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Disponibilidad: En existencia
ISBN: 9781292054094
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Edición: 5
Copyright: 2014
Páginas: 368

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Analysis with an Introduction to Proof (Ebook)


Descripción: To understand mathematics and mathematical arguments, it is necessary tohave a solid understanding of logic and the way in which known facts can becombined to prove new facts. Although many people consider themselves tobe logical thinkers, the thought patterns developed in everyday living areonly suggestive of and not totally adequate for the precision required inmathematics. In this chapter we take a careful look at the rules of logic andthe way in which mathematical arguments are constructed. Section 1presents the logical connectives that enable us to build compound statementsfrom simpler ones. Section 2 discusses the role of quantifiers. Sections 3and 4 analyze the structure of mathematical proofs and illustrate the variousproof techniques by means of examples.

1. Logic and Proof
2. Sets and Functions
3. The Real Numbers
4. Sequences
5. Limits and Continuity
6. Differentiation
7. Integration
8. Infinite Series