A transition to proof: an introduction to advanced mathematics
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton ; London ; New York
CRC Press
[2019]
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| Series: | Textbooks in mathematics
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | xiii, 450 Seiten Diagramme 23 cm |
| ISBN: | 9780367201579 0367201577 |
Staff View
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Record in the Search Index
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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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| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
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| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| indexdate | 2025-01-10T19:04:55Z |
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| isbn | 9780367201579 0367201577 |
| language | English |
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| physical | xiii, 450 Seiten Diagramme 23 cm |
| publishDate | 2019 |
| publishDateSearch | 2019 |
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| publisher | CRC Press |
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| series2 | Textbooks in mathematics |
| 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 Beweis (DE-588)4132532-1 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Proof theory Beweistheorie (DE-588)4145177-6 s DE-604 Beweis (DE-588)4132532-1 s Mathematik (DE-588)4037944-9 s 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 Beweis (DE-588)4132532-1 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4145177-6 (DE-588)4132532-1 (DE-588)4037944-9 |
| 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 Beweis (DE-588)4132532-1 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Beweistheorie Beweis Mathematik |
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