Produktbild: The Joy of Abstraction
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The Joy of Abstraction An Exploration of Math, Category Theory, and Life

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Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

04.04.2024

Verlag

Cambridge University Press

Seitenzahl

424

Maße (L/B/H)

22,8/15,2/3,7 cm

Gewicht

644 g

Sprache

Englisch

ISBN

978-1-108-70844-9

Beschreibung

Rezension

'This book is an educational tour de force that presents mathematical thinking as a right-brained activity. Most 'left brain/right brain' education-talk is at best a crude metaphor; but by putting the main focus on the process of (mathematical) abstraction, Eugenia Cheng supplies the reader (whatever their 'brain-type') with the mental tools to make that distinction precise and potentially useful. The book takes the reader along in small steps; but make no mistake, this is a major intellectual journey. Starting not with numbers, but everyday experiences, it develops what is regarded as a very advanced branch of abstract mathematics (category theory, though Cheng really uses this as a proxy for mathematical thinking generally). This is not watered-down math; it's the real thing. And it challenges the reader to think-deeply at times. We 'left-brainers' can learn plenty from it too.' Keith Devlin, Stanford University (Emeritus), author of The Joy of Sets

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

04.04.2024

Verlag

Cambridge University Press

Seitenzahl

424

Maße (L/B/H)

22,8/15,2/3,7 cm

Gewicht

644 g

Sprache

Englisch

ISBN

978-1-108-70844-9

EU-Ansprechpartner

José Abascal
561°
28003 Madrid
ES
eugpsr@cambridge.org

Herstelleradresse

Cambridge University Press & Assessment
The Triangle, Shaftesbury Avenue
CB2 8EA Cambridge
GB
eugpsr@cambridge.org

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  • Produktbild: The Joy of Abstraction
  • Prologue; Part I. Building Up to Categories: 1. Categories: the idea; 2. Abstraction; 3. Patterns; 4. Context; 5. Relationships; 6. Formalism; 7. Equivalence relations; 8. Categories: the definition; Interlude: A Tour of Math: 9. Examples we've already seen, secretly; 10. Ordered sets; 11. Small mathematical structures; 12. Sets and functions; 13. Large worlds of mathematical structures; Part II. Doing Category Theory: 14. Isomorphisms; 15. Monics and epics; 16. Universal properties; 17. Duality; 18. Products and coproducts; 19. Pullbacks and pushouts; 20. Functors; 21. Categories of categories; 22. Natural transformations; 23. Yoneda; 24. Higher dimensions; 25. Epilogue: thinking categorically; Appendices: A. Background on alphabets; B. Background on basic logic; C. Background on set theory; D. Background on topological spaces; Glossary; Further reading; Acknowledgements; Index.