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.

Zusatztext The writing is both rigorous and thorough, and the authors use compact presentations to support their explanations and proofs. Highly recommended. Informationen zum Autor 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 Pratchettand Jack CohenDavid 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). Klappentext 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. Zusammenfassung 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. Inhaltsverzeichnis 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 ...

Autorentext
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).

Inhalt

• 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