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4.2 out of 5 stars26
4.2 out of 5 stars
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on 13 March 2009
As a teacher of A level Maths and Further Maths, I found this book very helpful. I think every prospective maths student should read it, and do all the exercises, before starting their undergraduate mathematics course. It introduces in a rigorous but very readable style the vast majority of the topics that will be covered in the first year at university, and links them all together in a way that cultivates the more formal approach that university level mathematics requires. The author Dr Kevin Houston has been a maths lecturer at Leeds University for more than 15 years, and the book is based on his personal experience of helping to develop students' capacity for mathematical thinking and expression. There are over 300 exercises. Although the answers are not included, Dr Houston is planning to make them available on the internet over the next few months.

Conclusion--thoroughly recommended!
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on 6 August 2013
The text book is attractively laid out and the author communicates very clearly. A lot of thought has gone in to produce a book which is easy to read and understand. There are a lot of worked examples.

However, there is a major flaw with this book. There are no solutions to the exercises. If you are studying on your own then there is no way of checking your solutions and hence your understanding.

If you are an independent student you may want to consider very seriously whether this is the right book for you.
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on 12 December 2010
If you are, like I am, trying to get ready for university Maths by yourself, this is the book for you, easy to read, and the content is exactly what you need just after having taken a look back at the A level Maths (you will need at least to have another comprehensive book of A level maths at hand otherwise).

I thought twice about purchasing this book because the title makes it look like one of those "learn how to speak chinese in 15 days with no need to study". But this is not the case. It teaches you the basics of mathematical thinking so you are able to aproach a proof or a theorem with confidence, and above all, how to solve problems and study by yourself.

Also, I earn my living doing computer programming, and found that the book helped me quite a lot with my job as well. I now find myself thinking more logically and methodogically about any problem I come across, instead of rushing to type code and test.

Although it seems like a one day read when you receive it, it took me some 3 months to finnish it with about an hour a day. You have to do some research and be active with the learning (as the book will advice you to do), so it is not a book for a flight read.

I purchased "A Concise Introduction to Pure Mathematics" at the same time I bought this, but found it too hard to follow at first. But after finnished How to Think... the Concise Intro... fits nicely and I find it far far easier to read now.

By the way, I am in Spain and planning to study here, but the book is as good for UK as for any other country as far as I can see.
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on 20 August 2012
I decided that I must write a review after working through about a third of the book. The book is well-written and pitched at about the right level for first/second year undergraduates - however, the absence of solutions is intensely irritating.

After completing the exercises for the chapters concerning logical implications (ch 7,8 & 9), I find myself thinking that I probably got most/all(?) of the answers correct - but I'll never be sure. This is SO unsatisfactory! Just to add to your sense of unease, these chapters stress how easy it is to be fooled by interpreting/representing natural [English] language. Furthermore, the examples don't shed light on all the exercises.

I don't mind investing effort in thinking through the exercises, but, at the end of the day, I WANT TO KNOW IF I REALLY DO GET IT!!!

VERDICT: Don't buy it yet. When the book is complete, but it.
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on 1 June 2014
Many mathematical symbols do not show on kindle app they just appear as a box.. worse than useless. Do not buy on kindles, luckily I have a paper version as well which is excellent. Shame I cant give to reviews.
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VINE VOICEon 11 January 2013
* Physical

The book has a good font size printing in B&W text.

* Target Audience

This volume is clearly designed using feedback from students to help in the areas where perceived difficulties are common and repeatedly encountered. I feel this book's syllabus covers such a wide area it is capable of addressing new or refreshing forgotten knowledge gaps of many student's, beyond its initial design. Its so beautifully and carefully composed that I would be surprised if you were unable to find nothing totally new or refreshed by this book, almost independent of the level you may be at the moment.

* Personal areas

The parts that I particularly enjoyed were sections iii, iv, v, or to those without the book 'Definitions, Theorems and Proofs', 'Techniques of Proof', and 'Mathematics that all good mathematicians need'. As this is the stuff that I had understood, but things had become bit rusty. Its has a clear ability to remind the reader that scores with me. Its such a well - designed, helpful and monumentally clear exposition of these vital skills that I read it in 3 days and read for hours totally delighted by the way is written and the pitch its put to help its target audience.


Unfortunately, a number of pages from my copy became out of its binding, which is a pity. However, I stapled them together, and with regards of the authors skills I still consider the book as a recommended read and very enjoyable to go over topics in a fresh and entertaining manner.
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on 20 March 2010
There is a difference between Alevel maths and degree level. With this book you with find the transformation a lot easier. Read this over the summer holidays and you will have more time to get involved with all that freshers fun :P and hopefully enjoy getting those high grade. A great investment!
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on 11 November 2012
I would just like to start by stating my main cause of concern, the quality of the book itself is atrocious, the pages literally come right off!..and this is when it was brand new. Although knowledgeable, the book is not a must have.
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on 19 November 2011
How can a Book list exercises for the reader and not provide solutions so anyone who attempts to solve these exercises get a feedback to see If they are correct or not ? . Anyone is interested to check the solutions too and this is the purpose of any book to be helpful to the reader . Other Books I have purchased recently provide the solutions and the explanations on each exercise . This book only list exercises with no Solutions. I have not finished reading the whole book only the first chapter and I noticed this is the case in any other chapter.
Apart from this it seems well written but i have not finished the whole book to get a complete picture.
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on 29 December 2015
A very interesting read. This is a must have book for any undergraduate studying maths as it forms the bridge between A-Levels and university maths. This definitely gets you thinking and engages you from the first page. This book saved my degree!
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