Numbers, Sequences and Series

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Butterworth-Heinemann, 1995 - Mathematics - 198 pages
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Number and geometry are the foundations upon which mathematics has been built over some 3000 years. This book is concerned with the logical foundations of number systems from integers to complex numbers. The author has chosen to develop the ideas by illustrating the techniques used throughout mathematics rather than using a self-contained logical treatise. The idea of proof has been emphasised, as has the illustration of concepts from a graphical, numerical and algebraic point of view. Having laid the foundations of the number system, the author has then turned to the analysis of infinite processes involving sequences and series of numbers, including power series. The book also has worked examples throughout and includes some suggestions for self-study projects. In addition there are tutorial problems aimed at stimulating group work and discussion.

 

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Contents

Chapter 1 Sets and Logic
1
Chapter 2 The Integers
19
Chapter 3 The Rational Numbers
38
Chapter 4 Inequalities
55
Chapter 5 The Real Numbers
68
Chapter 6 Complex Numbers
83
Chapter 7 Sequences
106
Chapter 8 Infinite Series
137
Chapter 9 Decimals
164
Chapter 10 Further Developments
176
Answers to Exercises
183
Index
194
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