The Art of Proof Basic Training for Deeper Mathematics
The Art of Proof is designed for a one-semester or two-quarter course. A typical student will have studied calculus (perhaps also linear algebra) with reasonable success. With an artful mixture of chatty style and interesting examples, the student's previous intuitive knowledge is placed on sol...
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| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
New York, NY :
Springer New York
2010.
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| Colección: | Undergraduate Texts in Mathematics ;
0. Springer eBooks. |
| Acceso en línea: | Conectar con la versión electrónica |
| Ver en Universidad de Navarra: | https://innopac.unav.es/record=b3290812x*spi |
| Sumario: | The Art of Proof is designed for a one-semester or two-quarter course. A typical student will have studied calculus (perhaps also linear algebra) with reasonable success. With an artful mixture of chatty style and interesting examples, the student's previous intuitive knowledge is placed on solid intellectual ground. The topics covered include: integers, induction, algorithms, real numbers, rational numbers, modular arithmetic, limits, and uncountable sets. Methods, such as axiom, theorem and proof, are taught while discussing the mathematics rather than in abstract isolation. Some of the proofs are presented in detail, while others (some with hints) may be assigned to the student or presented by the instructor. The authors recommend that the two parts of the book -- Discrete and Continuous -- be given equal attention. The book ends with short essays on further topics suitable for seminar-style presentation by small teams of students, either in class or in a mathematics club setting. These include: continuity, cryptography, groups, complex numbers, ordinal number, and generating functions. |
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| Descripción Física: | XXII, 182 p., 23 il |
| Formato: | Forma de acceso: World Wide Web. |
| ISBN: | 9781441970237 |
