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Students will follow Pólya's four step approach: analyzing the problem, devising a plan to solve the problem, carrying out that plan, and then determining the implication of the result. In addition to the Pólya approach to proofs, this book places special emphasis on reading proofs carefully and writing them well. The authors have included a wide variety of problems, examples, illustrations and exercises, some with hints and solutions, designed specifically to improve the student's ability to read and write proofs.
Historical connections are made throughout the text, and students are encouraged to use the rather extensivebibliography to begin making connections of their own. While standard texts in this area prepare students for future courses in algebra, this book also includes chapters on sequences, convergence, and metric spaces for those wanting to bridge the gap between the standard course in calculus and one in analysis.
Students will follow Pólya's four step approach: analyzing the problem, devising a plan to solve the problem, carrying out that plan, and then determining the implication of the result. In addition to the Pólya approach to proofs, this book places special emphasis on reading proofs carefully and writing them well. The authors have included a wide variety of problems, examples, illustrations and exercises, some with hints and solutions, designed specifically to improve the student's ability to read and write proofs.
Historical connections are made throughout the text, and students are encouraged to use the rather extensivebibliography to begin making connections of their own. While standard texts in this area prepare students for future courses in algebra, this book also includes chapters on sequences, convergence, and metric spaces for those wanting to bridge the gap between the standard course in calculus and one in analysis.
New to the second edition:
A useful appendix of formal definitions that can be used as a quick reference
Second edition includes new exercises, problems, and student projects
An electronic solutions manual for instructors and individual users
Includes supplementary material: [...]
-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.
| Erscheinungsjahr: | 2013 |
|---|---|
| Fachbereich: | Grundlagen |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Reihe: | Undergraduate Texts in Mathematics |
| Inhalt: |
xiv
378 S. |
| ISBN-13: | 9781461429159 |
| ISBN-10: | 1461429153 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: |
Gorkin, Pamela
Daepp, Ulrich |
| Auflage: | 2nd ed. 2011 |
| Hersteller: |
Springer New York
Springer US, New York, N.Y. Undergraduate Texts in Mathematics |
| Maße: | 235 x 155 x 22 mm |
| Von/Mit: | Pamela Gorkin (u. a.) |
| Erscheinungsdatum: | 01.08.2013 |
| Gewicht: | 0,593 kg |
New to the second edition:
A useful appendix of formal definitions that can be used as a quick reference
Second edition includes new exercises, problems, and student projects
An electronic solutions manual for instructors and individual users
Includes supplementary material: [...]
-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.
| Erscheinungsjahr: | 2013 |
|---|---|
| Fachbereich: | Grundlagen |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Reihe: | Undergraduate Texts in Mathematics |
| Inhalt: |
xiv
378 S. |
| ISBN-13: | 9781461429159 |
| ISBN-10: | 1461429153 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: |
Gorkin, Pamela
Daepp, Ulrich |
| Auflage: | 2nd ed. 2011 |
| Hersteller: |
Springer New York
Springer US, New York, N.Y. Undergraduate Texts in Mathematics |
| Maße: | 235 x 155 x 22 mm |
| Von/Mit: | Pamela Gorkin (u. a.) |
| Erscheinungsdatum: | 01.08.2013 |
| Gewicht: | 0,593 kg |
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