Sheets 1 to 4 are available in .dvi and .pdf format.
|Sheet 3||dvi||Sheet 4||dvi||Enthusiast Sheet 1||dvi||Enthusiast Sheet 2||dvi|
Here I have written a small amount about a couple of questions that might cause confusion for one reason or another. (In particular, if you are supervised after only a week of the course, then there will be definitions that you have not yet come across. This page provides some of them.)
Here is a pdf file of the first draft (rough in places and I shall certainly make changes) of an article from a book I am editing and partly writing. You may find it useful preliminary/supplementary reading for the part of the course that deals with functions, relations, binary operations and so on.
The language and grammar of mathematics.
The following of my mathematical discussions are particularly suitable for those just starting a degree course in mathematics.
A dialogue concerning the existence of the square root of two.
What is wrong with thinking of real numbers as infinite decimals?
A dialogue concerning the need for the real number system.
Why is multiplication commutative?
What is naive about naive set theory?
Paradoxes concerning definability.
How to discover a proof of the fundamental theorem of arithmetic.
How to discover the statement and two proofs of Fermat's little theorem.
The definition of `definition'.
Is the phrase `well-defined' well-defined?
What is `solved' when one solves an equation?
The implication of implication.
Not perhaps directly relevant to the course, but in a very roundabout way it might help train you to cope with questions like Number 12 on Sheet 4.
This is here to help when we come to Examples Sheet 4. I hope it will be enough to enable you to tackle at least some of the questions on countability on the sheet. Countability is covered right at the end of the course - hence the need for this page.