Introduction to Real Analysis

Reviewed by Chad Scott, Professor, University of Wisconsin-Superior on 10/29/24

Comprehensiveness rating: 5 see less

This text comprehensively covers all of the content (and more) in a standard upper division undergraduate course in real analysis.

Content Accuracy rating: 5

It is very accurate with excellent, well constructed proofs and exercises.

Relevance/Longevity rating: 5

The text does not stray from the primary subject matter and the nature of the material provides for longevity.

Clarity rating: 5

Trench (the author) has a very personable way of writing that invites the reader to relax.  Narrative between theorems brings the reader to a point where they are well position to possibly provide proof of the upcoming theorems themselves.  That, coupled with well done but not verbose proof writing style makes the text very clear for undergraduate consumption vs many commercially available texts I have used in the past.

Consistency rating: 5

The writing style described in the clarity bullet above remains throughout the text.

Modularity rating: 4

There is some self reference as is necessary in mathematics.  At times, one needs to refer to previously established lemmas in order to understand proofs being presented in a given section.  But, to the extent possible for mathematics, the material is nicely divided into components most teachers of real analysis would expect.

Organization/Structure/Flow rating: 5

The text flows nicely in a way that I believe most teachers of real analysis would expect.

Interface rating: 5

The interface is via pdf so the content is very stable.  I've not found any oddly distorted images or cutoff content.  The interface seems very clean.

Grammatical Errors rating: 5

I've not found any significant errata.

Cultural Relevance rating: 5

Texts on Real Analysis are a necessary staple for a good undergraduate degree in math.  This text fills that need without any perceptible cultural bias.

Comments

I'd love someday to see this book in PreText so that it could be exported to more formats. It's very well done.