The Joy of Abstraction
Autor Eugenia Chengen Limba Engleză Paperback – 3 apr 2024
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|---|---|---|
| Paperback (1) | 100.01 lei 3-5 săpt. | +30.89 lei 6-12 zile |
| Cambridge University Pr. – 3 apr 2024 | 100.01 lei 3-5 săpt. | +30.89 lei 6-12 zile |
| Hardback (1) | 109.89 lei 3-5 săpt. | +26.68 lei 6-12 zile |
| Cambridge University Press – 12 oct 2022 | 109.89 lei 3-5 săpt. | +26.68 lei 6-12 zile |
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Specificații
ISBN-13: 9781108708449
ISBN-10: 1108708447
Ilustrații: Worked examples or Exercises
Dimensiuni: 152 x 228 x 37 mm
Greutate: 0.75 kg
Ediția:Nouă
Editura: Cambridge University Pr.
ISBN-10: 1108708447
Ilustrații: Worked examples or Exercises
Dimensiuni: 152 x 228 x 37 mm
Greutate: 0.75 kg
Ediția:Nouă
Editura: Cambridge University Pr.
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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
'Finally, a book about category theory that doesn't assume you already know category theory! In this inviting but rigorous introduction to what she calls 'the mathematics of mathematics', Eugenia Cheng brings the subject to us with insight, wit, and a point of view. Her story of finding joy-and advantage-in abstraction will inspire you to find it, too.' Patrick Honner, award-winning high school math teacher, columnist for Quanta Magazine, author of Painless Statistics
'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
'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