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A Course in Mathematical Analysis: Volume 1, Foundations and Elementary Real Analysis Paperback – 25 Apr 2013

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'Garling is a gifted expositor and the book under review really conveys the beauty of the subject, not an easy task. [It] comes with appropriate examples when needed and has plenty of well-chosen exercises as may be expected from a textbook. As the author points out in the introduction, a newcomer may be advised, on a first reading, to skip part one and take the required properties of the ordered real field as axioms; later on, as the student matures, he/she may go back to a detailed reading of the skipped part. This is good advice.' Felipe Zaldivar, MAA Reviews

'This work is the first in a three-volume set dedicated to real and complex analysis that 'mathematical undergraduates may expect to meet in the first two years or so … of analysis' … The exposition is superb: open and nontelegraphic. Highly recommended. Upper-division undergraduates and graduate students.' D. Robbins, Choice

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This is the first of three volumes that provide a full and detailed account of all those elements of real and complex analysis the undergraduate mathematics student can expect to encounter in their first two or three years of study. Numerous exercises, examples and applications are included.

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Great Introduction for Undergraduates 31 July 2015
By Emil Haugen - Published on
Format: Paperback
A really great introduction to real analysis which demands basically no prerequisites, something that fitted me very well. There is even a brief summary of set/number theory (in the Prologue) which is developed further in chapter two to deal with Abeilian groups,rings, fields, morphisms and some interesting -if not immedeately useful for this book- rudimentary number theory. For the better prepared student the author states clearly that the first section (chpts. 1,2 on set and number theory can be omitted but they're still nice to have in my opinion.) My only problem with that element of the book was that the first two chapters introduced a lot of new notation, sometimes without any clear explanation of what it meant. However, this is not vital to the understanding of the book and thus a pretty tiny drawback. The treatment of sequences and series and convergence and continuity to be particularly crisp and understandable. There is also a lot of "additional" material such as an introduction to Fourier series and a wide range of applications, for example the Gamma function and the Riemann Zeta function.

All in all a very concise book (even with the prologue), just shy of 300 pages but still comprehensive in its description of the fundamentals of real analysis. (And, for the undergraduate level, this is much better suited than Rudin, which to me seems like a better fit for more mature mathematicians (i.e. graduates).)
6 of 17 people found the following review helpful
symbols problem 7 Nov. 2013
By Erroll - Published on
Format: Kindle Edition Verified Purchase
Mathematical symbols do not show correctly in kindle book.
I think it is a great book in Mathematical analysis, but the kindle book dose not work well.
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