Numbers and Functions: Steps to Analysis - Softcover

Burn, R. P.

4.17

6 ratings by Goodreads

9780521457736: Numbers and Functions: Steps to Analysis

Softcover

ISBN 10: 0521457734 ISBN 13: 9780521457736

Publisher: Cambridge University Press, 1993

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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.

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Review:

."..any reader who works through a substantial number of the given questions would enhance considerably her/his mathematical knowledge...answers are given to almost all of the questionss, [so] even the person who just reads the book and checks out the details of an answer would probably benefit...I believe that a serious student of mathematics (and even some teachers of mathematics) would find conscientious study of this book of considerable value." Bob Prielipp, School Science & Mathematics

Book Description:

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.

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