Byers How Mathematicians Think

Using Ambiguity, Contradiction, and Paradox to Create Mathematics
Course Book
ISBN: 978-1-4008-3395-5
Verlag: De Gruyter
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 424 Seiten

No detailed description available for "How Mathematicians Think".

Autoren/Hrsg.

Byers, William

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Geschichte der Mathematik
• Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik

Inhaltsverzeichnis

Acknowledgments vii

INTRODUCTION: Turning on the Light 1

SECTION I: THE LIGHT OF AMBIGUITY 21

CHAPTER 1: Ambiguity in Mathematics 25

CHAPTER 2: The Contradictory in Mathematics 80

CHAPTER 3: Paradoxes and Mathematics: Infinity and the Real Numbers 110

CHAPTER 4: More Paradoxes of Infinity: Geometry, Cardinality, and Beyond 146

SECTION II: THE LIGHT AS IDEA 189

CHAPTER 5: The Idea as an Organizing Principle 193

CHAPTER 6: Ideas, Logic, and Paradox 253

CHAPTER 7: Great Ideas 284

SECTION III: THE LIGHT AND THE EYE OF THE BEHOLDER 323

CHAPTER 8: The Truth of Mathematics 327

CHAPTER 9: Conclusion: Is Mathematics Algorithmic or Creative? 368

Notes 389

Bibliography 399

Index 407

Über Autor(innen)

William Byers is professor of mathematics at Concordia University in Montreal. He has published widely in mathematics journals.