The foundations of mathematics / Ian Stewart and David Tall.
Tipo de material:
TextoIdioma: Inglés Fecha de copyright: Oxford : Oxford University Press, 2015Edición: Second EditionDescripción: xvi, 391 pages : illustrations ; 23 cmISBN: - 9780198706434 (pbk.)
- 019870643X (pbk.)
- 511.3 23
- QA9 .S755 2015
| Tipo de ítem | Biblioteca actual | Signatura | Copia número | Estado | Fecha de vencimiento | Código de barras | Reserva de ítems | |
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Colección general
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Biblioteca Yachay Tech | 511.3 S8497f 2015 (Navegar estantería(Abre debajo)) | Ej. 1 | Reservado | 005748 | 1 |
Includes index.
Includes bibliographical references (pages 383-385).
Part I. The intuitive background -- Mathematical thinking -- Number systems -- Part II. The beginnings of formalisation -- Sets -- Relations -- Functions -- Mathematical logic -- Mathematical proof -- Part III. The development of axiomatic systems -- Natural numbers and proof by induction -- Real numbers -- Real numbers as a complete ordered field -- Complex numbers and beyond -- Part IV. Using axiomatic systems -- Axiomatic systems, structure theorems, and flexible thinking -- Permutations and groups -- Cardinal numbers -- Infinitesimals -- Part V. Strengthening the foundations -- Axioms for set theory.
The transition from school to university mathematics is seldom straightforward. Students face a schism between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory. The authors have many years' experience of the potential difficulties involved, through teaching first-year undergraduates
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