# Customer Reviews

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8 of 9 people found the following review helpful
on 27 August 2012
This book is very approachable and spans the school to university mathematics. It presents in the first chapter 18 "test" statements that can be proved mathematically. The rest of the book takes the statements progressively and by explanation, further examples and student exercises it helps the reader to first clearly understand what each statement is saying then working through the proof.

Different wording of statements requires different approaches. For example:

Statement 4: IF 2^67 - 1 is prime then 2^67 + 1 is divisible by 3.

and

Statement 15: There exists a unique positive integer t such that t + 2 and t + 4 are all primes.

Most of the examples are from (simple) number theory since these are the most accessible and familiar to most readers.

I particularly like the discussion before the working of a proof that tries to work through the thinking that leads to the choice of a particular approach that is valid. Also it helps you read a mathematical statement so you can understand what is (are) the given(s) and what result you have to establish. I like example 1:

"300 000 067 110 605 737 is not a perfect square"

What are you being asked to prove? Is this statement actually true? The book clearly tackles such uncomfortable questions.

The exercises help to clarify and reinforce the approach in the worked example. The book is finished off by a discussion of fallacies and mistakes in proofs.

That's what the book contains and I think it does that job well. Beyond that, I think this is an important book because it introduces and develops skill in proof, a skill that is much neglected in school maths which focusses on applying methods without questioning if the approach is valid. If ever you are slightly bothered as to whether the mathematics you are writing is actually valid or are not clear as to what a mathematical question is asking you to show, then this may be the book for you.
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1 of 1 people found the following review helpful
on 22 March 2013
This book is good for readers that do not have too much mathematical background or those who need to brush up on some mathematical ideas of logic and rigorous mathematical thinking. Number Theory is used here only for illustration and because it's so familiar to all of us.
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2 of 3 people found the following review helpful
on 27 March 2013
This book is outstanding. There is a growing recognition that in teaching mathematics we are not just imparting knowledge but teaching students to think as mathematicians think. A corollary of this is that it is often helpful to say something about the historical individuals who discovered the major theorems. Allenby achieves both of these aims with flying colours. By expressing the chains of thought that might pass through a mathematician's head as he grapples with a wide range of carefully selected problems, often in a light-hearted vein, he encourages us to think for ourselves. By interspersing these with biographical sketches of some of the giants of mathematical history he reminds us that maths is an activity carried out by people. The result is a book which meets a need in a way that is well nigh unique and will attract and instruct many.
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5 of 7 people found the following review helpful
on 31 October 2011
Proof - the biggest and most powerful notion in mathematics, yet nowadays it's not properly introduced and defined until you hit Uni-level maths, crazy huh? I bought this book after sitting a module at uni specifically on proof itself, and can heartily recommend this as a bridge into higher level mathematics.

This books has an engaging, conversational style making it perfect for self-study or extra-curricula reading - it very much gave me the feeling of being in a tutorial at points! There are lots of exercises to hit home the important ideas and methods, to get you using the skills that you've learned. A very helpful text.
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16 of 22 people found the following review helpful
on 3 February 2007
I am very lucky to be taught by Dr Allenby and his teaching style carries through into this book. His enthusiasm for the subject is matched by his enthusiasm for you to understand the subject. I would recommend this book for any maths undergraduate trying to get to grips with proofs.
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on 31 May 2015
Simply found this book was one that I bought, flicked through and then set on a shelf never to look at again.
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on 4 January 2015
Excellent !
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on 10 November 2014
excellent
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0 of 1 people found the following review helpful
on 5 November 2013
The book was delivered in excellent condition and well within the timeframe offered. It has been very useful for my daughter preparing for University course
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0 of 1 people found the following review helpful
on 9 April 2013
I bought this Maths book for my son to take with him to University as he is studing Maths. It has been helpful especially in his first term.
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