Reading, Writing, and Proving A Closer Look at Mathematics
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 partof a collaborative effort. New features of the Second Edition include the addition of formal statements o...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
2011, 2011
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| Edition: | 2nd ed. 2011 |
| Series: | Undergraduate Texts in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- -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