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The Foundations of Mathematics

University level mathematics can be a daunting subject, and if you haven't studied maths to this level then you may think that those who have are speaking a different language. Well help is at hand in the form of a short book, The Foundations of Mathematics, by Ian Stewart and David Tall.

The book starts with a gentle introduction to ways of thinking about numbers and number systems. It then gets on to set theory, mathematical logic and formal proofs. The third part looks at number systems defined axiomatically, including the natural numbers, the real numbers and the complex numbers. The final chapter describes where axioms can lead, looking at axiomatic (as opposed to naive) set theory. Gödel's Incompleteness theorem is mentioned briefly - I couldn't help thinking that a whole chapter on this would have made a good finale.

The book would be useful to several different types of reader. Firstly, it would help those who are intending to study mathematics at university to prepare for what might be a difficult start. Secondly, it will be of use to those studying other sciences who want to understand their more mathematical colleagues. More generally, it will appeal to anyone who wants to get a grasp of the foundations of mathematics. The book has exercises for the reader in each chapter, and is well suited to independent study. Overall, I felt that the authors manage to deal with the foundations of mathematics in a way that doesn't get intimidating for the reader.

Amazon.com info

Paperback 276 pages
ISBN: 0198531656
Salesrank: 669083
Weight:0.94 lbs

Published: 1977 Oxford University Press, USA

Amazon price $63.00

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Amazon.co.uk info

Paperback 276 pages
ISBN: 0198531656
Salesrank: 66606
Weight:0.94 lbs

Published: 1977 OUP Oxford

Amazon price £31.83

Marketplace:New from £31.83:Used from £16.50

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Amazon.ca info

Paperback 276 pages
ISBN: 0198531656
Salesrank: 455764
Weight:0.94 lbs

Published: 1977 Oxford University Press

Amazon price CDN$ 80.50

Marketplace:New from CDN$ 74.95:Used from CDN$ 74.10

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Product Description
"There are many textbooks available for a so-called transition course from calculus to abstract mathematics. I have taught this course several times and always find it problematic. The Foundations of Mathematics (Stewart and Tall) is a horse of a different color. The writing is excellent and there is actually some useful mathematics. I definitely like this book."--The Bulletin of Mathematics Books

Product Description

"There are many textbooks available for a so-called transition course from calculus to abstract mathematics. I have taught this course several times and always find it problematic. The Foundations of Mathematics (Stewart and Tall) is a horse of a different color. The writing is excellent and there is actually some useful mathematics. I definitely like this book."--The Bulletin of Mathematics Books

Comprehensive and clear ****
Stewart and Tall have written some excellent mathematical texts, and this book is one of them. It deals with the basics of mathematics and treats them in a clear but thorough way. Although it is probably not essential, it is a good accompaniment to anybody starting a mathematics degree. They take the approach that one should already be familiar with an idea (via examples) before seeing its definition. This works well, although sometimes the effect is that the pace is slow and the exposition is drawn out.

Comprehensive and clear ****

Stewart and Tall have written some excellent mathematical texts, and this book is one of them. It deals with the basics of mathematics and treats them in a clear but thorough way. Although it is probably not essential, it is a good accompaniment to anybody starting a mathematics degree.

They take the approach that one should already be familiar with an idea (via examples) before seeing its definition. This works well, although sometimes the effect is that the pace is slow and the exposition is drawn out.

Excellent Book for the High School Mathsters ****
This book was written for those inquisitive/advanced high school students (6th formers in England) to give them an introduction to the number systems, formalization in mathematics and the concept of proof. Stewart is well-known for his clear writing and this book is an excellent example.

Excellent Book for the High School Mathsters ****

This book was written for those inquisitive/advanced high school students (6th formers in England) to give them an introduction to the number systems, formalization in mathematics and the concept of proof. Stewart is well-known for his clear writing and this book is an excellent example.

Unhelpful book ***
I'm going to start reading for a maths degree, and i found this book irritating. It is quite expensive, and brought it on recommendation, but found it to have too much waffle, and i hate it. Not touched on it much because i just couldn't stand the wordiness of it all...wish this book had more eqtns and formula and stuff...would liven it up a bit.

Unhelpful book ***

I'm going to start reading for a maths degree, and i found this book irritating. It is quite expensive, and brought it on recommendation, but found it to have too much waffle, and i hate it. Not touched on it much because i just couldn't stand the wordiness of it all...wish this book had more eqtns and formula and stuff...would liven it up a bit.

wordy text... **
i got this book as it was down on a reading list for the maths part of my course (bsc, computer science) as it came recommended. As a text, it covers a lot of material but i found it used older style notation and symbols and in my opinion/for my needs needed specific examples, but then it would be less concise, so it depends what you're looking for...

wordy text... **

i got this book as it was down on a reading list for the maths part of my course (bsc, computer science) as it came recommended. As a text, it covers a lot of material but i found it used older style notation and symbols and in my opinion/for my needs needed specific examples, but then it would be less concise, so it depends what you're looking for...

An excellent introduction to university mathematics *****
'The Foundations of Mathematics' is essential reading for anyone starting a mathematics degree. Its clear and precise style give an excellent insight into areas discussed in many different areas of mathematics, and so makes good preparatory reading. This book would also be suitable for anyone studying 'A' level maths who needed further inspiration on topics with which they were sruggling, or were contemplating studying maths at university. However, they might find many of the topics covered were superflous to their needs, as a lot of the book it not contained in the 'A' level syllabuses.

An excellent introduction to university mathematics *****

'The Foundations of Mathematics' is essential reading for anyone starting a mathematics degree. Its clear and precise style give an excellent insight into areas discussed in many different areas of mathematics, and so makes good preparatory reading.

This book would also be suitable for anyone studying 'A' level maths who needed further inspiration on topics with which they were sruggling, or were contemplating studying maths at university. However, they might find many of the topics covered were superflous to their needs, as a lot of the book it not contained in the 'A' level syllabuses.