Technology is an increasingly important part of education, not just for pedagogical purposes, but also as a bridge to the real-world work students will experience as they enter nearly any given industry beyond the classroom. Mathematica’s ease of use and the flexibility of the Wolfram Language feature in several recent textbooks, ranging from within applied mathematics, such as differential equations, to physical sciences like chemical engineering. We’re pleased to share our conversations with two authors whose works cover that range, and to highlight other recent releases featuring Wolfram technology.

Mathematica by Example and Differential Equations with Mathematica

Dr. Martha Abell, coauthor of Mathematica by Example and Differential Equations with Mathematica, is a professor and former dean of science and mathematics at Georgia Southern University. She received her Ph.D. at Georgia Tech in 1985 and has been a celebrated educator ever since, having received recognition for her outstanding instructional skills from her students and colleagues. For example, she won the Mathematical Association of America (MAA) Southeastern Section Distinguished Service Award in 2016, and was nominated by the same organization for their Meritorious Service Award in 2019. Her coauthor, Dr. James Braselton, is also an esteemed educator at Georgia Southern University and has been a prevalent author and peer of Dr. Abell for decades.

Mathematica by Example, sixth edition, published in 2021, was described by publisher Elsevier as “an essential resource for the Mathematica user, providing step-by-step instructions on achieving results from this powerful software tool.” Moreover, it praises the textbook for its thoroughness and recommends it to science students, researchers and anyone looking to utilize Mathematica.

Differential Equations with Mathematica, fifth edition, published in 2022, is a necessary resource for those interested in exploring concepts regarding linear algebra and calculus through Mathematica. Publisher Elsevier writes “it uses the fundamental concepts of the popular platform to solve (analytically, numerically, and/or graphically) differential equations of interest to students, instructors, and scientists.” We talked with Dr. Abell following the release of her new books.

Q: What were your intentions for Mathematica by Example? Were there any gaps in the literature that you were attempting to fill?

A: As my colleagues and I were learning how to use Mathematica, we realized that there were few resources available to assist us. As a result, Jim Braselton came up with the idea that we develop Mathematica by Example in the early 1990s. It bridges the gap between elementary handbooks and those references written for advanced Mathematica users. Mathematica by Example is driven by examples, where we introduce the basic commands based on typical examples of applications of those commands. In addition, the text includes commands useful in areas such as calculus, linear algebra, business mathematics, ordinary and partial differential equations, and graphics.

Q: How has your experience at Georgia Southern University led you to this type of work? What inspired you?

A: Computer algebra systems, like Mathematica, became more prevalent in the university setting as I started my career as a faculty member, so I became interested in finding ways to use Mathematica to enhance the instruction of my classes and augment the tools available for conducting mathematical research. I found that Mathematica was particularly helpful in allowing students to explore concepts graphically and numerically, which helped them to better understand the more theoretical areas of mathematics.

Reflecting on my days as a student, I remembered solving challenging problems but having no way to visualize the solutions, and I wanted my students to have a better experience. In my teaching, it became commonplace to graph solutions. For example, after we solved an applied problem involving partial differential equations such as the wave equation on a circular region to find the vibrations of a drumhead, we used Mathematica to observe the vibrations. My students always seemed to appreciate my efforts to bring mathematics “to life” with them.

Q: Why is Mathematica your language of choice? What are some of its “hidden gems”?

A: I appreciate Mathematica’s consistency. Commands rarely become obsolete, so we didn’t have to rewrite our code from previous projects when new versions of Mathematica were released.

Mathematica’s Manipulate command was a game-changer in the development of apps to help students explore concepts in the undergraduate mathematics curriculum. Anyone with an elementary knowledge of Mathematica can quickly write a command to help their students.

Q: Lastly, as a successful woman in science, what advice would you give to other women attempting to follow your footsteps?

A: I would recommend building a supportive network of colleagues and friends. My success was possible because I was part of a wonderful collaboration with Jim Braselton, and we were both lucky to be members of a department/college/university where our work was valued.

The expectations of faculty have increased over the years, so faculty need to be careful in balancing their workload, making sure that they are working on projects that will be positively reviewed on faculty evaluations (annual reviews, pre-tenure, tenure and promotion, etc.).

An ideal approach is to develop a research program that involves connections to teaching (such as research with undergraduates or graduate students, the scholarship of teaching and learning, etc.) and service (such as leading a committee within a professional organization, organizing research or professional development sessions, etc.).

