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Author Oberste-Vorth, Ralph W., 1959-
Title Bridge to abstract mathematics / Ralph W. Oberste-Vorth, Aristides Mouzakitis, Bonita A. Lawrence.
Imprint [Washington, DC] : Mathematical Association of America, [2012]

Author Oberste-Vorth, Ralph W., 1959-
Series MAA textbooks.
MAA textbooks.
Subject Logic, Symbolic and mathematical -- Textbooks.
Mathematics -- Textbooks.
Alt Name Mouzakitis, Aristides.
Lawrence, Bonita A., 1957-
Description 1 online resource (xix, 232 pages) : illustrations.
polychrome rdacc
Bibliography Note Includes bibliographical references (page 223) and index.
Note Print version record.
Contents 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 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
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
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
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
ISBN 9781614446064 (electronic bk.)
1614446067 (electronic bk.)
OCLC # 818906408
Additional Format Print version: Oberste-Vorth, Ralph W., 1959- Bridge to abstract mathematics. [Washington, DC] : Mathematical Association of America, ©2012 9780883857793 (OCoLC)809028598.

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