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Handbook of Constructive Mathematics (Encyclopedia of Mathematics and its Ap...
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Numero oggetto eBay:197239109452
Specifiche dell'oggetto
- Condizione
- Release Year
- 2023
- Book Title
- Handbook of Constructive Mathematics (Encyclopedia of Mathemat...
- ISBN
- 9781316510865
Informazioni su questo prodotto
Product Identifiers
Publisher
Cambridge University Press
ISBN-10
1316510867
ISBN-13
9781316510865
eBay Product ID (ePID)
5058378218
Product Key Features
Number of Pages
800 Pages
Publication Name
Handbook of Constructive Mathematics
Language
English
Publication Year
2023
Subject
General, Logic
Type
Textbook
Subject Area
Mathematics
Series
Encyclopedia of Mathematics and Its Applications Ser.
Format
Hardcover
Dimensions
Item Height
1.9 in
Item Length
9.8 in
Item Width
6.9 in
Additional Product Features
Dewey Edition
23
Illustrated
Yes
Dewey Decimal
511.3
Table Of Content
Preface Douglas Bridges, Hajime Ishihara, Michael Rathjen and Helmut Schwichtenberg; Part I. Introductory: 1. Introduction to intuitionistic logic Michael Rathjen; 2. Introduction to CZF: an appetizer Michael Rathjen; 3. Bishop's mathematics: a philosophical perspective Laura Crosilla; Part II. Algebra and Geometry: 4. Algebra in Bishop's style: a course in constructive algebra Henri Lombardi; 5. Constructive algebra: the Quillen-Suslin theorem Ihsen Yengui; 6. Constructive algebra and point-free topology Thierry Coquand; 7. Constructive projective geometry Mark Mandelkern; Part III. Analysis: 8. Elements of constructive analysis Hajime Ishihara; 9. Constructive functional analysis Hajime Ishihara; 10. Constructive Banach algebra theory Robin Havea and Douglas Bridges; 11. Constructive convex optimization Josef Berger and Gregor Svindland; 12. Constructive mathematical economics Matthew Hendtlass and Douglas Bridges; 13. Constructive stochastic processes Yuen-Kwok Chan; Part IV. Topology: 14. Bases of pseudocompact Bishop spaces Iosif Petrakis; 15. Bishop metric spaces in formal topology Tatsuji Kawai; 16. Subspaces in point free topology and measure theory Francesco Ciraulo; 17. Synthetic topology Davorin Lesnik; 18. Apartness on lattices and between sets Douglas Bridges; Part V. Logic and Foundations: 19. Countable choice Fred Richman; 20. The Minimalist Foundation and Bishop's constructive mathematics Maria Maietti, Giovanni Sambin; 21. Identity, equality, and extensionality in explicit mathematics Gerhard Jäger; 22. Inner and outer models for constructive set theories Robert Lubarsky; 23. An introduction to constructive reverse mathematics Hajime Ishihara; 24. Systems for constructive reverse mathematics Takako Nemoto; 25. Brouwer's fan theorem Josef Berger; Part VI. Aspects of Computation: 26. Computational aspects of Bishop's constructive mathematics Helmut Schwichtenberg; 27. Application of constructive analysis in exact real arithmetic Kenji Miyamoto; 28. Efficient algorithms from proofs in constructive analysis Mark Bickford; 29. On the computational content of choice principles Ulrich Berger and Monika Seisenberger; Index.
Synopsis
Constructive mathematics - mathematics in which 'there exists' always means 'we can construct' - is enjoying a renaissance. fifty years on from Bishop's groundbreaking account of constructive analysis, constructive mathematics has spread out to touch almost all areas of mathematics and to have profound influence in theoretical computer science. This handbook gives the most complete overview of modern constructive mathematics, with contributions from leading specialists surveying the subject's myriad aspects. Major themes include: constructive algebra and geometry, constructive analysis, constructive topology, constructive logic and foundations of mathematics, and computational aspects of constructive mathematics. A series of introductory chapters provides graduate students and other newcomers to the subject with foundations for the surveys that follow. Edited by four of the most eminent experts in the field, this is an indispensable reference for constructive mathematicians and a fascinating vista of modern constructivism for the increasing number of researchers interested in constructive approaches., This handbook gives a complete overview of modern constructive mathematics - mathematics in which 'there exists' always means 'we can construct' - and its applications. Written and edited by leading experts, it is an indispensable reference for established constructive mathematicians and guide to the field for graduate students and other newcomers.
LC Classification Number
QA9.56
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