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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York, NY :
Springer New York : Imprint: Springer,
2011.
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| Edición: | 2nd ed. 2011. |
| Colección: | Undergraduate Texts in Mathematics,
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| Temas: | |
| Acceso en línea: | Texto Completo |
Tabla de Contenidos:
- -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.