A transition to proof: an introduction to advanced mathematics
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton ; London ; New York
CRC Press
[2019]
|
| Schriftenreihe: | Textbooks in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xiii, 450 Seiten Diagramme 23 cm |
| ISBN: | 9780367201579 0367201577 |
Internformat
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| 245 | 1 | 0 | |a A transition to proof |b an introduction to advanced mathematics |c Neil R. Nicholson |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents Preface 1 ix Symbolic Logic 1.1 Statements and Statement Forms .......................................... 1.2 Conditional and Biconditional Connective.............................. 1.3 Arguments ................................................................................. 1.4 Logical Deductions .................................................................. 2 Sets 2.1 2.2 2.3 2.4 What is Proof? ........................................................................ Direct Proofs.............................................................................. Direct Proofs: Set Element Method ....................................... Proof by Contrapositive and Contradiction........................... Proof by Cases........................................................................... 4 Mathematical Induction 4.1 4.2 4.3 Basics of Mathematical Induction .......................................... Strong Mathematical Induction ............................................. Applications of Induction: Number Theory ........................... 5 Relations 5.1 5.2 5.3 5.4 Mathematical Relations............................................................ Equivalence Relations............................................................... Order Relations ........................................................................ Congruence Modulo m Relation ............................................. 6 Functions 6.1 6.2 6.3 2 16 28 37 49 Set Theory Basics ..................................................................... Properties of Sets
..................................................................... Quantified Statements............................................................... Multiple Quantifiers and Arguments with Quantifiers .... 3 Introduction to Proofs 3.1 3.2 3.3 3.4 3.5 1 Functions Defined ..................................................................... Properties of Functions ............................................................ Composition and Invertibility ................................................ 50 63 78 88 103 105 120 135 147 159 171 172 187 203 221 222 237 250 262 279 280 298 313 vii
viii Contents 7 Cardinality 7.1 The Finite .................................................................................... 7.2 The Infinite: Countable .............................................................. 7.3 The Infinite: Uncountable........................................................... 327 328 345 358 8 Introduction to Topology 8.1 Topologies and Topological Spaces............................................ 8.2 Subspace and Product Topologies ............................................ 8.3 Closed Sets and Closure.............................................................. 8.4 Continuous Functions ................................................................. 371 372 380 388 398 Appendix A: Properties of Real NumberSystem 409 Appendix B: Proof Writing Tips 413 Appendix C: Selected Solutions and Hints 421 Bibliography 441 Index 445
|
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| author | Nicholson, Neil R. |
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| author_facet | Nicholson, Neil R. |
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| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:33:52Z |
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| isbn | 9780367201579 0367201577 |
| language | English |
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| spelling | Nicholson, Neil R. Verfasser (DE-588)1185778829 aut A transition to proof an introduction to advanced mathematics Neil R. Nicholson Boca Raton ; London ; New York CRC Press [2019] xiii, 450 Seiten Diagramme 23 cm txt rdacontent n rdamedia nc rdacarrier Textbooks in mathematics Includes bibliographical references and index Beweistheorie (DE-588)4145177-6 gnd rswk-swf Proof theory Beweistheorie (DE-588)4145177-6 s DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031432928&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nicholson, Neil R. A transition to proof an introduction to advanced mathematics Beweistheorie (DE-588)4145177-6 gnd |
| subject_GND | (DE-588)4145177-6 |
| title | A transition to proof an introduction to advanced mathematics |
| title_auth | A transition to proof an introduction to advanced mathematics |
| title_exact_search | A transition to proof an introduction to advanced mathematics |
| title_full | A transition to proof an introduction to advanced mathematics Neil R. Nicholson |
| title_fullStr | A transition to proof an introduction to advanced mathematics Neil R. Nicholson |
| title_full_unstemmed | A transition to proof an introduction to advanced mathematics Neil R. Nicholson |
| title_short | A transition to proof |
| title_sort | a transition to proof an introduction to advanced mathematics |
| title_sub | an introduction to advanced mathematics |
| topic | Beweistheorie (DE-588)4145177-6 gnd |
| topic_facet | Beweistheorie |
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