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...
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| Auteurs principaux: | , , |
|---|---|
| 格式: | Livre numérique |
| 語言: | Anglais |
| 出版: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| 版: | Second edition. |
| 叢編: | Undergraduate Texts in Mathematics
|
| 主題: | |
| 在線閱讀: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| 提示: |
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 |
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| 009 | PPN153867698 | ||
| 020 | |a 9781441994790 | ||
| 020 | |a 9781441994790 | ||
| 041 | 0 | |a eng | |
| 082 | |a 511.3 | ||
| 084 | |a 00A35. 2010 | ||
| 084 | |a 00-01. 2010 | ||
| 100 | 1 | |a Daepp, Ulrich, |d 1948- | |
| 245 | 1 | 0 | |a Reading, writing, and proving : |b a closer look at mathematics |c Ulrich Daepp, Pamela Gorkin. |
| 250 | |a Second edition. | ||
| 260 | |a New York, NY : |b Springer New York. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 1 | |a Undergraduate Texts in Mathematics |x 2197-5604 | |
| 500 | |a Description d'après consultation du 14 mai 2012 | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliogr. p. 367-370 Index p. 371-376 | ||
| 505 | 1 | |a -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 | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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 great detail, but also assists and inspires students to develop the necessary abilities to read, write, and prove using mathematical definitions, examples, and theorems that are required for success in navigating advanced mathematics courses. In addition to an introduction to mathematical logic, set theory, and the various methods of proof, this textbook prepares students for future courses by providing a strong foundation in the fields of number theory, abstract algebra, and analysis. Also included are a wide variety of examples and exercises as well as a rich selection of unique projects that provide students with an opportunity to investigate a topic independently or as part of a collaborative effort. New features of the Second Edition include the addition of formal statements of definitions at the end of each chapter; a new chapter featuring the Cantor Schröder Bernstein theorem with a spotlight on the continuum hypothesis; over 200 new problems; two new student projects; and more. An electronic solutions manual to selected problems is available online. From the reviews of the First Edition: The book emphasizes Pòlya s four-part framework for problem solving (from his book How to Solve It) [it] contains more than enough material for a one-semester course, and is designed to give the instructor wide leeway in choosing topics to emphasize This book has a rich selection of problems for the student to ponder, in addition to "exercises" that come with hints or complete solutions I was charmed by this book and found it quite enticing. Marcia G. Fung for MAA Reviews A book worthy of serious consideration for courses whose goal is to prepare students for upper-division mathematics courses. Summing Up: Highly recommended. J. R. Burke, Gonzaga University for CHOICE Reviews | ||
| 650 | |a Mathématiques |x Étude et enseignement (supérieur) | ||
| 650 | |a Rédaction scientifique et technique | ||
| 700 | 1 | |a Gorkin, Pamela, |d 19..- |4 aut | |
| 700 | 1 | |a Gorkin, Pamela. |4 aut | |
| 776 | 0 | |0 155633848 |t Reading, writing, and proving |o a closer look at mathematics |f Ulrich Daepp, Pamela Gorkin |e Second edition |d 2011 |c New York |n Springer |p 1 vol. (XIII-376 p.) |s Undergraduate texts in mathematics |z 978-1-4419-9478-3 | |
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