The tools of mathematical reasoning:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2016]
|
| Schriftenreihe: | Pure and applied undergraduate texts
26 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xiii, 217 Seiten Illustrationen, Diagramme |
| ISBN: | 9781470428990 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804176898616459264 |
|---|---|
| adam_text | Titel: The tools of mathematical reasoning
Autor: Lakins, Tamara J
Jahr: 2016
Contents
Preface ix
To Students xii
Acknowledgements xiii
Chapter 1. Language, Logic, and Proof 1
1.1. Language and logic 1
1.2. Proof 16
Chapter 2. Techniques of Proof 25
2.1. More direct proofs 25
2.2. Indirect proofs: Proofs by contradiction and contrapositive 38
2.3. Two important theorems 44
2.4. Proofs of statements involving mixed quantifiers 47
Chapter 3. Induction 53
3.1. Principie of Mathematical Induction 53
3.2. Strong induction 61
Chapter 4. Sets 67
4.1. The language of sets 67
4.2. Operations on sets 74
4.3. Arbitrary unions and intersections 83
4.4. Axiomatic set theory 89
Chapter 5. Functions 93
5.1. Definitions 93
5.2. Function composition 104
5.3. One-to-one and onto functions 107
vii
viii
Contents
5.4. Invertible functions 114
5.5. Functions and sets 121
Chapter 6. An Introduction to Number Theory 131
6.1. The Division Algorithm and the Well-Ordering Principie 131
6.2. Greatest common divisors and the Euclidean Algorithm 135
6.3. Relatively prime integers and the Fundamental Theorem
of Arithmetic 141
6.4. Congruences 145
6.5. Congruence classes 149
Chapter 7. Equivalence Relations and Partitions 155
7.1. Introduction 155
7.2. Equivalence relations 157
7.3. Partitions 162
Chapter 8. Finite and Infinite Sets 167
8.1. Introduction 167
8.2. Finite sets 170
8.3. Infinite sets 179
8.4. What next? 188
Chapter 9. Foundations of Analysis 191
9.1. Introduction 191
9.2. The Completeness Axiom 193
9.3. The Archimedean Property and its consequences 202
9.4. What next? 207
Appendix. Writing Mathematics 209
Bibliography 211
Index 213
|
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| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-10T07:39:30Z |
| institution | BVB |
| isbn | 9781470428990 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029358330 |
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| physical | xiii, 217 Seiten Illustrationen, Diagramme |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Pure and applied undergraduate texts |
| series2 | Pure and applied undergraduate texts The Sally series |
| spelling | Lakins, Tamara J. 1963- Verfasser (DE-588)1120044596 aut The tools of mathematical reasoning Tamara J. Lakins Providence, Rhode Island American Mathematical Society [2016] xiii, 217 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Pure and applied undergraduate texts 26 The Sally series Includes bibliographical references and index Beweisführung (DE-588)4227233-6 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Mathematik (DE-588)4037944-9 s Beweisführung (DE-588)4227233-6 s DE-604 Pure and applied undergraduate texts 26 (DE-604)BV035489189 26 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029358330&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lakins, Tamara J. 1963- The tools of mathematical reasoning Pure and applied undergraduate texts Beweisführung (DE-588)4227233-6 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4227233-6 (DE-588)4037944-9 |
| title | The tools of mathematical reasoning |
| title_auth | The tools of mathematical reasoning |
| title_exact_search | The tools of mathematical reasoning |
| title_full | The tools of mathematical reasoning Tamara J. Lakins |
| title_fullStr | The tools of mathematical reasoning Tamara J. Lakins |
| title_full_unstemmed | The tools of mathematical reasoning Tamara J. Lakins |
| title_short | The tools of mathematical reasoning |
| title_sort | the tools of mathematical reasoning |
| topic | Beweisführung (DE-588)4227233-6 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Beweisführung Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029358330&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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