabus.
Answer all questions.
Advice on learning, revision and exams.

Info | Lectures | Tutorials | Exams | Other material | FAQs

General information


Administrative information

Course descriptions and syllabus

Your working week

Each module is designed to fill one-quarter of a full-time 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:

Lectures, notes, and books


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.


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 ("know-what"), it is about learning methods ("know-how"). Methods and techniques cannot be learnt without practice. As Confucius (551-479BCE) 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.


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?

Assessment and examinations

10% of the assessment for this course is based on the mid-term 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 1-4.
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. 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.

Mid-term 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: Advice on revision: Advice on exams:

Other course material

Web Resources

Frequently asked questions

Robert A. Wilson

Created 11 September 2012
Updated 11 March 2013