Bridge to Abstract Mathematics. (Record no. 79879)
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| fixed length control field | 07652nam a22005053i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC3330426 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240729125050.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2012 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781614446064 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9780883857793 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC3330426 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL3330426 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (CaPaEBR)ebr10733069 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)929120364 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA36.O24 2012eb |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 511.3 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Oberste-Vorth, Ralph W. |
| 245 10 - TITLE STATEMENT | |
| Title | Bridge to Abstract Mathematics. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Providence : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2012. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2012. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (254 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | AMS/MAA Textbooks Series ; |
| Volume/sequential designation | v.56 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | front cover -- copyright page -- title page -- Contents -- Some Notes on Notation -- To the Students -- To Those Beginning the Journey into Proof Writing -- How to Use This Text -- Do the Exercises! -- Acknowledgments -- For the Professors -- To Those Leading the Development of Proof Writing for Students in a Broad Range of Disciplines -- I THE AXIOMATIC METHOD -- Introduction -- The History of Numbers -- The Algebra of Numbers -- The Axiomatic Method -- Parallel Mathematical Universes -- Statements in Mathematics -- Mathematical Statements -- Mathematical Connectives -- Symbolic Logic -- Compound Statements in English -- Predicates and Quantifiers -- Supplemental Exercises -- Proofs in Mathematics -- What is Mathematics? -- Direct Proof -- Contraposition and Proof by Contradiction -- Proof by Induction -- Proof by Complete Induction -- Examples and Counterexamples -- Supplemental Exercises -- How to THINK about mathematics: A Summary -- How to COMMUNICATE mathematics: A Summary -- How to DO mathematics: A Summary -- II SET THEORY -- Basic Set Operations -- Introduction -- Subsets -- Intersections and Unions -- Intersections and Unions of Arbitrary Collections -- Differences and Complements -- Power Sets -- Russell's Paradox -- Supplemental Exercises -- Functions -- Functions as Rules -- Cartesian Products, Relations, and Functions -- Injective, Surjective, and Bijective Functions -- Compositions of Functions -- Inverse Functions and Inverse Images of Functions -- Another Approach to Compositions -- Supplemental Exercises -- Relations on a Set -- Properties of Relations -- Order Relations -- Equivalence Relations -- Supplemental Exercises -- Cardinality -- Cardinality of Sets: Introduction -- Finite Sets -- Infinite Sets -- Countable Sets -- Uncountable Sets -- Supplemental Exercises -- III NUMBER SYSTEMS -- Algebra of Number Systems. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Introduction: A Road Map -- Primary Properties of Number Systems -- Secondary Properties -- Isomorphisms and Embeddings -- Archimedean Ordered Fields -- Supplemental Exercises -- The Natural Numbers -- Introduction -- Zero, the Natural Numbers, and Addition -- Multiplication -- Supplemental Exercises -- Summary of the Properties of the Nonnegative Integers -- The Integers -- Introduction: Integers as Equivalence Classes -- A Total Ordering of the Integers -- Addition of Integers -- Multiplication of Integers -- Embedding the Natural Numbers in the Integers -- Supplemental Exercises -- Summary of the Properties of the Integers -- The Rational Numbers -- Introduction: Rationals as Equivalence Classes -- A Total Ordering of the Rationals -- Addition of Rationals -- Multiplication of Rationals -- An Ordered Field Containing the Integers -- Supplemental Exercises -- Summary of the Properties of the Rationals -- The Real Numbers -- Dedekind Cuts -- Order and Addition of Real Numbers -- Multiplication of Real Numbers -- Embedding the Rationals in the Reals -- Uniqueness of the Set of Real Numbers -- Supplemental Exercises -- Cantor's Reals -- Convergence of Sequences of Rational Numbers -- Cauchy Sequences of Rational Numbers -- Cantor's Set of Real Numbers -- The Isomorphism from Cantor's to Dedekind's Reals -- Supplemental Exercises -- The Complex Numbers -- Introduction -- Algebra of Complex Numbers -- Order on the Complex Field -- Embedding the Reals in the Complex Numbers -- Supplemental Exercises -- IV TIME SCALES -- Time Scales -- Introduction -- Preliminary Results -- The Time Scale and its Jump Operators -- Limits and Continuity -- Supplemental Exercises -- The Delta Derivative -- Delta Differentiation -- Higher Order Delta Differentiation -- Properties of the Delta Derivative -- Supplemental Exercises -- V HINTS. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Hints for (and Comments on) the Exercises -- Hints for Chapter 2 -- Hints for Chapter 3 -- Hints for Chapter 4 -- Hints for Chapter 5 -- Hints for Chapter 6 -- Hints for Chapter 7 -- Hints for Chapter 8 -- Hints for Chapter 9 -- Hints for Chapter 10 -- Hints for Chapter 11 -- Hints for Chapter 12 -- Hints for Chapter 13 -- Hints for Chapter 14 -- Hints for Chapter 15 -- Hints for Chapter 16 -- Bibliography -- Index -- About the Authors -- Back Cover. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | A Bridge to Abstract Mathematics will prepare the mathematical novice to explore the universe of abstract mathematics. Mathematics is a science that concerns theorems that must be proved within the constraints of a logical system of axioms and definitions rather than theories that must be tested, revised, and retested. Readers will learn how to read mathematics beyond popular computational calculus courses. Moreover, readers will learn how to construct their own proofs. The book is intended as the primary text for an introductory course in proving theorems, as well as for self-study or as a reference. Throughout the text, some pieces (usually proofs) are left as exercises. Part V gives hints to help students find good approaches to the exercises. Part I introduces the language of mathematics and the methods of proof. The mathematical content of Parts II through IV were chosen so as not to seriously overlap the standard mathematics major. In Part II, students study sets, functions, equivalence and order relations, and cardinality. Part III concerns algebra. The goal is to prove that the real numbers form the unique, up to isomorphism, ordered field with the least upper bound. In the process, we construct the real numbers starting with the natural numbers. Students will be prepared for an abstract linear algebra or modern algebra course. Part IV studies analysis. Continuity and differentiation are considered in the context of time scales (nonempty, closed subsets of the real numbers). Students will be prepared for advanced calculus and general topology courses. There is a lot of room for instructors to skip and choose topics from among those that are presented. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Mathematics. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Mouzakitis, Aristides. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Lawrence, Bonita A. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Oberste-Vorth, Ralph W. |
| Title | Bridge to Abstract Mathematics |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c2012 |
| International Standard Book Number | 9780883857793 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | AMS/MAA Textbooks Series |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3330426">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3330426</a> |
| Public note | Click to View |
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