Interesting read
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This book manages to give a flavour of what mathematics is like at university level.
I obtained mathematics at school at 'A' level 30 years ago and then read for a degree in engineering. I later obtained an accountancy qualification.
I have always been interested in philosophy and logic as well and I worked through some popular puzzle type books on mathematics and also spent some time looking at Euclid's Elements a few years ago.
While numerate and logically minded, I think that mathematics at degree level may well be beyond me but I found that this book did give one an overview of what mathematics is about as a subject in its own right. It begins with an example taken from mechanics (or physics or applied maths if you prefer) and moves on to various properties of numbers and the nature of mathematical proof.
This book may also be of some interest to people other than potential mathematicians such as those interested in computer science, logic, philosophy or physics.
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Making Sense of Mathematics
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I have become addicted to the "Very Short Introduction" series, offering the knowledge-hungry layman a great way to gain insight into a wide variety of topics. For me, mathematics is a subject which I was happy to close the book on in upper school, and it seems I was not alone in lacking enthusiasm for the subject which was impressed upon hapless students as being so important (why maths is so dreaded by many is a question this book seeks to answer, amongst many other "FAQ's" of this kind).
Rather than presenting a mass of complex formulae to prove various points, the book takes the approach of explaining the practical applications of mathematics, such as why modelling is relevant in many different situations, and how an understanding of patterns can be of value. Teaching mathematics from such a practical stand-point is a trick modern school education may be missing, yet the book suggests this might be the key for a new generation to understand what's being taught and actually getting excited about the subject.
Rather than being a dry read best left for boffins and insomniacs, this is a book which provokes thought and puts this fascinating subject in a whole new light.
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Pragmatic Mathematics
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An introduction to mathematics could be just that; elementary arithmetic and geometry, or it could be an outline history or finally, it could introduce the philosophical aspects of the subject. Gowers does none of those, although he does touch on the history and philosophy of mathematics. This is really an introduction to higher mathematics, for readers who have reached what in Britain is GCSE standard, roughly eleventh grade in the US. Philosophically, Gowers is a pragmatist. To him, problematic concepts like infinity and irrational numbers have meaning in as much as they are useful, and are true in as much as they give true results. As a European, Gowers credits Wittgenstein with these ideas. An American author would have credited William James. Gowers sidesteps rather than resolves philosophical problems, thus giving reassurance to mathematicians and irritation to philosophers. The book is a random selection of topics rather than a continuous narrative, but succeeds because each topic is fascinating and the writing is clear throughout. Under "Further Reading", Gowers includes his own website address, where you can find sections that did not make it into the book. What a good idea! The site is as full of good stuff as the book, and gives links to further sites that will give you as much mathematics as you will ever want.
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Great book
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This book demystifies puzzling concepts such as infinity, curved space, n-dimensional space and fractional dimensions. His emphasis on the abstract method - the focus on what mathetical objects DO rather than what they really ARE - as the key to understanding all these concepts is amazingly powerful, truly an eye-opener. A basic knowledge of mathematics is an advantage
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A Very Very Good Introduction
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I've recently gotten interested in Mathematics again (after finding it very difficult and boring at school) and was looking for a good general book to serve as an introduction. I really don't think I could have done any better than this. If you have even the slightest interest/curiosity about maths - you should buy this book.
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