Reading, Writing, and Proving A Closer Look at Mathematics /

• Κύριοι συγγραφείς: Daepp, Ulrich (Συγγραφέας), Gorkin, Pamela (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: New York, NY : Springer New York, 2011.
• Σειρά: Undergraduate Texts in Mathematics,
• Θέματα: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Mathematical logic.; Number theory.; Mathematical Logic and Foundations.; Analysis.; Number Theory.

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...

Πίνακας περιεχομένων:

• -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.