How We Got from There to Here (Record no. 38469)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 03215nam a2200373 i 4500 |
| 001 - CONTROL NUMBER | |
| control field | OTLid0000200 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MnU |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20241120064009.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS--GENERAL INFORMATION | |
| fixed length control field | m o d s |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 180907s2014 mnu o 0 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781312348691 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MnU |
| Language of cataloging | eng |
| Transcribing agency | MnU |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA1 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Rogers, Robert |
| Relator term | author |
| 245 00 - TITLE STATEMENT | |
| Title | How We Got from There to Here |
| Remainder of title | A Story of Real Analysis |
| Statement of responsibility, etc | Robert Rogers |
| 264 #2 - | |
| -- | Minneapolis, MN |
| -- | Open Textbook Library |
| 264 #1 - | |
| -- | [Place of publication not identified] |
| -- | Open SUNY |
| -- | [2014] |
| 264 #4 - | |
| -- | ©2014. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 490 0# - SERIES STATEMENT | |
| Series statement | Open textbook library. |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 1 Numbers, Real (R) and Rational (Q) -- 2 Calculus in the 17th and 18th Centuries -- 3 Questions Concerning Power Series -- 4 Convergence of Sequences and Series -- 5 Convergence of the Taylor Series: A “Tayl” of Three Remainders -- 6 Continuity: What It Isn't and What It Is -- 7 Intermediate and Extreme Values -- 8 Back to Power Series -- 9 Back to the Real Numbers |
| 520 0# - SUMMARY, ETC. | |
| Summary, etc | The typical introductory real analysis text starts with an analysis of the real number system and uses this to develop the definition of a limit, which is then used as a foundation for the definitions encountered thereafter. While this is certainly a reasonable approach from a logical point of view, it is not how the subject evolved, nor is it necessarily the best way to introduce students to the rigorous but highly non-intuitive definitions and proofs found in analysis. This book proposes that an effective way to motivate these definitions is to tell one of the stories (there are many) of the historical development of the subject, from its intuitive beginnings to modern rigor. The definitions and techniques are motivated by the actual difficulties encountered by the intuitive approach and are presented in their historical context. However, this is not a history of analysis book. It is an introductory analysis textbook, presented through the lens of history. As such, it does not simply insert historical snippets to supplement the material. The history is an integral part of the topic, and students are asked to solve problems that occur as they arise in their historical context. This book covers the major topics typically addressed in an introductory undergraduate course in real analysis in their historical order. Written with the student in mind, the book provides guidance for transforming an intuitive understanding into rigorous mathematical arguments. For example, in addition to more traditional problems, major theorems are often stated and a proof is outlined. The student is then asked to fill in the missing details as a homework problem. |
| 542 1# - | |
| -- | Attribution-NonCommercial-ShareAlike |
| 546 ## - LANGUAGE NOTE | |
| Language note | In English. |
| 588 0# - | |
| -- | Description based on print resource |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Mathematics |
| Form subdivision | Textbooks |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Boman, Eugene |
| Relator term | author |
| 710 2# - ADDED ENTRY--CORPORATE NAME | |
| Corporate name or jurisdiction name as entry element | Open Textbook Library |
| Relator term | distributor |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://open.umn.edu/opentextbooks/textbooks/200">https://open.umn.edu/opentextbooks/textbooks/200</a> |
| Public note | Access online version |
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