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A Primer of Real Functions (Mathematical Association of America Textbooks), by Ralph P. Boas, Harold P. Boas
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This is a revised, updated, and augmented edition of a classic Carus monograph with a new chapter on integration and its applications. Earlier editions covered sets, metric spaces, continuous functions, and differentiable functions. To that, this edition adds sections on measurable sets and functions and the Lebesgue and Stieltjes integrals. The book retains the informal chatty style of the previous editions. It presents a variety of interesting topics, many of which are not commonly encountered in undergraduate textbooks, such as the existence of continuous everywhere-oscillating functions; two functions having equal derivatives, yet not differing by a constant; application of Stieltjes integration to the speed of convergence of infinite series. For readers with a background in calculus, the book is suitable either for self-study or for supplemental reading in a course on advanced calculus or real analysis. Students of mathematics will find here the sense of wonder that was associated with the subject in its early days.
- Sales Rank: #2156230 in Books
- Brand: Brand: The Mathematical Association of America
- Published on: 1997-01-30
- Original language: English
- Number of items: 1
- Dimensions: 8.50" h x 1.18" w x 5.43" l, .85 pounds
- Binding: Hardcover
- 319 pages
- Used Book in Good Condition
Review
'It is a great pleasure to see the new, the fourth edition of this gem which is well-known all over the world where mathematicians live. This is an important work especially for teachers and even for (trained) students.' Acta. Sci. Math.
Most helpful customer reviews
8 of 8 people found the following review helpful.
A "must have" book if you love real analysis.
By Luis F. Moreno
I've always enjoyed Ralph Boas' mathematical writing style. He is at his best in this small book. He covers topics in introductory and intermediate real analysis of one variable, but with an enthusiasm that pulls you along, like a good novel. This does not mean, however, that Boas skimps on theory and proof. This is an excellent resource for undergraduate/graduate study. The "Notes" section is a cornucopia of references to advanced topics by leaders in the field. And every exercise is answered, or at least addressed.
2 of 2 people found the following review helpful.
Great on Cantor's middle third set
By Tim Jones
Boas adds humor and curious anecdotes to his presentation of real functions. His book includes Lebesque integration and gives an excellent presentation of the Cantor set.
1 of 2 people found the following review helpful.
Why can't other mathematicians make their topics sing like Boas does??
By William D. Fusfield
This is such a fine, fine book; one of the very best on its topic. Unlike virtually every other author who has written a "Real Analysis" textbook, Boas makes the subject truly interesting and even fascinating. [How one could possibly make the legion mysteries of the Cantor Set boring is beyond me, but most of the other books on Real Analysis I've read or looked through somehow manage to do so.] Boas is a true teacher. He always prioritizes first getting his readers to understand intuitively the various theorems he then proves. I am told that the newer Thomson et. al. Elementary Real Analysis is also well written and quite intuitive, and thus interesting to read and contemplate. But I haven't yet read that book so I can't judge it. I have read and re-read this one over the years, however, and can assure you that if you don't enjoy and use this book frequently, well then, you simply don't like mathematics.
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