Math in Society: Mathematics for liberal arts majors

Reviewed by Larissa Shatalova, Instructor, PhD, Math department, Lane Community College on 8/24/25

Comprehensiveness rating: 4 see less

The textbook provides broad coverage of the essential topics for a liberal arts mathematics course, including logic, probability, statistics, financial mathematics, and voting theory. The sequencing is clear, and each section includes definitions, worked examples, and exercises. In general, the material is sufficient for a one-term course, and instructors can select topics as needed.

One area that could benefit from additional clarity is the introduction of truth tables in the logic section. While the mechanics of constructing and reading truth tables are explained, the text does not fully highlight their purpose — namely, how truth tables serve as a systematic tool to verify logical equivalence, test the validity of arguments, and connect symbolic logic to everyday reasoning. A brief discussion of why we use truth tables, beyond the procedural steps, would make this section more meaningful to students, especially those encountering formal logic for the first time.

Content Accuracy rating: 5

he content of the textbook is accurate and free from obvious errors. Explanations of mathematical concepts are consistent with standard treatments, and examples are carefully worked out. Numerical values and calculations check out correctly, which supports student trust in the material. The text avoids bias and presents information in a neutral, accessible way.

Overall, the accuracy is strong; occasional places where more context could be added (e.g., clarifying the applied purpose of truth tables or highlighting the assumptions behind financial formulas) do not detract from the overall reliability of the text.

Relevance/Longevity rating: 5

The textbook addresses topics that are highly relevant to students in a liberal arts mathematics course: logic, probability, statistics, finance, and applications to civic life. These areas are unlikely to become obsolete, since the underlying mathematical principles remain stable over time. Examples are generally drawn from everyday contexts, such as personal finance or voting systems, which makes the material relatable.

Because some examples (e.g., tax brackets or electoral numbers) may change periodically, instructors may need to provide updated data. However, the structure of the book allows for such updates without undermining the longevity of the text. Overall, the book has lasting value as a foundational resource.

Clarity rating: 4

The textbook is written in a clear and accessible style. Definitions are introduced with straightforward language, and worked examples help reinforce new concepts. Most explanations avoid unnecessary jargon, which supports students with limited mathematical background.

At the same time, certain sections could benefit from an added sentence or two of “why this matters” (e.g., truth tables or compound interest formulas). This would help students see not only how to perform a procedure but also its purpose. Overall, the text is understandable and well-suited for a diverse audience, including first-generation and ESL learners.

Consistency rating: 5

The textbook maintains consistent terminology, formatting, and structure throughout. Each chapter begins with clear objectives, introduces definitions, and follows with examples and exercises in a similar pattern. Symbols and notation are standard and align with common mathematical conventions, reducing the cognitive load on students.

The tone of explanations is also steady, presenting material in a supportive and neutral way. This consistency makes it easier for students to move from one section to the next without adjusting to a new style of presentation.

Modularity rating: 5

The textbook is organized in a way that allows instructors to use chapters and sections independently. Each unit begins with its own definitions and examples, so it can stand alone without requiring students to have read the entire preceding material. This structure makes it easy to adapt the book to different course formats — whether a full-term sequence or a shorter, topic-focused class.

For example, an instructor can focus only on logic, finance, or probability without losing coherence. The modular design also supports integration with supplementary materials, such as interactive slides or AI-based explanations, enhancing flexibility in delivery.

Organization/Structure/Flow rating: 5

The textbook is well-structured, with a logical progression of topics appropriate for a liberal arts mathematics course. Each chapter builds on prior knowledge without assuming extensive mathematical background, which makes the flow accessible to a wide range of students. Sections follow a predictable pattern of definitions, examples, and exercises, which creates a sense of continuity.

The flow between major themes (logic → probability/statistics → finance → voting theory) is generally smooth, though occasionally transitions could be strengthened with brief connections to show how one area leads into the next. Overall, the structure is coherent, student-friendly, and adaptable to different instructional approaches.

Interface rating: 4

The online interface of the textbook is clean and functional. Navigation is straightforward, with chapters and sections clearly labeled, and links that work reliably. The text displays well across different devices, and mathematical notation renders clearly without distortion.

At the same time, the interface is relatively plain: it relies heavily on static text and could be enhanced by integrating more visual elements or interactive components. While this simplicity keeps the resource stable and easy to access, additional multimedia would make the learning experience more engaging for today’s students.

Grammatical Errors rating: 5

The textbook is free from significant grammatical or typographical errors. Sentences are clear and correctly structured, and mathematical notation is used consistently. Any minor issues do not interfere with comprehension or readability.

