How to Read and do Proofs by Daniel Solow

This book will help any 'A'-Level maths learner to make the step-change from 'showing' to proving. From needing the textbook, or Google, or a well-meaning friend, to show you, to trying to work it out for yourself.

And I get the impression that if you can prove it, you're getting there, whatever stage of mathematics you are at. So being able to work it out for yourself is no bad thing.

The subject material of the book is not too advanced for the beginner mathematician, which immediately fuels a sense of 'I can do this'. The structure of the book is a tad confusing in places, with repetitions of material which add to the length of the text.

But you can gloss over those bits. The actual meat of the text is worth chewing over carefully. Solow takes pains to walk the reader through each example 'Proposition' step-by-step.

And there are a good number of these 'Propositions', all complete with explanatory notes, which can form the basis of a bank of proofs which you can then take with you into further work.

Exercises are included for the reader to have a go on their own. The answers are written in similar detail to the examples. Solow clearly wants the reader to 'get it'.

This book encourages you to actively look out for proofs in references and structure your own mathematics around them. At 'A'-Level, reading around coursebooks may or may not be what teachers advise but it can be worth it if done with a discerning eye.

Most texts at 'A'- Level, including Further Maths texts, are brief about what proof is and how it is done and the learner may end up reliant on working through lots of examples, perhaps without ever generating a sense of what it is all being done for.

Without any notion of what a Truth Table is, or how it might be used, without an armoury of techniques to employ, proof could be perceived as a desperate scrabble to find algebra which 'works out' okay- luck comes into the equation, perhaps in an undue way.

Writing a proof may be a journey into the unknown at the elite levels of mathematics, but with the contents of this book in mind, the 'A'-Level learner can stroll the more familiar algebraic byways with the confident air of someone at home in their surroundings.

Bogan