Real analysis through modern infinitesimals / (Record no. 517832)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 02888nam a22003618i 4500 |
| 001 - CONTROL NUMBER | |
| control field | CR9780511740305 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | UkCbUP |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20200124160233.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS--GENERAL INFORMATION | |
| fixed length control field | m|||||o||d|||||||| |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr|||||||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 100408s2011||||enk o ||1 0|eng|d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780511740305 (ebook) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Cancelled/invalid ISBN | 9781107002029 (hardback) |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | UkCbUP |
| Language of cataloging | eng |
| Description conventions | rda |
| Transcribing agency | UkCbUP |
| 050 00 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA300 |
| Item number | .V28 2011 |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 515 |
| Edition number | 22 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Vakil, Nader, |
| Relator term | author. |
| 245 10 - TITLE STATEMENT | |
| Title | Real analysis through modern infinitesimals / |
| Statement of responsibility, etc | Nader Vakil. |
| 264 #1 - Production, Publication, Distribution, Manufacture, and Copyright Notice (R) | |
| Place of production, publication, distribution, manufacture (R) | Cambridge : |
| Name of producer, publisher, distributor, manufacturer (R) | Cambridge University Press, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2011. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (xix, 565 pages) : |
| Other physical details | digital, PDF file(s). |
| 336 ## - Content Type (R) | |
| Content type term (R) | text |
| Content type code (R) | txt |
| Source (NR) | rdacontent |
| 337 ## - Media Type (R) | |
| Media type term (R) | computer |
| Media type code (R) | c |
| Source (NR) | rdamedia |
| 338 ## - Carrier Type (R) | |
| Carrier type term (R) | online resource |
| Carrier type code (R) | cr |
| Source (NR) | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| სერიის ცნობა | Encyclopedia of mathematics and its applications ; |
| Volume number/sequential designation | volume 140 |
| 500 ## - GENERAL NOTE | |
| General note | Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Preface; Introduction; Part I. Elements of Real Analysis: 1. Internal set theory; 2. The real number system; 3. Sequences and series; 4. The topology of R; 5. Limits and continuity; 6. Differentiation; 7. Integration; 8. Sequences and series of functions; 9. Infinite series; Part II. Elements of Abstract Analysis: 10. Point set topology; 11. Metric spaces; 12. Complete metric spaces; 13. Some applications of completeness; 14. Linear operators; 15. Differential calculus on Rn; 16. Function space topologies; A. Vector spaces; B. The b-adic representation of numbers; C. Finite, denumerable, and uncountable sets; D. The syntax of mathematical languages; References; Index. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | Real Analysis Through Modern Infinitesimals provides a course on mathematical analysis based on Internal Set Theory (IST) introduced by Edward Nelson in 1977. After motivating IST through an ultrapower construction, the book provides a careful development of this theory representing each external class as a proper class. This foundational discussion, which is presented in the first two chapters, includes an account of the basic internal and external properties of the real number system as an entity within IST. In its remaining fourteen chapters, the book explores the consequences of the perspective offered by IST as a wide range of real analysis topics are surveyed. The topics thus developed begin with those usually discussed in an advanced undergraduate analysis course and gradually move to topics that are suitable for more advanced readers. This book may be used for reference, self-study, and as a source for advanced undergraduate or graduate courses. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Mathematical analysis. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Set theory. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Display text | Print version: |
| International Standard Book Number | 9781107002029 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Encyclopedia of mathematics and its applications ; |
| Volume number/sequential designation | v. 140. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://doi.org/10.1017/CBO9780511740305">https://doi.org/10.1017/CBO9780511740305</a> |
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