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A classic overview of pure mathematics
on 7 February 2001
A wide-ranging overview of pure mathematics, first published in the 1940s, now re-issued and brought up to date with an additional chapter by Ian Stewart, this book is at the level of a capable student at the higher end of high school mathematics (A-level in the UK) or the beginning of a mathematics degree.
The scope of this book is awesome, covering number theory, geometry, topology, calculus, and much more. The chapter on projective geometry is a real treat, as it explores a beautiful topic that has dropped out of the modern maths syllabus. The only noticeable omission is group theory, which gets only a passing mention.
The style is clear, although the pace is rapid, and the reader is expected to fill in some details. There is an emphasis throughout on rigour - where this is relaxed for the sake of brevity, this is clearly signalled.
An appendix of problems and exercises (without answers) encourages further exploration of each topic.
A true classic and an enhancement to any mathematician's bookshelf.