Comprehensiveness rating: 4 read less

Given that this course is not well established in the mathematics curriculum generally, it is not appropriate for this reviewer to comment comprehensiveness. However, the topics that were selected by the author were covered in a comprehensive fashion.

Accuracy rating: 4

Overall, the author is very accurate. There is one minor item that has to be corrected. It has to do with Exercise 9 of Section !.2. The Twin Prime Conjecture is no longer. Yitang Zhang, lecturer in mathematics at the University of New Hampshire, has proved it recently. The author may have written the textbook before such an event and I am certain he is aware of this but perhaps has not had the opportunity to make the correction.

Relevance/Longevity rating: 4

The author made a strong case for content of this nature to be part of the main stream mathematics curriculum. The idea is indeed very relevant and the idea will prevail as all mathematics programs look for ways to close the wide gap that exists between the Calculus type courses and the proof based courses. As to the specific content that will decide the longevity of such an idea, the question remains to be decided. The author chose excellent topics, but those topics may not be the prime choice of most mathematics curricula.

Clarity rating: 4

The author writing style is excellent and goes in great lengths to provide adequate context for terminology. The historical annecdotes the author used are indeed very relevant, useful, and above all, very motivating.

Consistency rating: 3

I have to admit that I was very pleasantly surprised when I started reading this text. In the beginning, the author is very eloquent, precise, and yet somewhat informal. Being informal in the early stages is an excellent idea and of course justifies the gentle nature of its title. However, I continued my review and got further in this review process, I developed the sense that the author left that behind and adopted a different style in which he is in a constant dialog with the reader (the learner). This, in itself is a great idea, but there is somewhat of a break, intended and gradual perhaps, but nonetheless a break.

Modularity rating: 4

Within the framework of the author's vision for what he wanted to accomplish with students, and particularly the direct dialog, the result is often very long paragraphs. While the content of such long paragraphs is indeed very relevant and often fascinating, the concern is that students are typically not good readers of mathematics textbooks and this may be even more discouraging to them. It should also be mentionned that the text is in PDF format and perhaps, there are limitations for breaking those paragraphs and preserve the integrity of the discussion. Having said that, the text is certainly amenable to changes that would make the student more interested if not excited about reading it.

Organization/Structure/Flow rating: 4

once again, given that a course of this nature is not established as part of the mathematics curriculum, the author selected great topics as another author with the same intentions and objective would have chosed others. The selected topics by the author are excellent in my view and are presented in a logical fashion.

Interface rating: 4

This reviewer used a PC running Windows 7 and reviewed the text as a PDF file. Within these tools, this reviewer did not notice and problems pertaining to navigation or distortion.

Grammatical Errors rating: 5

This reviewer did not discern any grammatical problems. I believe the author is very thourough.

Cultural Relevance rating: 5

The author used historical annecdotes throughout the text. In doing so, I believe he approached with accuracy, integrity, and a sometimes with a sense of humor. This reviewer applaudes the author for including culturally relevant historical notes.

Comments

Overall, the author did an excellent job. One of his major objectives is for students to actually read the textbook. The good mathematics students will enjoy such a text. I believe however, that the average student will have difficulty using it and its valuable content.
The number of exercises per section is too small. Of course this can remedied by adding more.
No resources are being made available to students nor for instructors beyond the textbook.