Mathematical Analysis, Approximation and Discrete Processes

- Preface

- Real Numbers and Natural Numbers

- Sequences of Real Numbers

- Integer Numbers: Congruences, Counting and Infinity

- Complex Numbers

- Polynomials, Rational Functions and Trigonometric Polynomials

- Series

- Power Series

- Discrete Processes

- Mathematicans and Other Scientists

- Bibliographical Notes

- Index.

"This self-contained book aims to introduce the main ideas for studying approximation processes, more generally discrete processes at graduate level. The use of computers induces a growing need for studying discrete processes.... A key feature this lively yet rigorous and systematic treatment is the historical accounts of ideas and methods of the subject. Ideas in mathematics develop in cultural, historical and economical contexts, thus the authors made brief accounts of those aspects and used a large number of beautiful illustrations.... Each chapter has a short summary where the most important facts discussed are collected and described. There is also a large number of exercises inserted at various points into the text....The book is meant principally for graduate students in mathematics, physics, engineering, and computer science, but it can be used at technological and scientific faculties by anyone who wants to approach these topics. It may also be used in graduate seminars and courses or as a reference text by mathematicians, physicists, and engineers." -- Zentralblatt MATH

"Mathematical Analysis does contain a substantial amount of material that is unusual in terms of an introductory text in real analysis...These are all interesting topics that have gained increasing importance in modern applications of mathematics, albeit outside the traditional area of analysis. It is very nice to have these topics developed outside a specialized textbook, in, e.g., combinatorics, dynamical systems, or number theory. The authors do a very good job presenting this material...Mathematical Analysis includes substantial amounts of historical background...The book also contains a lot of examples...I can happily recommend Mathematical Analysis as a good resource for instructors of introductory analysis courses, especially in terms of providing some unusual applications of analysis and developments of some basic classic topics that are often shortchanged in standard texts." --