About this product

Product Identifiers

PublisherOxford University Press, Incorporated

ISBN-10019870643X

ISBN-139780198706434

eBay Product ID (ePID)16038261050

Product Key Features

Number of Pages416 Pages

Publication NameFoundations of Mathematics

LanguageEnglish

SubjectGeneral, Logic

Publication Year2015

TypeTextbook

AuthorIan Stewart, David Tall

Subject AreaMathematics

FormatTrade Paperback

Dimensions

Item Height1 in

Item Weight17.9 Oz

Item Length8.4 in

Item Width5.6 in

Additional Product Features

Edition Number2

Intended AudienceScholarly & Professional

LCCN2014-946122

Reviews"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, '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, "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, "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, 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.

Dewey Edition23

TitleLeadingThe

IllustratedYes

Dewey Decimal511.3

Table Of ContentI: The Intuitive Background1. Mathematical Thinking2. Number SystemsII: The Beginnings of Formalisation3. Sets4. Relations5. FunctionsIII: The Development of Axiomatic Systems8. Natural Numbers and Proof by Induction9. Real Numbers10. Real Numbers as a Complete Ordered Field11. Complex Numbers and BeyondIV: Using Axiomatic Systems12. Axiomatic Structures and Structure Theorems13. Permutations and Groups14. Infinite Cardinal Numbers15. InfinitesimalsV: Strengthening the Foundations16. Axioms for Set Theory

SynopsisThe 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., 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., 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., 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.

LC Classification NumberQA9.S755 2015