Resource Guide for Real Analysis Real analysis, often called mathematical analysis or simply analysis, may be regarded as a formidable counterpart of calculus. It is a subject where one revisits notions encountered in calculus, but with greater rigor and sometimes with greater generality. Beginning with the attempt to find a more flexible alternative to the standard Riemann integral:
where
the function f has to be bounded and also continuous at almost all the points of interval [a,b], mathematicians normally take a comprehensive course in real analysis as early as possible. Some good sources on real analysis are provided in the following guide.
Books Elementary Analysis: The theory of Calculus Call number: QA303.R824 This book bridges the gap between elementary calculus and an in-depth-study of real analysis. Real analysis: Modern Techniques and Their Applications Call number: QA300.F667 Treating the theory of measure and integral generally, this book covers differentiation of measures in abstract measure space and, via the Hardy-Littlewood maximal function, on . Read analysis (4th edition) Call number: QA331.5.R888 2010 Real Analysis, Fourth Edition, covers the basic material that every reader should know in the classical theory of functions of a real variable, measure and integration theory, and some of the more important and elementary topics in general topology and normed linear space theory. Real and Complex Analysis Call number: QA300.R916 Written in the elegant and distinctive style, the text is this book is challenging, but rewarding. It covers the most important topics on general theory of measure and integration. Please take note that this books is circulated for 2 hours only. Theory of functions of a real variable Call number: QA331.5.N272 This is a very classical book, including 2 volumes, where you can find and try dozens of interesting exercises.
References A Handbook of Terms Used in Algebra and Analysis Call number: XX(795780.1) [Cataloging] Handbook of Integration Call number: QA299.3.Z97 Created by Eric Liu for Mathematics in June 2011 All Rights Reserved. NTU Library
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This is a dictionary of mathematical topics in the subject of integration theory.
eBook A Course in Calculus and Real Analysis This book attempts to give a self-contained and rigorous introduction to calculus of functions of one variable. The presentation and sequencing of topics emphasizes the structural development of calculus. At the same time, due importance is given to computational techniques and applications. Real Analysis and Applications: Theory in Practice This book provides an introduction both to real analysis and to a range of important applications that depend on this material. Three-fifths of the book is a series of essentially independent chapters covering topics from Fourier series and polynomial approximation to discrete dynamical systems and convex optimization. Basic Real Analysis Advanced Real Analysis The two books develop concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. The books are written as textbooks, and their primary audience is students who are learning the material for the first time and who are planning a career in which they will use advanced mathematics professionally. They together contain what the young mathematician needs to know about real analysis in order to communicate well. A Problem Book in Real Analysis This book aims to give independent students the opportunity to discover Real Analysis by themselves through problem solving. Real Analysis and Applications This book contains a series of essentially independent chapters covering topics from Fourier series and polynomial approximation to discrete dynamical systems and convex optimization, which may help to improve understanding of real analysis and prepare for more intensive work in each topic.
Journals The American Mathematical Monthly [e-journal] ISSN: 0002-9890 Accessible to undergraduates. Russian Mathematical Surveys = Uspekhi Matematicheskikh Nauk [e-journal] ISSN: 0036-0279 Publishes major survey articles on various subjects including analysis. Real Analysis Exchange [e-journal] ISSN: 0147-1937 Created by Eric Liu for Mathematics in June 2011 All Rights Reserved. NTU Library
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Covers real analysis & related subjects such as geometric measure theory, analytic set theory, onedimensional dynamics, the topology of real functions, & the real variable aspects of Fourier analysis & complex analysis.
Web Resources Real Analysis [WikiBooks] Unlike most print books, it has not been designed to supplement any course or instruction. As such, it contains several ideas and concepts stacked together which might baffle the uninitiated reader. Real Analysis Course notes on the web by Prof Terrence Tao from UCLA
Created by Eric Liu for Mathematics in June 2011 All Rights Reserved. NTU Library
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