Applied Finite Mathematics

Reviewed by Eric Landquist, Associate Professor, Kuztown University on 5/15/19

Comprehensiveness rating: 4 see less

The text was quite comprehensive, covering all of the topics in a typical finite mathematics course: linear equations, matrices, linear programming, mathematics of finance, sets, basic combinatorics, and probability. The text explores more advanced topics as well: Markov chains and game theory. Each content chapter is followed by a homework chapter with a copious number of exercises and solutions to odds and occasional even-numbered problems. There is even a practice final exam. At the end of the textbook, there is a very brief glossary and a short index in the PDF version that is not in the HTML version on the OpenStax website; the text would be improved with an expanded glossary or index in both the PDF and HTML versions of the text.

Historical notes on linear programming were a nice addition to the text. There was also a summary section in the chapter on the mathematics of finance that gave students tips on how to classify financial problems. This is helpful to many students.

The textbook could be improved with an appendix or a chapter before Chapter 9: Mathematics of Finance on exponential and logarithmic functions and geometric series, since many students struggle with those concepts.

Content Accuracy rating: 5

The content is accurate and unbiased as far as I could tell. There are some inconsistencies with the notation that could confuse students.

Relevance/Longevity rating: 4

The content is certainly relevant for the long term. Linear equations, systems of linear equations, linear programming, financial mathematics, combinatorics, and probability will only become more relevant for students who take this course.

I only rate this 4/5 because I could not find the source code that produced the PDF file anywhere online. The XML source is available at OpenStax, but if the average mathematician wants to revise the text for his own purposes, he will want the LaTeX source instead.

Clarity rating: 5

At my university, it is mostly business majors who take this course. In light of that fact, I found the the narrative to be at a very appropriate and engaging level for these students. The text is very readable.

Consistency rating: 4

The overall framework of the text is consistent. There is a front-to-back cohesiveness to the text in terms of its format and terminology.

That said, there are some inconsistencies with the notation and typesetting. One bit of notation that was nonstandard and inconsistent was that of the complement of a set. Chapter 11 uses a $\Psi$ above $A$ to denote the complement of $A$, rather than the more standard $\bar{A}$ or $A^C$. This notation was mixed in Example 11.5. However, the notation $A^C$ is used in Chapter 13 on probability. Regarding the typesetting, there are numerous locations in with mathematical expressions are partly in "math mode" or not at all.

Any of this can be clarified in class and since this is an open-source textbook, anyone is welcome to revise to their liking.

Modularity rating: 5

The textbook is certainly modular. The text is broken up into logical chapters and sections within each chapter, thus allowing for the text to be remixed with other resources. Homework sets are even separate chapters.

Organization/Structure/Flow rating: 5

The textbook is organized in a logical way, though, as noted, a review of exponential functions before the chapter on the mathematics of finance might be helpful for a number of students. Linear programming appropriately follows matrices, which appropriately follows linear equations, etc.

Interface rating: 2

The textbook would be significantly improved with better and sharper images, graphs, tables, and figures. The author notes, however, that the course uses a TI-85 graphing calculator at his university. The graphs in the text show what would be seen on a TI-85, so it makes sense in that context. However, an update using open-source software like SageMath, GeoGebra, or Matplotlib to create the graphics would appeal to a broader audience. There are occasional inconsistencies with the mathematical typesetting, as noted earlier. The PDF version of the text isn't flashy and polished, but the webpage version on the OpenStax website has a more polished look and feel and is easily navigable. This is one area in which the community could improve this text.

Grammatical Errors rating: 5

I noticed very few grammatical errors. The text was very readable and engaging.

Cultural Relevance rating: 5

I echo the comments of another reviewer. The textbook is as culturally relevant as a textbook could be. The only lack of diversity that I noticed was that U.S. dollars were the only unit of currency used for financial applications. Since this book was designed to be used for a university in the United States, this is expected. Since this is an open-source textbook, this is something that could be modified for any currency that one wanted.

Comments

First for all, I'd like to thank Dr. Sekhon for writing this textbook. It is not a quick and easy task to write a textbook, especially one as accurate and comprehensive as this one. My students and I are very appreciative of all his work and for the many others who have contributed to the open educational resource movement. My students are especially thankful for not needing to pay for a book or a homework access code.

I should note that there is another open applied finite mathematics textbook: Business Precalculus by David Lippman. That book has much of the same content, but also has a number of homework exercises and ancillary materials available in MyOpenMath, a free and open alternative to MyMathLab developed by David Lippman. These resources complemented Dr. Sekhon's book well.

I noted this earlier, but I think it deserves another mention here. The only source code or source material for the textbook is a zip file download from the OpenStax website with the XML source. Since a LaTeX format is not available, this restricts the number of people able to contribute to the development of the text. (A Microsoft Word document would be fine too; that can be converted into LaTeX to make it look more professional.) Anyone who wants to revise the text in its current form needs some familiarity with XML. It would help, therefore, for the documents that produced the PDF file to be posted online somewhere, such as GitHub, OpenStax, or here at the Open Textbook Network.

Reviewed by Kyle Moninger, Instructor, Bowling Green State University on 2/1/18

Comprehensiveness rating: 5 see less

The text covered a comprehensive extent of topics; ranging from introductory topics of linear equations to more advanced topics such as Game Theory.

Content Accuracy rating: 4

The text was accurate and unbiased. There were very few grammar/spelling errors.

Relevance/Longevity rating: 5

The text was very relevant in its content and examples. I don't foresee any major required updates in the near future.

Clarity rating: 5

Depending on the author's style and desired audience, math texts can often be overly complex. But this text was simple and straightforward.

Consistency rating: 4

The text was consistent and had no major problems of terminology or framework.

Modularity rating: 4

The modularity of the text was appropriate as far as PDF textbooks go. The content was organize and laid out in a thoughtful manner.

Organization/Structure/Flow rating: 5

The topics were organized well and flowed from one to the other.

Interface rating: 2

Most of the charts and images were a little rough around the edges and lacked visual appeal.

Grammatical Errors rating: 5

There were very few grammatical errors.

Cultural Relevance rating: 4

It was as culturally relevant as a math textbook could be.