The Foundations of Mathematics

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9780198706434: The Foundations of Mathematics

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.

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Recensione:

give[s] a very comprehensive overview of the mathematics involved in part of a first year mathematics degree. It would be of most value to tutors and lecturers in encouraging them to think about teaching methodologies and how they might modify them to help students in their thinking of mathematical ideas and their development of a coherent structure of mathematical concepts. ( John Sykes, Maths in School)

Review from previous edition 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)

Recensione:

The writing is both rigorous and thorough, and the authors use compact presentations to support their explanations and proofs. Highly recommended. ( N. W. Schillow, CHOICE)

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Stewart, Ian; David Tall, David Tall
ISBN 10: 019870643X ISBN 13: 9780198706434
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Ian Stewart, David Tall
Editore: Oxford University Press, United Kingdom (2015)
ISBN 10: 019870643X ISBN 13: 9780198706434
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Descrizione libro Oxford University Press, United Kingdom, 2015. Paperback. Condizione libro: New. 2nd Revised edition. 214 x 138 mm. Language: English . Brand New Book. 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. Codice libro della libreria AOP9780198706434

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Ian Stewart, David Tall
Editore: Oxford University Press, United Kingdom (2015)
ISBN 10: 019870643X ISBN 13: 9780198706434
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Descrizione libro Oxford University Press, United Kingdom, 2015. Paperback. Condizione libro: New. 2nd Revised edition. 214 x 138 mm. Language: English . Brand New Book. 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. Codice libro della libreria AOP9780198706434

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David Tall; Ian Stewart
ISBN 10: 019870643X ISBN 13: 9780198706434
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Descrizione libro Condizione libro: New. Depending on your location, this item may ship from the US or UK. Codice libro della libreria 97801987064340000000

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Descrizione libro OUP Oxford 2015-03-12, 2015. Condizione libro: New. Brand new book, sourced directly from publisher. Dispatch time is 24-48 hours from our warehouse. Book will be sent in robust, secure packaging to ensure it reaches you securely. Codice libro della libreria NU-LBR-01505424

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Ian Stewart, David Tall
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Descrizione libro Oxford University Press. Paperback. Condizione libro: new. BRAND NEW, The Foundations of Mathematics (2nd Revised edition), Ian Stewart, David Tall, 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. Codice libro della libreria B9780198706434

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Stewart, Ian, Tall, David
Editore: Oxford University Press (2015)
ISBN 10: 019870643X ISBN 13: 9780198706434
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Descrizione libro Oxford University Press, 2015. Condizione libro: New. The transition from school 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. This book bridges the divide. Num Pages: 416 pages, 113 b/w line drawings. BIC Classification: PBC. Category: (UU) Undergraduate. Dimension: 218 x 138 x 25. Weight in Grams: 506. . 2015. 2nd Edition. Paperback. . . . . . Codice libro della libreria V9780198706434

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Descrizione libro Paperback. Condizione libro: New. Not Signed; 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. book. Codice libro della libreria ria9780198706434_rkm

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Descrizione libro Oxford University Press. Condizione libro: New. Brand New. Codice libro della libreria 019870643X

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10.

Ian Stewart, David Tall
Editore: Oxford University Press 2015-03-26, Oxford (2015)
ISBN 10: 019870643X ISBN 13: 9780198706434
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Descrizione libro Oxford University Press 2015-03-26, Oxford, 2015. paperback. Condizione libro: New. Codice libro della libreria 9780198706434

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