Real Analysis

by John M. Howie

Understanding the concepts and methods of real analysis is an essential skill for every undergraduate mathematics student. Written in an easy-to-read style, Real Analysis is a comprehensive introduction to this core subject and is ideal for self-study or as a course textbook for first and second-year undergraduates. Combining an informal style with precision mathematics, Real Analysis covers all the key topics with fully worked examples and exercises with solutions.

Sequences and series - considering the central notion of a limit.- Continuous functions.- Differentiation.- Integration.- Logarithmic and exponential functions.- Uniform convergence.- Circular functions All these concepts and techniques are deployed in examples in the final chapter to provide the student with a thorough understanding of this challenging subject.

Genres: Mathematics

288 pages, Paperback

First published April 27, 2001

Reviews

[Erickson · Rating 4 out of 5]

I think as an introduction to real analysis this book is excellent, in the sense that it is very accessible to students or readers who only has first-year calculus as background. In fact, the first chapter also covers foundation of mathematics like sets and mathematical induction, so you probably don't even need anything beyond high school calculus to actually make this book work.

This books is something you can go for if you really want very low level, but otherwise quick refresher on basic techniques of real analysis. The fact that it has solutions for ALL exercises make it very useful for self-study, although as people say (correctly) mathematics is learnt by doing; looking at solutions do not make you an expert at this.

The only reason for 1-star less, which is really subjective for me, is that Chapter 7 onwards the book felt "tired"; it was more engaging in the first half, though the book is nonetheless well-written for the second half. The miscellaneous examples, though aptly titled, is a bit too random --- but I appreciate the appearance of Wallis' formula and how to derive Stirling's approximation using this (which gives both upper and lower bounds).

Overall, I think I prefer Abbott's book better (which I did not quite finish) because it has better scope and depth without going to Rudin/Zorich's level of rigour (which may be overkill for anyone who is not doing pure mathematics for career). If one needs more rigour than Howie/Abbott, I think reading/skimming these two are not bad in itself.

Highly recommended for people who want to learn basics of real analysis without getting lost in the forest, especially those who do not see themselves as having huge talent in mathematics but nonetheless want to appreciate the subject.

[Robert · Rating 4 out of 5]

Best I've seen.