These notes are based on lectures given in the Mathematics Department of King's College London as part of the B.Sc. and M.Sci. programmes. This was a compulsory first term course for all students of mathematics - both single subject and joint honours students.
Much of the material will have been seen in some form or another by most students, but, nevertheless, such repetition is but a small price to pay for a confident working knowledge and a sound background across the whole student intake. Of course, it also means that all results here become available to all subsequent courses without further ado.
The aim of these notes is to provide a gentle and reasoned account of some
of the essentials of mathematics but certainly not
a cookbook collection of various recipes. It is taken for granted that the
reader is interested in mathematics and wishes to enhance their understanding
rather than simply their memory.
In this regard, these notes might provide stimulus for enthusiastic
(I would like to thank Peter Sollich (King's College) for comments.)
A natural sequel to this material would be a course on Real Analysis.
Maths: A Student's Survival Guide, by J. Olive, Cambridge University Press, 2003.
Calculus Lite, by F. Morgan, A.K.Peters/CRC Press, 2001
A First Course in Calculus, by S. Lang, Undergraduate Texts in Mathematics, Springer, 1986.
Analysis by Its History, by E. Hairer and G. Wanner, Springer, 2008.
MacTutor History of Mathematics Archive
- further available material.