“The Case for Open-Source Math Textbooks”
The Case for Open-Source Math Textbooks
By Jason Block
Textbooks are expensive. A 2021 study conducted by the Educational Data Initiative found that on average, full time undergraduate students spend $1,240 a year on course materials. The study also found that 25% of students worked extra hours and 11% skipped meals in order to afford textbooks. Many students choose courses based on textbook costs and will often not buy required texts, even though this puts them at a serious disadvantage.
But there is a way that universities can reduce this cost for students: free and open access textbooks. While not suitable for every class (some English courses, for example, might require students to read specific books that are not public domain), many required textbooks can be replaced with open materials. This is especially true in mathematics, where open source materials are available for nearly all courses. We discuss what makes math classes suitable for open source textbooks, what has kept universities and instructors from making the switch to open source textbooks, and argue that free textbooks should become a universal feature of all undergraduate math courses.
Undergraduate math curricula are fairly standard across institutions. A list of typical undergraduate math courses is shown in Appendix 1. Furthermore, the material covered in each course is also fairly standard. For example, almost every single-variable calculus sequence (usually split between two or three semesters) will cover the same topics: limits, differentiation, integration, sequences and series. As a result, the material covered in undergraduate math textbooks is also highly standardized, and this extends to open source textbooks as well. Thus, the textbooks currently being used to teach undergraduate courses can easily be replaced with open source equivalents.
Many people hold the notion that free textbooks must be of lower quality than traditional textbooks. After all, if these books are good, why would the authors give them away for free? This is a false assumption. Appendix 2 provides examples and short descriptions of free textbooks that can be used for each of the courses mentioned in Appendix 1. Almost all of these books have been approved by the American Institute of Mathematics (AIM). To be approved, an open source textbook must be shown to meet the AIM editorial board’s evaluation criteria and thus, “be able to serve as the primary text in a mainstream mathematics course at the undergraduate level in U.S. colleges and universities.” Furthermore, since many of these books can be viewed online, they contain features that traditional print books do not have. These include the ability to randomly generate as many examples/exercises as desired, the ability for exercise solutions to be evaluated as they are completed, interactive graphs and diagrams, and hyperlinks that make navigating the text easier. Additionally, authors and editors can fix typos and add additional sections to the books at any time. This eliminates the need to release multiple editions of the same book.
Another factor that has prevented universities from switching to open source texts is the widely held belief that students prefer physical textbooks to PDF and online versions. A study led by American University Professor Naomi S. Baron for her book, Words onscreen: The fate of reading in a digital world, found that 92% of American students preferred physical textbooks over digital ones. This study is often cited as evidence that students do not want to use online textbooks. However, there are a few things that must be noted about this study. First, the students in this study were surveyed in 2010. As online learning has become more and more prevalent in recent years, students have become more accustomed to using digital resources. Second, a subsequent 2013 study by the same author found that 80% or students surveyed in the United States, Germany, and Japan said they preferred physical textbooks to digital textbooks IF the cost of both were the same. Likely, many of those students would have chosen the digital option over the paper option had the digital one been free. Not to mention, many open source textbooks do have low-cost print versions (typically about $25), and students can also print out PDF versions if they really want it in print.
Access to college math courses is essential, even for non math majors. Math classes are prerequisites for many majors, both STEM and non-STEM, and a good deal of graduate programs and entry level jobs require a decent math background. As previously mentioned, students factor in the cost of textbooks when choosing their courses. Thus, a high textbook cost can not only discourage students from enrolling in a course, but can discriminate against those with less economic means. Additionally, when students have no option but to take courses with a high textbook cost, those who do not have money for books are put at a severe disadvantage. By mandating that instructors only use free textbooks, math departments would not only save students money, but would create fairer and more equitable access to mathematics. Not to mention, it may also encourage students who normally would not take any math courses to enroll.
Hence, it is clear that using free math textbooks would be immensely beneficial for students and math departments alike. Not only must individual instructors begin to use open source textbooks, but math departments should implement this as policy. Given the wide availability of high quality free textbooks, the importance of math courses to college students, and the ever rising price of education, forcing students to buy expensive textbooks from for profit companies is, simply put, unacceptable.
Appendix:
The following is a list of classes typically taken by an undergraduate math major. Next to each course are some of the most commonly used textbooks, the price for each on Amazon, and then some free alternatives.
Calculus I, Calculus II: Single Variable Calculus by Stewart: $135 New/ $71 Used
Free alternatives:
Openstax.org Calculus Volume 1 - Covers standard Calc I material. That is, limits, derivatives, integrals, applications of derivatives/integrals. The book can be downloaded as a PDF or viewed online. The online viewer allows students to highlight and take notes that are saved. Hyperlinks make navigating the book easy.
Openstax.org Calculus Volume 2 - Covers standard Calc II material. That is, advanced integration techniques, basic differential equations, sequences and series, polar coordinates and parametric equations. The book can be downloaded as a PDF or viewed online. The online viewer allows students to highlight and take notes that are saved. Hyperlinks make navigating the book easy.
