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Real Analysis with an Introduction to Wavelets and Applications

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Real Analysis is based on the real numbers, and it is naturally involved in practical mathematics. On the other hand, it has taken on subject matter from set theory, harmonic analysis, integration theory, probability theory, theory of partial differential equations, etc., and has provided these areas with important ideas and basic concepts. This relationship continues even today. This book, contains the basic matter of “real analysis” and an introduction to “wavelet analysis,” a popular topic in “applied real analysis.”

Nowadays, students studying real analysis come from different backgrounds and have diverse objectives. A course in this subject may serve both undergraduates and graduates, students not only in mathematics but also in statistics, engineering, etc., and students who are seeking master’s degrees and those who plan to pursue doctoral degrees in the sciences. Written with the student in mind, this book is suitable for students with a minimal background. In particular, this book is written as a textbook for the course usually called Real Analysis as presently offered to first or second year graduate students in American universities with a master’s degree program in mathematics.
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