A Primer of Real Analysis

Reviewed by Seonguk Kim, Assistant of Professor of Mathematics, DePauw University on 9/20/19

Comprehensiveness rating: 4 see less

This book consists of all essential sections that students should know in the class, Analysis or Introduction of Real Analysis. First, in chapter 1, it has crucial prerequisite contents. Second, from chapter 2 to 8, the order of sections is reasonable and well-organized. But some instructors may skip chapters, 3, 4 and 8 because of the limit of time. Finally, I like the composition adding the exercises after the theorems because the student may be able to have ideas much easier.

Content Accuracy rating: 4

The content looks good and little error. Even though some notations are ambiguous and not easily understandable, overall is good.

Relevance/Longevity rating: 4

In the class, Analysis, students learn about the fundamental mathematical structures and concepts, and the related textbook also does not have any space adding the up to date contents. Nevertheless, I feel that this textbook provides a new view of the concepts.

Clarity rating: 5

All text is from the mathematics terminology that makes the writing lucid and readable.

Consistency rating: 5

In every chapter, it has used consistent letters and terminologies. Also, the composition is uniform using the order,
1. A brief description of the concepts,
2. Related definitions
3. Theorems
4. Examples
5. Exercise students should think about more.

Modularity rating: 5

The book breaks into separated sections, and each part is short and consists of readable and accessible text.

Organization/Structure/Flow rating: 3

The order of topics is in general. But it depends on the instructors. For example, I like to introduce the basic concepts, sets including cardinality (chapter 3), functions, logics before starting the sequences. Also, I have explained the idea, topology (chapter 4). So, in my opinion, it is better to organize the order of topics from fundamentals, including cardinality to more functions and to add the appendix, topology.

Interface rating: 5

This text has a lot of essential and useful figures and formulas. I believe the figures and graphs make students understand more easily.

Grammatical Errors rating: 5

It looks no grammatical errors. At least, I could not find them.

Cultural Relevance rating: 5

This textbook is for pure mathematics. So, I believe it has no inclusive issues about races, ethnicities, and backgrounds at all.

Comments

Overall, the textbook is very well-organized. I like the way how to organize the chapters. It is essential and nothing of unnecessary sections. Specifically, I like the composition adding the exercises after theorems and examples. If I use the book, I do not have to add more examples and suggest the students with the exercise problems. There are also some drawbacks to the book like ordering the topics. Nevertheless, I value this book in teaching the course Analysis.