Calculus by Gilbert Strang - Covers all material typical of Calc I - Calc III. Only available as a PDF.
Multivariable Calculus (Calc III): Multivariable Calculus by Stewart: $101 New/ $61 Used
Free alternatives:
Openstax.org Calculus Volume 3 - Covers standard Calc III material. That is, vectors, multivariable derivatives, multiple integrals, vector calculus, second order differential equations. The book can be downloaded as a PDF or viewed online. The online viewer allows students to highlight and take notes that are saved. Hyperlinks make navigating the book easy.
Calculus by Gilbert Strang - Covers all material typical of Calc I - Calc III. Only available as a PDF.
Linear Algebra: Linear Algebra by Friedberg et al. : $160 New/ $85 Used
Free alternatives:
A First Course in Linear Algebra by Robert Beezer - Standard material for a one semester Linear Algebra course. That is, systems of equations, matrices, vector spaces, eigenvalues, determintates, linear transformations, representations. The book is available as a PDF or can be viewed online.
Linear Algebra by Jim Hefferon - Standard material for a first semester Linear Algebra course. Available as a PDF. Also has a solution guide that covers all exercises and ready made lecture slides that can be used by instructors.
Differential Equations: A First Course in Differential Equations by Logan: $60 New/ $45 Used
Free alternatives:
Elementary Differential Equations by William Trench - Covers all the material of a standard one or two semester course on the subject. Available as a PDF.
Intro to Proofs: Proofs and Fundamentals by Bloch: $51 New/ $40 Used
Free alternatives:
Book of Proofs by Richard Hammack - Designed to be used as a bridge to advanced mathematics. Covers sets, basic logic, various proof techniques, mathematical writing, induction, cardinality of sets, etc. Available as a PDF. Website has direct links to specific sections of the PDF.
A Gentle Introduction to the Art of Mathematics by Joseph Fields - Covers the same material as above mentioned book. This book has more of a conversational style and a strong emphasis on examples. Available as a PDF, LaTeX file, or can be viewed online.
Real Analysis: A First Course in Real Analysis by Protter and Morrey: $47 New/ $28 Used
Free alternatives:
Introduction to Real Analysis by William Trench - Covers standard material for a two semester undergraduate real analysis sequence. Available as a PDF
How We Got from There to Here: A Story of Real Analysis by Rogers and Boman - Covers the typical material of a one semester course but from a historical perspective. Ideas are presented mostly in the order that they were developed, and the reader is made to prove many of the results through exercises which are included within the chapters (instead of at the end of chapters, which is typical of most math texts).
Complex Analysis: Complex Analysis by Theodore Gamelin: $55 New/ $25 Used
Free alternatives:
A First Course in Complex Analysis by Beck et al. - Standard undergraduate complex analysis material. That is, differentiation/integration, Cauchy’s theorem, harmonic/power series, Taylor/Laurent series, singularities and residue theorem. Available as a (hyperlinked) PDF.
Abstract Algebra: Abstract Algebra a First Course by Saracino: $61 New/ $43 Used
Free alternatives:
Abstract Algebra Theory and Applications by Tom Judson - Covers all topics typically taught in undergraduate algebra courses. That is, groups, rings, fields, isomorphisms, vector spaces, galois theory. Also includes applications such as cryptography. Available as a PDF or online in both english AND spanish.
Algebra: Abstract and Concrete by Frederick Goodman - Covers mostly the same as the previously mentioned book, but from a slightly more advanced perspective and with less examples. Also covers more module theory than the above book. Available as a PDF.
Additionally, many non-math majors often take these courses as well as math courses not typically taken by math majors such as:
Precalculus/College Algebra: Algebra and Trigonometry by Stewart et al. : $74 New/ $54 Used
Free alternatives:
Precalculus: An Investigation of Functions by Lippman and Rasmussen - Covers standard precalculus material. That is, functions, linear functions, polynomial and rational functions, exponential and logarithmic functions, trigonometry, conic sections. Available as a PDF
Openstax.org Algebra and Trigonometry - Covers standard precalculus material. The book can be downloaded as a PDF or viewed online. The online viewer allows students to highlight and take notes that are saved. Hyperlinks make navigating the book easy.
Statistics: Probability and Statistics by Blom: $90 New/ $70 Used
Free alternatives:
Openstax.org Introductory Statistics - Covers standard undergraduate statistics material. That is, sampling, probability, random variables, normal distributions, confidence intervals, hypothesis testing, linear regression. The book can be downloaded as a PDF or viewed online. The online viewer allows students to highlight and take notes that are saved. Hyperlinks make navigating the book easy.
Sources:
Hanson, Melanie. “Average Cost of College Textbooks” EducationData.org, August 12, 2021,
https://educationdata.org/average-cost-of-college-textbooks
https://aimath.org/textbooks/approved-textbooks/
Baron, N. S. (2015). Words onscreen: The fate of reading in a digital world. Oxford University Press.
https://www.techtimes.com/articles/131055/20160205/more-than-90-percent-of-college-students-prefer-reading-paper-books-over-e-books.htm
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