Mathematical Reasoning: Writing and Proof, Version 2.1

Reviewed by Kenneth Ward, Professorial Lecturer, Mathematics & Statistics, American University on 2/1/18

Comprehensiveness rating: 4

This text addresses most major components of proof methods, with suitable exploration exercises for the mathematical novice/undergraduate major which do not overly burden the reader with prerequisite knowledge.

Content Accuracy rating: 5

The book has accurate and only contains minimal typographical errors. The mathematics in the book is correct.

Relevance/Longevity rating: 5

This text will be relevant for a long while. Students who become math or statistics majors need to understand proof, and the basic methods used in proof and mathematical logic have not significantly changed (and will not) over time.

Clarity rating: 5

This is a strong point of the text. The writing is extremely clear and simple, making it easy for the undergraduate reader to follow where ,any other books fail. The examples lead the reader gently towards an understanding of logic and proof. Especially good are the sections where the author clarifies how to write a proof for your audience.

Consistency rating: 5

Excellent. There are simply no problems with the consistency of the mathematical work or exposition.

Modularity rating: 4

This can generally be done, although it takes a bit of work. Mathematics courses are often linear in this way. Despite this, with a little extra effort by an instructor, most sections can be separated. For example, it is difficult to speak of correspondences without the notion of a function, but an instructor can simply introduce the function definition to address correspondences without covering the entire chapter on functions. (By the way, one of the topics covered is “modular” arithmetic, so I am inclined to say that those parts are quite modular!)

Organization/Structure/Flow rating: 5

The presentation is clear and allows the instructor to develop a natural flow to a course.

Interface rating: 5

There are no issues with the interface. It is an easy-to-read pdf, of small size.

Grammatical Errors rating: 5

The grammar is mostly good, with only a minor error or two: so minor that it is easy to not notice them.

Cultural Relevance rating: 3

This book is not culturally insensitive. It is simply mathematics, and doesn’t include any offensive content in the main chapters or exercises. I am rating this a 3 as it is therefore neutral in this regard.

Comments

This book is very useful either as a primary course text for an Introduction to Proof course, or as a supplementary text in a course in philosophical logic or mathematics content course at roughly the level of Calculus I or beyond.