Numbers and functions : steps into analysis

Burn, R. P.

ISBN 10: 0521457734 / ISBN 13: 9780521457736

Editore: Cambridge : Cambridge University Press, 1992

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Near fine paperback copy; edges very slightly dust-dulled and nicked. Remains particularly well-preserved overall; tight, bright, and clean. Physical description: xix, 328 p. : figs ; 23 cm. Notes: Includes bibliography, index. Subjects: Mathematical analysis; Functions (Mathematics). 1 Kg. Codice articolo 418756

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Titolo: Numbers and functions : steps into analysis

Casa editrice: Cambridge : Cambridge University Press

Data di pubblicazione: 1992

Legatura: Rilegato

Edizione: 1st edition.

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Riassunto:

The transition from studying calculus in schools to studying mathematical analysis at university is notoriously difficult. In this book, Dr Burn follows a route that proved successful with A Pathway to Number Theory and Groups: A Path to Geometry. He invites the student reader to tackle each of the key concepts in turn, progressing from experience (using computers for graph drawing where appropriate) through a structured sequence of several hundred problems to concepts, definitions and proofs of classical real analysis. The sequence of problems, which all have solutions supplied, draws students into constructing definitions and theorems for themselves. This natural development is informed by historical insight and complemented by historical discussion. The sequence also takes into account recent research which has shown how intuitive ideas about numbers, limits, functions and infinity may be at odds with the standard definitions. The novel approach to rigorous analysis offered here is designed to enable students to grow in confidence and skill and thus overcome the traditional difficulties. Teachers in sixth forms will find that questions at the beginning of every chapter provide ways of preparing those at school for university mathematics. Lecturers in universities will be challenged to rethink their conventions about the best way to introduce the central ideas of analysis to undergraduates.

Descrizione del libro:

The novel approach to rigorous analysis offered here is designed to enable students to grow in confidence and skill and thus overcome the traditional difficulties. Teachers in sixth forms will find that the beginning questions in every chapter provide ways of preparing those at school for university mathematics. Lecturers in universities will be challenged to rethink their conventions about the best way to introduce the central ideas of analysis to undergraduates.