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03913cam a2200457 i 4500 |
| 001 - CONTROL NUMBER |
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u10595 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
SA-PMU |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20210418123709.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
140716s2015 enka b 001 0 eng |
| 010 ## - LIBRARY OF CONGRESS CONTROL NUMBER |
|---|
| LC control number |
2014946122 |
| 040 ## - CATALOGING SOURCE |
|---|
| Original cataloging agency |
DLC |
| Language of cataloging |
eng |
| Description conventions |
rda |
| Transcribing agency |
DLC |
| Modifying agency |
CUD |
| -- |
YDXCP |
| -- |
LTSCA |
| -- |
OCLCF |
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MNY |
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VP@ |
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CDX |
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OCLCQ |
| -- |
OCL |
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VMI |
| 019 ## - |
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| -- |
905066266 |
| -- |
905486162 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9780198706441 |
| Qualifying information |
(hbk.) |
| 035 ## - SYSTEM CONTROL NUMBER |
|---|
| System control number |
(OCoLC)908132554 |
| Canceled/invalid control number |
(OCoLC)905066266 |
| -- |
(OCoLC)905486162 |
| 042 ## - AUTHENTICATION CODE |
|---|
| Authentication code |
pcc |
| 050 00 - LIBRARY OF CONGRESS CALL NUMBER |
|---|
| Classification number |
QA9 |
| Item number |
.S755 2015 |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER |
|---|
| Classification number |
511.3 |
| Edition number |
23 |
| 029 1# - OTHER SYSTEM CONTROL NUMBER (OCLC) |
|---|
| OCLC library identifier |
AU@ |
| System control number |
000054954700 |
| 029 1# - OTHER SYSTEM CONTROL NUMBER (OCLC) |
|---|
| OCLC library identifier |
NZ1 |
| System control number |
15993592 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Stewart, Ian, |
| Dates associated with a name |
1945- |
| Relator term |
author. |
| 245 14 - TITLE STATEMENT |
|---|
| Title |
The foundations of mathematics / |
| Statement of responsibility, etc. |
Ian Stewart and David Tall. |
| 250 ## - EDITION STATEMENT |
|---|
| Edition statement |
Second edition. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE |
|---|
| Place of production, publication, distribution, manufacture |
Oxford : |
| Name of producer, publisher, distributor, manufacturer |
Oxford University Press, |
| Date of production, publication, distribution, manufacture, or copyright notice |
2015. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
xvi, 391 pages : |
| Other physical details |
illustrations ; |
| Dimensions |
23 cm |
| 336 ## - CONTENT TYPE |
|---|
| Content type term |
text |
| Content type code |
txt |
| Source |
rdacontent |
| 337 ## - MEDIA TYPE |
|---|
| Media type term |
unmediated |
| Media type code |
n |
| Source |
rdamedia |
| 338 ## - CARRIER TYPE |
|---|
| Carrier type term |
volume |
| Carrier type code |
nc |
| Source |
rdacarrier |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
|---|
| Bibliography, etc. note |
Includes bibliographical references (pages 383-385) and index. |
| 520 ## - SUMMARY, ETC. |
|---|
| Summary, etc. |
The transition from school to university mathematics is seldom straightforward. Students face a schism between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory. The authors have many years' experience of the potential difficulties involved, through teaching first-year undergraduates and researching the ways in which students and mathematicians think. This book explains the motivation behind abstract foundational material based on students' experiences of school mathematics, and explicitly suggests ways students can make sense of formal ideas. This second edition takes a significant step forward by not only making the transition from intuitive to formal methods, but also by reversing the process, using structure theorems to prove that formal systems have visual and symbolic interpretations that enhance mathematical thinking. This is exemplified by a new chapter on the theory of groups. While the first edition extended counting to infinite cardinal numbers, the second also extends the real numbers rigorously to larger ordered fields. This links intuitive ideas in calculus to the formal epsilon--delta methods of analysis. The approach here is not the conventional one of 'nonstandard analysis', but a simpler, graphically based treatment which makes the notion of an infinitesimal natural and straightforward. This allows a further vision of the wider world of mathematical thinking in which formal definitions and proofs lead to amazing new ways of defining, proving, visualising, and symbolising mathematics beyond previous expectations. -- Back cover. |
| 505 0# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
Part I. The intuitive background -- 1. Mathematical thinking -- 2. Number systems -- Part II. The beginnings of formalisation -- 3. Sets -- 4. Relations -- 5. Functions -- 6. Mathematical logic -- 7. Mathematical proof -- Part III. The development of axiomatic systems -- 8. Natural numbers and proof by induction -- 9. Real numbers -- 10. Real numbers as a complete ordered field -- 11. Complex numbers and beyond -- Part IV. Using axiomatic systems -- 12. Axiomatic systems, structure theorems, and flexible thinking -- 13. Permutations and groups -- 14. Cardinal numbers -- 15. Infinitesimals -- Part V. Strengthening the foundations -- 16. Axioms for set theory. |
| 596 ## - |
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| -- |
1 2 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Logic, Symbolic and mathematical. |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Logic, Symbolic and mathematical. |
| Source of heading or term |
fast |
| Authority record control number or standard number |
(OCoLC)fst01002068 |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
|---|
| Personal name |
Tall, David Orme, |
| Relator term |
author. |
| 938 ## - |
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Coutts Information Services |
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COUT |
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28729422 |
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YBP Library Services |
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YANK |
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12034252 |
| 938 ## - |
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YBP Library Services |
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YANK |
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12034253 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Koha item type |
Books |
| 994 ## - |
|---|
| -- |
Z0 |
| -- |
SUPMU |
| 948 ## - LOCAL PROCESSING INFORMATION (OCLC); SERIES PART DESIGNATOR (RLIN) |
|---|
| h (OCLC) |
NO HOLDINGS IN SUPMU - 211 OTHER HOLDINGS |