First Semester in Numerical Analysis with Python

Reviewed by Chad Westphal, Professor of Mathematics and Computer Science, Wabash College on 2/27/21

Comprehensiveness rating: 4 see less

The topics covered by the book are overall appropriate and presented at a reasonable level for undergraduate students with a background in calculus, linear algebra, and programming. It gives a brief introduction to python, which would be sufficient for a student with some programming experience. The numerical analysis concepts are often explained through worked (and narrated) examples implemented in python. This pragmatic approach generally works well, though there are times where specific implementation issues crowd out the fundamental idea at issue. On the spectrum between an implementation-focused numerical methods course and a theorem-proof numerical analysis course, this text is definitely more on the methods end. The range of topics is limited for a typical robust undergraduate course in numerical analysis. There is no coverage of numerical methods for differential equations or numerical linear algebra. There are some exercises given throughout the text, and these are often implementation/computation focused. An instructor using the text for a course will likely want to supplement the text with additional exercises, assignments, and/or projects.

Content Accuracy rating: 4

The text of the main body of the book is generally clear and error-free. The index has references to code in Julia, where it should be to python. (This seems to be an artifact of the conversion of the original text that used the programming language Julia).

Relevance/Longevity rating: 5

The general subject matter is very relevant to a wide range of disciplines and is unlikely to lose relevance soon. The design of the text incorporates python code throughout the text, so the shelf-life of the book is closely tied to how the language evolves. It will certainly be possible to update examples, code implementations, etc., though not trivially.

Clarity rating: 4

The tone of the presentation is generally straightforward and uses typical, concise mathematical conventions. As a stand-alone reference for a student working alone, it is light on providing motivation and context for the subject. As such, this book is better suited as a course text, where the experienced instructor can provide some of this additional framing. The book gives several extended example applications posed with the recurring fictional student Arya. These sections do add some levity to the narrative, but can also be a little distracting. Sometimes they are used as motivation to introduce a new topic, and in other places as a way to illustrate a specific problem. The overall readability of the text would be more clear if these sections were delineated more consistently (... are we still helping Arya understand her problem now, or have we moved on to a new topic?)

Consistency rating: 4

Overall the text uses consistent and appropriate terminology throughout. However, it could do a better job of distinguishing between rate and order of convergence. It uses big-O notation somewhat inconsistently throughout.

Modularity rating: 5

For the subject matter it is reasonably modular. Much of the material is inherently hierarchical, so there would be little motivation for wanting to rearrange sections. That said, there are a few sections that can be skipped, which is quite appropriate for an advanced undergraduate text. As noted above, it would be helpful to have chapters on numerical ODEs and/or numerical linear algebra.

Organization/Structure/Flow rating: 5

The organization of the text is appropriate for the subject and the depth of coverage.

Interface rating: 5

There is appropriate use of hypertext links in the pdf version, and these work well. The typesetting, images, and referencing are all done well. Switching between the main text and imbedded python code could be improved if the code were more visually offset (perhaps a light gray background?).

Grammatical Errors rating: 5

No grammar or copy edit issues were noted.

Cultural Relevance rating: 5

There is nothing in this book that can be considered culturally insensitive.

Comments

There are many forms that a first course in numerical analysis can take, with relative emphasis on different aspects of the field (implementation, empirical testing, applications, theory, etc.). This book could be a good component of a course that wishes to focus on implementation in python and doesn't need to cover topics beyond rootfinding, interpolation and numerical integration/differentiation.