| Description |
1 online resource (xix, 232 pages) : illustrations |
| Series |
MAA textbooks |
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MAA textbooks.
|
| 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 |
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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 |
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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 |
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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 |
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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 |
| 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 |
| Bibliography |
Includes bibliographical references (page 223) and index |
| Notes |
Print version record |
| Subject |
Logic, Symbolic and mathematical -- Textbooks
|
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Mathematics -- Textbooks
|
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MATHEMATICS -- Infinity.
|
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MATHEMATICS -- Logic.
|
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Logic, Symbolic and mathematical
|
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Mathematics
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|
Beweis
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Mathematik
|
| Genre/Form |
Textbooks
|
| Form |
Electronic book
|
| Author |
Mouzakitis, Aristides
|
|
Lawrence, Bonita A., 1957-
|
| ISBN |
9781614446064 |
|
1614446067 |
|
9781470453039 |
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1470453037 |
|
