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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About the Author:


Ian Stewart, Emeritus Professor, University of Warwick,David Tall, Emeritus Professor, University of Warwick

Ian Stewart is Emeritus Professor of Mathematics at the University of Warwick. He remains an active research mathematician and is a Fellow of the Royal Society. Famed for his popular science writing and broadcasting, for which he is the recipient of numerous awards, his bestselling books include: Does God Play Dice?, Nature's Numbers, and Professor Stewart's Cabinet of Mathematical Curiosities. He also co-authored The Science of Discworld series with Terry Pratchett and Jack Cohen

David Tall is Emeritus Professor of Mathematical Thinking at the University of Warwick. Internationally known for his contributions to mathematics education, his most recent book is How Humans Learn to Think Mathematically (2013).

Review:


"In their writing of Foundations of Mathematics, the authors motivate, encourage and teach their readers. If I were to offer a future course in foundations, I would certainly use this book and highly recommend it to others, both as a reference and as a text." --Frank Swetz, MAA Reviews


"The writing is both rigorous and thorough, and the authors use compact presentations to support their explanations and proofs. Highly recommended." --CHOICE


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Editore: OUP Oxford (2015)
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Descrizione libro OUP Oxford, 2015. Paperback. Condizione libro: New. BRAND NEW ** SUPER FAST SHIPPING FROM UK WAREHOUSE ** 30 DAY MONEY BACK GUARANTEE. Codice libro della libreria mon0001471783

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Descrizione libro Oxford University Press, United Kingdom, 2015. Paperback. Condizione libro: New. 2nd Revised edition. 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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Descrizione libro Oxford University Press, United Kingdom, 2015. Paperback. Condizione libro: New. 2nd Revised edition. 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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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 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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Descrizione libro OUP Oxford 2015-03-12, Oxford, 2015. paperback. Condizione libro: New. Codice libro della libreria 9780198706434

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Descrizione libro Oxford University Press Mrz 2015, 2015. Taschenbuch. Condizione libro: Neu. Neuware - 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. 391 pp. Englisch. Codice libro della libreria 9780198706434

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Descrizione libro OUP Oxford, 2015. PAP. Condizione libro: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Codice libro della libreria FU-9780198706434

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Descrizione libro OUP Oxford, 2015. Condizione libro: New. Codice libro della libreria L9780198706434

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