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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]

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.
Bibliography Note Includes bibliographical references (page 223) and index.
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 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""; ""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""
Note Print version record.
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