The Joy of Abstraction

An Exploration of Math, Category Theory, and Life
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ISBN-13:
9781108477222
Veröffentl:
2022
Erscheinungsdatum:
13.10.2022
Seiten:
424
Autor:
Eugenia Cheng
Gewicht:
764 g
Format:
240x155x30 mm
Sprache:
Englisch
Beschreibung:

This popular undergraduate quantum mechanics textbook is now available in a more affordable printing from Cambridge University Press. Suitable for undergraduate physics students, worked examples are included throughout and end of chapter problems act to reinforce and extend key concepts. A fully worked solutions manual is available for instructors.
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.

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