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Bridge to abstract mathematics /
Of the Properties of the Nonnegative IntegersThe 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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
[Washington, DC] :
Mathematical Association of America,
©2012.
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| Colección: | MAA textbooks.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Oberste-Vorth, Ralph W., |d 1959- | |
| 245 | 1 | 0 | |a Bridge to abstract mathematics / |c Ralph W. Oberste-Vorth, Aristides Mouzakitis, Bonita A. Lawrence. |
| 260 | |a [Washington, DC] : |b Mathematical Association of America, |c ©2012. | ||
| 300 | |a 1 online resource (xix, 232 pages) : |b illustrations | ||
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| 504 | |a Includes bibliographical references (page 223) and index. | ||
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| 505 | 0 | |a 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 | |
| 505 | 8 | |a Mathematical ConnectivesSymbolic 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 | |
| 505 | 8 | |a Intersections and UnionsIntersections 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 | |
| 505 | 8 | |a Supplemental ExercisesCardinality -- Cardinality of Sets: Introduction -- Finite Sets -- Infinite Sets -- Countable Sets -- Uncountable Sets -- Supplemental Exercises -- III NUMBER SYSTEMS -- Algebra of Number Systems -- 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 | |
| 505 | 8 | |a Summary of the Properties of the Nonnegative IntegersThe 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 | |
| 520 | |a Of the Properties of the Nonnegative IntegersThe 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 | ||
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