Holdings: Proofs and fundamentals

Proofs and fundamentals: a first course in abstract mathematics

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Bibliographic Details
Main Author:	Bloch, Ethan D. 1956- (Author)
Format:	Book
Language:	English
Published:	Boston [u.a.] Birkhäuser 2000
Subjects:	Ensembles, Théorie des Preuve, Théorie de la Proof theory Set theory Beweistheorie
Online Access:	Inhaltsverzeichnis
Physical Description:	XX, 424 S. Ill., graph. Darst.
ISBN:	9780817641115 3764341114 0817641114

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Record in the Search Index

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adam_text	Contents Introduction ix To the Student xiii To the Instructor xix Parti PROOFS 1 1 Informal Logic 3 1.1 Introduction ......................... 3 1.2 Statements .......................... 4 1.3 Relations Between Statements ............... 18 1.4 Valid Arguments ...................... 31 1.5 Quantifiers .......................... 41 2 Strategies for Proofs 55 2.1 Mathematical Proofs — What They Are and Why We Need Them .................... 55 2.2 Direct Proofs ........................ 63 2.3 Proofs by Contrapositive and Contradiction ........ 67 2.4 Cases, and If and Only If .................. 74 2.5 Quantifiers in Theorems .................. 81 2.6 Writing Mathematics .................... 93 Partii FUNDAMENTALS 105 3 Sets 107 3.1 Introduction ......................... 107 3.2 Sets — Basic Definitions .................. 109 3.3 Set Operations ........................ 119 3.4 Indexed Families of Sets .................. 129 4 Functions 135 4.1 Functions ..........................135 4.2 Image and Inverse Image .................. 145 4.3 Composition and Inverse Functions ............. 152 4.4 Injectivity, Surjectivity and Bijectivity ........... 161 4.5 Sets of Functions ...................... 170 5 Relations 177 5.1 Relations .......................... 177 5.2 Congruence ......................... 184 5.3 Equivalence Relations .................... 191 6 Infinite and Finite Sets 203 6.1 Cardinality of Sets ..................... 203 6.2 Cardinality of the Number Systems ............. 218 6.3 Mathematical Induction ................... 226 6.4 Recursion .......................... 236 Partili EXTRAS 249 7 Selected Topics 251 7.1 Binary Operations ...................... 251 7.2 Groups ............................ 258 7.3 Homomorphisms and Isomorphisms ............ 267 7.4 Partially Ordered Sets .................... 273 7.5 Lattices ........................... 284 7.6 Counting: Products and Sums ................ 294 7.7 Counting: Permutations and Combinations ......... 304 8 Number Systems 323 8.1 Back to the Beginning ................... 323 8.2 The Natural Numbers .................... 324 8.3 Further Properties of the Natural Numbers ......... 333 8.4 The Integers ......................... 338 8.5 The Rational Numbers ................... 348 8.6 The Real Numbers and the Complex Numbers ....... 352 8.7 Appendix: Proof of Theorem 8.2.1............. 361 9 Explorations 363 9.1 Introduction ......................... 363 9.2 Greatest Common Divisors ................. 364 9.3 Divisibility Tests ...................... 366 9.4 Real-Valued Functions ................... 367 9.5 Iterations of Functions ................... 368 9.6 Fibonacci Numbers and Lucas Numbers .......... 369 9.7 Fuzzy Sets .......................... 371 Appendix: Properties of Numbers 375 Hints for Selected Exercises 379 References 405 Index 413
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indexdate	2024-07-09T18:41:55Z
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isbn	9780817641115 3764341114 0817641114
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spelling	Bloch, Ethan D. 1956- Verfasser (DE-588)143980874 aut Proofs and fundamentals a first course in abstract mathematics Ethan D. Bloch Boston [u.a.] Birkhäuser 2000 XX, 424 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Ensembles, Théorie des Preuve, Théorie de la Proof theory Set theory Beweistheorie (DE-588)4145177-6 gnd rswk-swf Beweistheorie (DE-588)4145177-6 s DE-604 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009007887&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Bloch, Ethan D. 1956- Proofs and fundamentals a first course in abstract mathematics Ensembles, Théorie des Preuve, Théorie de la Proof theory Set theory Beweistheorie (DE-588)4145177-6 gnd
subject_GND	(DE-588)4145177-6
title	Proofs and fundamentals a first course in abstract mathematics
title_auth	Proofs and fundamentals a first course in abstract mathematics
title_exact_search	Proofs and fundamentals a first course in abstract mathematics
title_full	Proofs and fundamentals a first course in abstract mathematics Ethan D. Bloch
title_fullStr	Proofs and fundamentals a first course in abstract mathematics Ethan D. Bloch
title_full_unstemmed	Proofs and fundamentals a first course in abstract mathematics Ethan D. Bloch
title_short	Proofs and fundamentals
title_sort	proofs and fundamentals a first course in abstract mathematics
title_sub	a first course in abstract mathematics
topic	Ensembles, Théorie des Preuve, Théorie de la Proof theory Set theory Beweistheorie (DE-588)4145177-6 gnd
topic_facet	Ensembles, Théorie des Preuve, Théorie de la Proof theory Set theory Beweistheorie
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