The purpose of this book is to provide the student beginning
undergraduate mathematics with a solid foundation in the basic
logical concepts necessary for most of the subjects encountered in
a university mathematics course. The main distinction between most
school mathematics and university mathematics lies in the degree of
rigour demanded at university level. In general, the new student
has no experience of wholly rigorous definitions and proofs, with
the result that, although competent to handle quite difficult
problems in, say, the differential calculus, he/she is totally lost
when presented with a rigorous definition oflimits and derivatives.
In effect, this means that in the first few weeks at university the
student needs to master what is virtually an entire new language
{'the language of mathematics'} and to adopt an entirely new mode
ofthinking. Needless to say, only the very ablest students come
through this process without a great deal of difficulty.
General
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