In his autobiography [12], Winston Churchill remembered his struggles with
Latin at school. ' ... even as a schoolboy I questioned the aptness of the
Classics for the prime structure of our education. So they told me how Mr
Gladstone read Homer for fun, which I thought served him right.' 'Naturally'
he says 'I am in favour of boys learning English. I would make them all learn
English; and then I would let the clever ones learn Latin as an honour, and
Greek as a treat.'
This book is intended for those students who might find rigorous anal-
ysis a treat. The content of this book is summarised in Appendix J and
corresponds more or less (more rather than less) to a recap at a higher
level of the first course in analysis followed by the second course in analysis
at Cambridge in 2004 together with some material from various methods
courses (and thus corresponds to about 60 to 70 hours of lectures). Like
those courses, it aims to provide a foundation for later courses in functional
analysis, differential geometry and measure theory. Like those courses also,
it assumes complementary courses such as those in mathematical methods
and in elementary probability to show the practical uses of calculus and
strengthen computational and manipulative skills. In theory, it starts more
or less from scratch, but the reader who finds the discussion of Section 1.1
baffling or the e, 5 arguments of Section 1.2 novel will probably find this
book unrewarding. I assume a fair degree of algebraic fluency and, from
Chapter 4 onwards, some exposure to linear algebra.
This book is about mathematics for its own sake. It is a guided tour of a
great but empty Opera House. The guide is enthusiastic but interested only
in sight-lines, acoustics, lighting and stage machinery. If you wish to see the
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