First Semester in Numerical Analysis with Julia

Reviewed by Namyong Lee, Professor, Minnesota State University Mankato on 3/4/24

Comprehensiveness rating: 4 see less

The textbook seemed more focused on brief one-semester material. It has the most essential topics in the first course in Numerical Methods for college students. Some other textbooks have a topic in numerical linear algebra which is missing in this textbook. However, as the textbook seems to aim for a brief exposition of the numerical methods for one semester, it serves the goal.

Content Accuracy rating: 4

The textbook's contents, including the theorems, proofs, and examples are concise and accurate. One of the reasons is that the textbook wisely avoids any complicated part of the proof and exposition by simply mentioning some references.

Relevance/Longevity rating: 5

The textbook contents are aligned with standard topics for an introductory course in undergraduate numerical methods class. These topics didn't change for a long time.

Clarity rating: 5

The main advantage of the textbook is the brief but clear exposition of the topics. To achieve this goal, the author bravely skipped many proofs and lengthy development of the topics.

Consistency rating: 5

Overall, the textbook is internally consistent and field-tested to achieve this goal. I don't see any unnatural part of the textbook from the consistency of the terminologies and frameworks in the textbook.

Modularity rating: 5

The textbook is already very brief (about 220 pages) to be covered in a semester (15 weeks) course but can be adequate for a quarter (10 weeks) term situation. Each chapter (from 2 to 5) is quite independent and as a result, one may skip a chapter without much trouble.

Organization/Structure/Flow rating: 5

The textbook is written in a standard and logical order. I may suggest that the author may add a few samplers or concrete applications in the introduction chapter to give a more clear overview for students. (From an instructor's perspective, it is not a problem. However, if the introduction part is not interesting, often students stop to read the textbook any further.)

Interface rating: 5

The textbook does not have any serious interface issues as it is the standard PDF format. Every detail is presented clearly in the PDF reader. My only suggestion is the author provides sample code in the textbook also on a website, such as GitHub. That would benefit students to play with the sample code.

Grammatical Errors rating: 5

The textbook is written concisely and clearly to the reader. Each sentence and topic exposition is brief and grammatically correct. It was easy to read most of the parts of the textbook.

Cultural Relevance rating: 5

I don't find any part of the textbook material culturally insensitive or offensive. Indeed, one feature I like about the textbook is the author introduces a comic character (Arya, followed by the author's daughter's name) and uses it as a gentle introduction to the application problems.

Comments

As I briefly mentioned in the above questionnaires, I may suggest strengthening the introduction chapter with more applications and examples. Also, posting the sample code to GitHub in the form of the Jupyter Notebook would benefit students.

Reviewed by Yaning Liu, Assistant Professor, University of Colorado Denver on 5/5/20

Comprehensiveness rating: 4 see less

This book covers the topics of computer arithmetic, iterative methods for nonlinear equations, interpolation methods, numerical quadrature and differentiation, and least squares problems, which are typically discussed in a first course of numerical analysis.

Content Accuracy rating: 5

No errors are found.

Relevance/Longevity rating: 5

The book uses a lot of examples that are highly related to the author's research and are not commonly seen in other textbooks, and the rising Julia programming language is used to illustrate the algorithms, both making the book up-to-date and unique.

Clarity rating: 5

The text reads very well.

Consistency rating: 5

The book uses consistent terminology.

Modularity rating: 5

The book divides each topic into a few smaller sections and an instructor can cover each in one or two lectures at their convenience.

Organization/Structure/Flow rating: 5

The organization of the topics is logical and clear.

Interface rating: 5

The book uses a lot of high-quality figures to help understand the material, without distracting the reader at all. No navigation problems are found.

Grammatical Errors rating: 5

No grammatical errors are found.

Cultural Relevance rating: 5

No culturally offensive examples are found in this book.

Comments

The book treats the commonly discussed topics in the first-semester numerical analysis with Julia and uses a lot of unique examples related to the author's research, which provides the readers a fresh experience with learning numerical analysis. I would like to highly recommend using the book.

Reviewed by Sangphil Kim, Assistant Professor, Minnesota State University System on 2/18/20

Comprehensiveness rating: 4 see less

This book doesn't cover several topics in numerical analysis such as differential equations and eigenvalue if we compare it with conventional textbooks. However, this textbook covers enough topics in numerical analysis for undergraduate students. As you can see in the title, it would be good enough for one semester.

Content Accuracy rating: 5

Content is accurate, error-free and unbiased.

Relevance/Longevity rating: 5

Adapting Julia is more than up-to-date. It is proactive. I don't find anything out-of-date. The necessary updates will be minor or none and easy to implement.

Clarity rating: 5

One of the strengths of this text is abundant examples. It explains concepts in mathematical expressions and followed by examples with codes.

Consistency rating: 5

Each chapter is consistent in format, structure as well as terminology.

Modularity rating: 5

The first chapter introduces Julia which will be used for all the rest chapters. Except for the first chapter, the text has well-divided chapters so that an instructor can change the order of chapters or omit some chapters, without any problem.

Organization/Structure/Flow rating: 5

The topics in the text are presented in a logical, clear fashion.

Interface rating: 5

The text is free of significant interface issues. Charts and codes are in different colors so that easy to distinguish them from the main text.

Grammatical Errors rating: 5

No grammatical errors found.

Cultural Relevance rating: 5

It is very technical. The text can not be culturally insensitive

Comments

"Walk like Python, Run like C" Julia is a programming language designed for scientific computation. I believe Julia will become one of the major programming languages, especially in Engineering and Quantitative Economics. I am glad to see an open textbook about Julia so early. I like the book not only because of Julia but also because of the solid mathematics parts.