Reading, writing, and proving : a closer look at mathematics
Reading, Writing, and Proving is designed to guide mathematics students during their transition from algorithm-based courses such as calculus, to theorem and proof-based courses. This text not only introduces the various proof techniques and other foundational principles of higher mathematics in gre...
Salvato in:
| Autori principali: | , , |
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| Natura: | Livre numérique |
| Lingua: | Anglais |
| Pubblicazione: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| Edizione: | Second edition. |
| Serie: | Undergraduate Texts in Mathematics
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| Soggetti: | |
| Accesso online: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Description d'après consultation du 14 mai 2012 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Reading, writing, and proving, a closer look at mathematics, Ulrich Daepp, Pamela Gorkin, Second edition, 2011, New York, Springer, 1 vol. (XIII-376 p.), Undergraduate texts in mathematics, 978-1-4419-9478-3 |
Sommario:
- -Preface. -1. The How, When, and Why of Mathematics 2. Logically Speaking 3.Introducing the Contrapositive and Converse 4. Set Notation and Quantifiers 5. Proof Techniques 6. Sets 7. Operations on Sets 8. More on Operations on Sets 9. The Power Set and the Cartesian Product 10. Relations 11. Partitions 12. Order in the Reals 13. Consequences of the Completeness of (\Bbb R) 14. Functions, Domain, and Range.- 15. Functions, One-to-One, and Onto 16. Inverses 17. Images and Inverse Images 18. Mathematical Induction 19. Sequences 20. Convergence of Sequences of Real Numbers 21. Equivalent Sets 22. Finite Sets and an Infinite Set 23. Countable and Uncountable Sets 24. The Cantor-Schröder-Bernstein Theorem 25. Metric Spaces 26. Getting to Know Open and Closed Sets 27. Modular Arithmetic 28. Fermat s Little Theorem 29. Projects Appendix References Index