Designed for a first course in real variables, this text encourages intuitive thinking and offers background for more advanced mathematical work. Topics include complex variables, measure theory, differential equations, functional analysis, and probability. Detailed solutions to the problems appear at the back of the book, making it ideal for independent study. 1993 edition.
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5.0 out of 5 stars
A Lucid Presentation of the Theory of Real Variables,
This review is from: Real Variables with Basic Metric Space Topology (Dover Books on Mathematics) (Paperback)
I congratulate Prof Ash for his splendid presentation of real variables theory in such a clear manner which is unseen in many books of its kind. Prof Ash seems to know the mentality and anxiety of students taking a course on real variables at this level as he probably faced the same sort of problems when he first took to pure mathematics, having been an engineer by training. What I like about the book is its clarity and the many examples that elucidate the rather hard concepts like uniform convergence. The steps in the proofs are given in great detail which makes reading easy, unlike many other similar books which leave lots of gaps between steps, often leaving the student in a complete state of bewilderment. Nothing is more eirksome to the reader than seeing a phrase like "It is easy to see that blah blah blah" when it is easy to the author who has spent his entire academic life mulling over it but is certainly not easy to the reader who sees it the first time. All writers must understand this. Another good thing about the book is that there are solutions to the exercises that makes self-learning a joy and not a toil.
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