The Foundations of Mathematics (inbunden)
Inbunden (Hardback)
Antal sidor
OUP Oxford
Tall, David
113 b/w line drawings
216 x 145 x 28 mm
590 g
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The Foundations of Mathematics (inbunden)

The Foundations of Mathematics

Inbunden Engelska, 2015-03-12
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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.
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N. W. Schillow, CHOICE The writing is both rigorous and thorough, and the authors use compact presentations to support their explanations and proofs. Highly recommended.

The Bulletin of Mathematics Books 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.

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Övrig information

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).


I: THE INTUITIVE BACKGROUND ; 1. Mathematical Thinking ; 2. Number Systems ; II: THE BEGINNINGS OF FORMALISATION ; 3. Sets ; 4. Relations ; 5. Functions ; III: THE DEVELOPMENT OF AXIOMATIC SYSTEMS ; 8. Natural Numbers and Proof by Induction ; 9. Real Numbers ; 10. Real Numbers as a Complete Ordered Field ; 11. Complex Numbers and Beyond ; IV: USING AXIOMATIC SYSTEMS ; 12. Axiomatic Structures and Structure Theorems ; 13. Permutations and Groups ; 14. Infinite Cardinal Numbers ; 15. Infinitesimals ; V: STRENGTHENING THE FOUNDATIONS ; 16. Axioms for Set Theory