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Product Description
Review
"In this book, Houston has created a primer on the fundamental abstract ideas of mathematics; the primary emphasis is on demonstrating the many principles and tactics used in proofs. The material is explained in ways that are comprehensible, which will be a great help for people who seem to hit the wall regarding what to do when confronted with the creation of a proof... In this book, Houston takes a systematic and gentle approach to explaining the ideas of mathematics and how tactics of reasoning can be combined with those ideas to generate what would be considered a convincing proof."
Charles Ashbacher, Journal of Recreational Mathematics
"The author provides concise, crisp explanations, including definitions, examples, tips, remarks, warnings, and idea-reinforcing questions. Houston expresses thoughts clearly and concisely, and includes succinct remarks to make points, clarify arguments, and reveal subleties."
W.R. Lee, Choice Magazine
Charles Ashbacher, Journal of Recreational Mathematics
"The author provides concise, crisp explanations, including definitions, examples, tips, remarks, warnings, and idea-reinforcing questions. Houston expresses thoughts clearly and concisely, and includes succinct remarks to make points, clarify arguments, and reveal subleties."
W.R. Lee, Choice Magazine
Product Description
Looking for a head start in your undergraduate degree in mathematics? Maybe you've already started your degree and feel bewildered by the subject you previously loved? Don't panic! This friendly companion will ease your transition to real mathematical thinking. Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. The material has been tested by real students over many years so all the essentials are covered. With over 300 exercises to help you test your progress, you'll soon learn how to think like a mathematician.
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Most Helpful Customer Reviews
24 of 25 people found the following review helpful
Format:Paperback
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!
Conclusion--thoroughly recommended!
15 of 16 people found the following review helpful
Format:Paperback
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.
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.
11 of 14 people found the following review helpful
Format:Paperback
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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Most Recent Customer Reviews
Expected more not just list exercises with no solutions or other...
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 ? . Read more
Published 6 months ago by Mich740
Beware if you are self studying
Good book but the Kindle version, at least, does not include solutions to the exercises. You can get partial solutions from the web but not to all of the exercises, which limits... Read more
Published 7 months ago by Gordon W
Mathematically enlightening
Really good book, does exactly what it says on the tin. Filled with lots of info and exercises that get you thinking about mathematics in a different way. Read more
Published 8 months ago by Philip
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