Cultural Relevance rating: 5

The textbook presents material in a culturally neutral and inclusive way. Most examples are drawn from everyday contexts such as finance, voting, and general problem solving, which makes them broadly accessible. The text does not include offensive or culturally insensitive content. That said, many examples are somewhat generic and U.S.-centric (e.g., tax brackets, electoral systems). Incorporating a wider variety of cultural perspectives or international contexts could strengthen student engagement, particularly for diverse or global classrooms.

The second edition of Math in Society shows noticeable improvements in clarity and structure, particularly in Chapter 1. The additional repetition and reinforcement of key ideas in the opening sections help students who may be encountering formal logic for the first time. This scaffolding strengthens comprehension without overwhelming learners.

Overall, the updates enhance accessibility, making the text more effective as an entry point for liberal arts mathematics students.

Reviewed by Heather Kahler, Assistant Teaching Professor, University of Wisconsin - Superior on 1/23/23

Comprehensiveness rating: 3 see less

The book does not cover as many topics as I am used to seeing in liberal arts mathematics texts. The topics that are covered are done well. I was especially impressed with the thorough section on Contingency Tables under Probability. I would, however, like to see further coverage on Percentiles (other than quartiles) and Counting (Permutations, Combinations, Fundamental Counting Rule).

Content Accuracy rating: 4

Errors are minimal (such as a missing period). Comments regarding bias are included in the cultural section.

Relevance/Longevity rating: 4

Examples are interesting and transcendently relevant across time and people groups. For example, the price of peanut butter is used to illustrate descriptive statistics. It would be reasonable to expect an instructor to update these numbers when they become obsolete or even to provide actual data. Some topics focus on news and current cultural interests and may need to be revisited in the future. However, their presence can be a strength for current students.

Clarity rating: 4

The text uses some jargon, without explanation. However, when the wording is difficult, thorough examples are given to demonstrate the concepts.

Consistency rating: 5

Layout is consistent and predictable in the best sense possible. Terminology is consistent.

Modularity rating: 5

Each smaller section includes its own set of problems. There is some self-referencing, such as “in the last section” or “in this chapter”, but this seems reasonable and can be reworded easily if a section is omitted. Most of the time, example data is changed so that a problem can be omitted without needing to change several others.

Organization/Structure/Flow rating: 5

Topics are arranged in a logical order that builds upon the topic before.

Interface rating: 5

There are no issues here.

Grammatical Errors rating: 5

I noticed 1-2 two small errors (missing punctuation, wrong word used). Overall, the grammar is excellent.

Cultural Relevance rating: 4

The content is intentionally inclusive but is biased toward current trends in our culture of what is politically correct. I would prefer more neutral terms and examples.

The authors of this book obviously put in a lot of time and effort to create a relevant, accurate, and user-friendly resource. Thank you.

Reviewed by Shannon Benes, Adjunct Associate Math Professor, Johnson County Community College on 6/3/22

Comprehensiveness rating: 5 see less

We do not teach a course like this at our school, but I wanted to review this textbook and see what would be included in a curriculum for such a course. Each chapter in the book covered a topic that was very appropriate for a Math in Society course. The topics were comprehensive for the audience this book was tailored to cater to.

Content Accuracy rating: 4

Nothing makes me more upset than finding typos and errors in a math textbook. I did not read this cover to cover nor have I used it to teach from, but in all that I did read, I did not find any errors. In the first few pages, the book lists the errors that have been found since its last printing. I do wish the several BLANK pages throughout would be omitted so that any student wanting to print the book could have a more consolidated copy. I feel this book is unbiased as different genders and ethnically diverse people were shown with a brief account of their lives and contributions.

Relevance/Longevity rating: 4

I wish this book had more graphics to make it interesting to look at, however, it is the graphics that sometimes make a book out of date more quickly (ex a graphic of a flip phone, car, or some other image that has been replaced by a new and improved version.) There are some tutorials about using Excel that I wonder might become out-of-date as Microsoft puts out new updates. I might suggest inserting a link to irs.gov for using current tax year values.

Clarity rating: 5

There is a lot of text in this book, but it was easy to follow and descriptive when it needed to be.

Consistency rating: 5

A perfect example of this is in Chapter 5.2- Voting Methods. Each different type of voting method is explained. A reader could look up a definition of each type for a further understanding, but it would not be necessary as the author has explained each type and given an example using a possible situation.

