Limits, Limits Everywhere: The Tools of Mathematical Analysis - David Applebaum
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Présentation Limits, Limits Everywhere: The Tools Of Mathematical Analysis de David Applebaum Format Broché
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Résumé :
An account of elementary real analysis positioned between a popular mathematics book and a first year college or university text. This book doesn't assume knowledge of calculus and, instead, the emphasis is on the application of analysis to number theory.
Biographie:
David Applebaum obtained his PhD at the University of Nottingham in 1984. After postdoctoral appointments in Rome and Nottingham, he became a lecturer in mathematics at Nottingham Trent University (then Trent Polytechnic) in 1987 and was promoted to reader in 1994 and to a chair in 1998. He was Head of Department 1998-2001. He left Nottingham Trent for a chair in Sheffield in 2004 and served as Head of Department of Probability and Statistics there from 2007-10.
Sommaire:
INTRODUCTION ; I APPROACHING LIMITS ; 1. A Whole Lot of Numbers ; 2. Let's Get Real ; 3. The Joy of Inequality ; 4. Where Do You Go To, My Lovely ; 5. Bounds for Glory ; 6. You Cannot be Series ; II EXPLORING LIMITS ; 7. Wonderful Numbers ; 8. Infinite Products ; 9. Continued Fractions ; 10. How Infinite Can You Get? ; 11. Constructing the Real Numbers ; 12. Where to Next in Analysis? The Calculus ; 13. Some Brief Remarks About the History of Analysis ; FURTHER READING ; APENDICES ; 1. The Binomial Theorem ; 2. The Language of Set Theory ; 3. Proof by Mathematical Induction ; 4. The Algebra of Numbers ; HINTS AND SELECTED SOLUTIONS
Recommended in the Times Higher Education's Textbook Guide 2012. Noel-Ann Bradshaw, Times Higher Education This is an excellent book which should appeal to teachers and pre-University or undergraduate students looking for a hands-on introduction to mathematical analysis. Mario Cortina Borja, Significance The book is devoted to the discussion of one of the most difficult concepts of mathematical analysis, the concept of limits. The presentation is instructive and informal. It allows the author to go much deeper than is usually possible in a standard course of calculus. Moreover, each portion of the material is supplied by an explanation why and what for it is necessary to study (and to teach) the corresponding part of calculus ... the book can be recommended for interested students as well as for teachers in mathematics. Zentralblatt MATH
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