MARC details
| 000 -LEADER |
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05486cam a2200577Mu 4500 |
| 001 - CONTROL NUMBER |
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| control field |
ocn883570436 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
OCoLC |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20240925134500.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS |
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m d |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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cr cnu---unuuu |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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140712s2014 si o 000 0 eng d |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
EBLCP |
| Language of cataloging |
eng |
| Transcribing agency |
EBLCP |
| Modifying agency |
CDX |
| -- |
N$T |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9789814596107 (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9814596108 (electronic bk.) |
| 035 ## - SYSTEM CONTROL NUMBER |
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| System control number |
(OCoLC)883570436 |
| 035 ## - SYSTEM CONTROL NUMBER |
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| System control number |
810377 |
| -- |
(N$T) |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA37.3 .S33 2014 |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
MAT |
| Subject category code subdivision |
039000 |
| Source |
bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE |
|---|
| Subject category code |
MAT |
| Subject category code subdivision |
023000 |
| Source |
bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE |
|---|
| Subject category code |
MAT |
| Subject category code subdivision |
026000 |
| Source |
bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
510 |
| 049 ## - LOCAL HOLDINGS (OCLC) |
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| Holding library |
N$TA |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Schäffer, Juan Jorge. |
| 9 (RLIN) |
1953 |
| 245 10 - TITLE STATEMENT |
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| Title |
Basic Language of Mathematics |
| Medium |
[electronic resource]. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication, distribution, etc. |
Singapore : |
| Name of publisher, distributor, etc. |
World Scientific Publishing Company, |
| Date of publication, distribution, etc. |
2014. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
1 online resource (321 p.) |
| 500 ## - GENERAL NOTE |
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| General note |
Description based upon print version of record. |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
PREFACE; Some symbols; CONTENTS; Index of terms; Index of names; Index of conditions; Index of symbols; Chapter 1. SETS; 11. Introduction; 12. Sets and their members; 13. Inclusion; 14. Set formation; 15. Special sets; 16. Basic operations; 17. Pairs; product sets; 18. Partitions; Chapter 2. MAPPINGS; 21. The concept of a mapping; 22. The graph of a mapping; 23. The range of a mapping; images and pre-images; the partition of a mapping; 24. Inclusion, identity, and partition mappings; 25. Composition of mappings; diagrams; restrictions and adjustments; 26. Mappings from a set to itself |
| 505 8# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Chapter 3. PROPERTIES OF MAPPINGS31. Constants; 32. Injective, surjective, and bijective mappings; 33. Inverses and invertibility; 34. Injectivity, surjectivity, and bijectivity: The induced mappings; 35. Cancellability; 36. Factorization; Chapter 4. FAMILIES; 41. The concept of a family; 42. Special families; 43. Families of sets; 44. Products and direct unions; 45. General associative and distributive laws; 46. Set-products and set-coproducts; Chapter 5. RELATIONS; 51. Relations in a set; 52. Images and pre-images; 53. Reversal, composition, and restriction of relations |
| 505 8# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
54. Relations from set to set functional relations; 55. Properties of relations; 56. Order; 57. Equivalence relations; Chapter 6. ORDERED SETS; 61. Basic concepts; 62. Isotone mappings; 63. Products; 64. Properties of ordered sets; 65. Lexicographic products and ordered direct unions; Chapter 7. COMPLETELY ORDERED SETS; 71. Completely ordered sets; 72. Pre-completely ordered sets; 73. Closure mappings; 74. Galois correspondences; 75. The fixed-point theorem for isotone mappings; Chapter 8. INDUCTION AND RECURSION; 81. Proof by induction; 82. Recursive definitions |
| 505 8# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Chapter 9. THE NATURAL NUMBERS91. Principles of counting; 92. Order; 93. General induction and recursive definitions; 94. Iteration; 95. Essential uniqueness of counting systems; 96. Addition and subtraction; 97. Multiplication and division; 98. Divisors and multiples; Chapter 10. FINITE SETS; 101. Finite sets and their cardinals; 102. Induction; 103. Operations with finite sets; 104. Factorials and binomial coefficients; 105. Orders in finite sets; 106. Finiteness without counting; Chapter 11. FINITE SUMS; 111. Commutative monoids; 112. Finite sums; 113. Sums of families with finite support |
| 505 8# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
114. Repeated and double sums115. Natural multiples; 116. The Inclusion-Exclusion Principle; 117. Sums in monoids of families; 118. Sums without zero; Chapter 12. COUNTABLE SETS; 121. Countable sets; 122. Some uncountable sets; 123. Another characterization of finiteness; Chapter 13. SOME ALGEBRAIC STRUCTURES; 131. Commutative monoids and groups; 132. Commutative rings; 133. Fields; Chapter 14. THE REAL NUMBERS: COMPLETE ORDERED FIELDS; 141. Introduction; 142. Ordered fields; 143. Complete ordered fields; 144. Essential uniqueness of complete ordered fields; Chapter 15. THE REAL-NUMBER SYSTEM |
| 500 ## - GENERAL NOTE |
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| General note |
151. The Real-Number System |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
This book originates as an essential underlying component of a modern, imaginative three-semester honors program (six undergraduate courses) in Mathematical Studies. In its entirety, it covers Algebra, Geometry and Analysis in One Variable. The book is intended to provide a comprehensive and rigorous account of the concepts on sets, mapping, family, order, number (both natural and real), as well as such distinct procedures like Proof by Induction and Recursive Definition , and the interaction between these ideas; with attempts at including insightful notes on historic and cultural settings and. |
| 650 #4 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematical analysis. |
| 9 (RLIN) |
3100 |
| 650 #4 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Mathematics -- History. |
| 9 (RLIN) |
1016481 |
| 650 #4 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Mathematical analysis. |
| 9 (RLIN) |
3100 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
MATHEMATICS / Essays |
| Source of heading or term |
bisacsh |
| 9 (RLIN) |
175516 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
MATHEMATICS / Pre-Calculus |
| Source of heading or term |
bisacsh |
| 9 (RLIN) |
175515 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
MATHEMATICS / Reference |
| Source of heading or term |
bisacsh |
| 9 (RLIN) |
175514 |
| 655 #4 - INDEX TERM--GENRE/FORM |
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| Genre/form data or focus term |
Electronic books. |
| 9 (RLIN) |
396 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
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| Relationship information |
Print version: |
| Main entry heading |
Schäffer, Juan Jorge |
| Title |
Basic Language of Mathematics |
| Place, publisher, and date of publication |
Singapore : World Scientific Publishing Company,c2014 |
| International Standard Book Number |
9789814596091 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
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| Materials specified |
EBSCOhost |
| Uniform Resource Identifier |
<a href="https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=810377">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=810377</a> |
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EBL - Ebook Library |
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EBLB |
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EBL1730185 |
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Coutts Information Services |
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COUT |
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28616133 |
| 938 ## - |
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EBSCOhost |
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EBSC |
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810377 |
| 910 ## - USER-OPTION DATA (OCLC) |
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| User-option data |
cpp1723AUTO |
| 994 ## - |
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02 |
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N$T |