Modularity rating: 3

This book would benefit from a consultation with a graphic designer. There were enormous blocks of text. As I read line upon line of text, I wondered how many liberal arts majors taking "Math in Society" will actually take the time to read the textbook. A few times as I read, the book reminded me of some of my master's level math textbooks that had a tendency to put me to sleep because of the lack of graphics or any kind of attention getters.

Organization/Structure/Flow rating: 5

This book was very organized and each section was clearly labeled in a logical way with good flow from one idea to the next.

Interface rating: 4

No images were distorted or anything like that. Sometimes, when typing math, formulas do not transfer the way intended, occasionally even the latex code will pop up unintentionally. This never happened in this book. There were no distracting display features or any images that were confusing or misplaced. All of the wrap-around with text and images were correct and flowed well.

Grammatical Errors rating: 5

I did not find any grammatical errors.

Cultural Relevance rating: 5

As mentioned previously, several individuals from various diverse populations are summarized at the beginning of each chapter. I wonder if one of the errors listed in the first few pages of the book is an attempt to correct what may have been taken as an insensitive way of stating the Rodney King tragedy.

I loved the chapter on logic! I would like to see my school create a Math in Society course. If I did not use this textbook for the course, I would definitely use it as a reference as I taught the course.

Reviewed by Jessica Knoch, Mathematics Instructor, Lane Community College on 1/2/22

Comprehensiveness rating: 4 see less

All the topics for Math 105 are covered in some way in this textbook, and some additional topics are included that could be covered in Math 105, depending on your school. Some of the instructors at my school found the removal of some probability topics not to their liking, but in my mind the removed topics are not necessary for students to use probability in making decisions in their lives. I did not find an index in either the PDF version or the online version, although the PDF is searchable.

Content Accuracy rating: 5

A few small errors are included in some sections, but overall the mathematics is correct and the English is clear.

Relevance/Longevity rating: 4

The content is highly relevant and up-to-date as of Fall 2021. Some of the sections, notably in the "Mathematics of Democracy" chapter, will need to be updated in a short time or else feel stale and out of date. Including data on current census numbers and representation in Congress is a good way to make the math feel relevant to students, with the caveat that it must also be kept up-to-date in the future.

Clarity rating: 5

The language is very clear. I had a small number of students who said that some concepts were not explained enough different ways for their liking, but my experience as an instructor tells me this is not a fault of the book. Most of the time, I'd rather have one or two simple and clear explanations that will make sense to most students, and that is what this book provides.

Consistency rating: 5

The textbook is internally consistent in terminology and framework. Interestingly, the authors seem to have sidestepped the confusion of "annuity" and its various meanings, and talk instead about loans and savings plans. This seems to be a good thing, because students can have difficulty with Lippman's original use of the terms "annuity" and "savings annuity."

Modularity rating: 4

The book is divided into five chapters, some of which could be rearranged if desired. There is language throughout the text that borrows from early sections about logic and Venn diagrams, so I believe that should still be covered early in term. It would be more difficult to use this text if you wanted to remove the sections on Sets and Logic (which are not universally covered in Math 105 in Oregon).

Organization/Structure/Flow rating: 5

The book's structure and organization are strong points: sections are clearly labeled and are presented in a clear, logical manner. Chapter reviews are included, as well as some optional topics.

Interface rating: 5

The online textbook has an excellent interface, using PreTeXt/MathJaX which has become more common in recent years. I found it easy to navigate and didn't receive any comments from students about the logistics of using the online textbook. The PDF version is a little more difficult to use, because of needing to scroll to various sections, but this is common to all PDF textbooks and not unique to this one.

Grammatical Errors rating: 5

I don't recall finding any grammatical errors.

Cultural Relevance rating: 5

Another shining strength of this textbook is the emphasis on inclusion and representation of a variety of races and backgrounds. Each chapter begins with a highlight of a relevant mathematician from an underrepresented group, and these highlights can be incorporated into your teaching or not, as you like. Many examples from Lippman's original text have been reworked or rewritten for greater inclusion and diversity. I will not say that no one could be offended by the way some material in the book is presented -- it may be uncomfortable for some students and instructors to read about the historical context of slavery in the formation of Congressional representation in the United States, for example. However, these honest confrontations of true facts in our country's history are an important step to raise awareness, which can then one day lead to progress and change in our society.

Although it isn't perfect, this textbook is an excellent example of relevant math text that students can find more in common with than they ever have in a math course. Using this textbook to teach Math 105 has made it easier for me to change students' minds about math and their relationship with it.