The Foundations of Mathematics PDF
By:Ian Stewart,David Tall
Published on 2015-03-12 by OUP Oxford
The transition from school mathematics to university mathematics is seldom straightforward. Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory. The authors have many years' experience of the potential difficulties involved, through teaching first-year undergraduates and researching the ways in which students and mathematicians think. The book explains the motivation behind abstract foundational material based on students' experiences of school mathematics, and explicitly suggests ways students can make sense of formal ideas. This second edition takes a significant step forward by not only making the transition from intuitive to formal methods, but also by reversing the process- using structure theorems to prove that formal systems have visual and symbolic interpretations that enhance mathematical thinking. This is exemplified by a new chapter on the theory of groups. While the first edition extended counting to infinite cardinal numbers, the second also extends the real numbers rigorously to larger ordered fields. This links intuitive ideas in calculus to the formal epsilon-delta methods of analysis. The approach here is not the conventional one of 'nonstandard analysis', but a simpler, graphically based treatment which makes the notion of an infinitesimal natural and straightforward. This allows a further vision of the wider world of mathematical thinking in which formal definitions and proof lead to amazing new ways of defining, proving, visualising and symbolising mathematics beyond previous expectations.
This Book was ranked at 36 by Google Books for keyword mathematics about sets.
Book ID of The Foundations of Mathematics's Books is xSN-BwAAQBAJ, Book which was written byIan Stewart,David Tallhave ETAG "FRl/e+fxZHM"
Book which was published by OUP Oxford since 2015-03-12 have ISBNs, ISBN 13 Code is 9780191016486 and ISBN 10 Code is 0191016489
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Book which have "432 Pages" is Printed at BOOK under CategoryMathematics
Book was written in en
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