The Joy of Abstraction: An Exploration of Math, Category Theory, and Life
Autor Eugenia Chengen Limba Engleză Hardback – 12 oct 2022
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Specificații
ISBN-10: 1108477224
Pagini: 438
Dimensiuni: 158 x 235 x 30 mm
Greutate: 0.77 kg
Ediția:Nouă
Editura: Cambridge University Press
Colecția Cambridge University Press
Locul publicării:New York, United States
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Cuprins
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.
Recenzii
'Eugenia Cheng loves mathematics—not the ordinary sort that most people encounter, but the most abstract sort that she calls 'the mathematics of mathematics.' And in this lovely excursion through her abstract world of Category Theory, she aims to give those who are willing to join her a glimpse of that world. The journey will change how they view mathematics. Cheng is a brilliant writer, with prose that feels like poetry. Her contagious enthusiasm makes her the perfect guide.' John Ewing, President, Math for America
'Eugenia Cheng's singular contribution is in making abstract mathematics relevant to all through her great ingenuity in developing novel connections between logic and life. Her latest book, The Joy of Abstraction, provides a long awaited fully rigorous yet gentle introduction to the 'mathematics of mathematics,' allowing anyone to experience the joy of learning to think categorically.' Emily Riehl, Johns Hopkins University, author of Category Theory in Context
'Archimedes is quoted as having said once: 'Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty.' In this fascinating book, Eugenia Cheng approaches the abstract mathematical area of Category Theory with pure love, to reveal its beauty to anybody interested in learning something about contemporary mathematics.' Mario Livio, astrophysicist, author of The Golden Ratio and Brilliant Blunders
'Eugenia Cheng's latest book will appeal to a remarkably broad and diverse audience, from non-mathematicians who would like to get a sense of what mathematics is really about, to experienced mathematicians who are not category theorists but would like a basic understanding of category theory. Speaking as one of the latter, I found it a real pleasure to be able to read the book without constantly having to stop and puzzle over the details. I have learnt a lot from it already, including what the famous Yoneda lemma is all about, and I look forward to learning more from it in the future.' Sir Timothy Gowers, Collège de France, Fields Medalist, main editor of The Princeton Companion to Mathematics
'At last: a book that makes category theory as simple as it really is. Cheng explains the subject in a clear and friendly way, in detail, not relying on material that only mathematics majors learn. Category theory – indeed, mathematics as a whole – has been waiting for a book like this.' John Baez, University of California, Riverside
'Many people speak derisively of category theory as the most abstract area of mathematics, but Eugenia Cheng succeeds in redeeming the word 'abstract'. This book is loquacious, conversational, and inviting. Reading this book convinced me I could teach category theory as an introductory course, and that is a real marvel, since it is a subject most people leave for experts.' Francis Su, Harvey Mudd College, author of Mathematics for Human Flourishing
'This higher category theory is the mathematics of the twenty-first century (at least my corner of it). If you'd like a taste of it, I recommend Dr. Cheng's book. The first half is an accessible and thought-provoking insight into categorical thinking. The second half climbs into the rarified air of theoretic math, but it is worth a read to get a feel for what some parts of modern mathematics look like.' Jonathan Kujawa, 3 Quarks Daily
Descriere
Mathematician and popular science author Eugenia Cheng is on a mission to show you that mathematics can be flexible, creative, and visual. This joyful journey through the world of abstract mathematics into category theory will demystify mathematical thought processes and help you develop your own thinking, with no formal mathematical background needed. The book brings abstract mathematical ideas down to earth using examples of social justice, current events, and everyday life – from privilege to COVID-19 to driving routes. The journey begins with the ideas and workings of abstract mathematics, after which you will gently climb toward more technical material, learning everything needed to understand category theory, and then key concepts in category theory like natural transformations, duality, and even a glimpse of ongoing research in higher-dimensional category theory. For fans of How to Bake Pi, this will help you dig deeper into mathematical concepts and build your mathematical background.