Involvement in programs such as Project NExT (MAA) and research interest groups associated with professional organizations (MAA, American Mathematical Society, Society for Industrial and Applied Mathematics) also helps faculty to build a community in which they can grow and succeed.

Introduction to Chemical Engineering Analysis Using Mathematica: For Chemists, Biotechnologists and Materials Scientists »

Dr. Henry Foley is the current president of the New York Institute of Technology and former chancellor of the University of Missouri-Columbia. He earned his Ph.D. in 1982 at Pennsylvania State University and has been incredibly involved in academia throughout the United States, having held scholarly positions at numerous universities. Not only has Dr. Foley been a distinguished lecturer at the University of Utah and the University of Notre Dame, but he has also been awarded the Academy of Science-St. Louis Award and the Science Leadership Award. In addition, he has been acknowledged as a fellow of the American Association for the Advancement of Science, the American Chemical Society and the Industrial and Engineering Chemistry Division.

Introduction to Chemical Engineering Analysis Using Mathematica: For Chemists, Biotechnologists and Materials Scientists, second edition, was published by Elsevier in 2021. According to Elsevier, the textbook reviews “the processes and designs used to manufacture, use, and dispose of chemical products using Mathematica… covering the core concepts of chemical engineering, ranging from the conservation of mass and energy to chemical kinetics.” Moreover, the textbook is a valuable resource that incorporates easy-to-use technology with complex concepts. We discussed the new book with Dr. Foley.

Q: What was your first encounter with Mathematica and the Wolfram Language?

A: It’s 1988 and I was teaching chemical engineering at the University of Delaware; we were trying to bring computing into the classroom. This was pretty funny, because we literally had to carry large desktop computers into the classroom to work with them. That’s beside the point. I was trying to find a way to get students to do more computing. So, I was looking around for something that would allow us to do that, and there were a few things that were on the market at the time. Then, Mathematica came out that year and I was astonished. I was just blown away by what I could do and started using it immediately, and it was so easy to use because even then it was, relative to other programming languages, much closer to natural language programming than anything we’d ever seen. You got text, graphics and plotting all for free. I started off using it with honors students in the committee program. So you know, chemical engineers are better than your average student, and the honors students among them were even better than those students, so they could kind of handle it, and they got it and it was fun.

Q: What were your goals for Introduction to Chemical Engineering Analysis Using Mathematica: For Chemists, Biotechnologists and Materials Scientists, second edition? How is your textbook different than others on the subject?

A: I decided to start to write a book on it based on everything I’d learned in the classroom, how I taught it and my own research. The primary goal was how to think like a chemical engineer, and then how to do modeling and computing all at the same time. At the time there were books that taught you how to think like a chemical engineer, how to build a model, but not how to solve it. There were also books that were all about trend programming and chemical engineering. But I wanted to do something new. So, we brought all those pieces together, trying to teach people computational thinking.

If you have a big job to do, and you have to do it many times, like some big calculation for thermodynamics, then you carefully write a program to do that. And whenever you need to do that calculation, you’ve got it. But it takes a lot of work and a lot of effort—it’s not a homework problem.

So you aren’t really thinking computationally, you’re more thinking like a programmer, because you get so deeply involved in the programming. But with Mathematica and the Wolfram Language, we can start to get people beyond that—get them to think beyond that which is the physical process, the chemical process that’s happening. We wanted to teach people how to use advanced technology, Mathematica, to improve their understanding of physical concepts.

Q: If you had to describe your book in one sentence, not in the synopsis, what would you say?

A: So the first part of the book is how to use Mathematica, and that goes almost one hundred pages. Then, the next eight hundred pages are examples of how to do things that are of importance to chemical engineers, chemists, material scientists, maybe even physicists or chemical physicists. It’s really two books in one; you get a how-to book, and then you get a book on the topical concepts.

Q: How has your experience at the New York Institute of Technology inspired your research?

A: I never knew that I would be a president, but I really love it and I find it incredibly rewarding. However, it’s also been very difficult because these are obviously very unusual times. One of the great things about the pandemic for me was I had much too much time, and on evenings and weekends and vacations, I could review 20 years or so of material. I was able to look back on all of my years of experience, using them to the fullest extent. I think I put them together in this new book, which is really the second edition of the first book, but it might as well be a new book. And so the pandemic turned out to be productive for me, and my work was kind of how I kept myself sane, by working on this every day in between my regular work.

Q: Do you see examples of concepts from your academic/career life in your personal life? Do the two ever mix? Does your personal life inspire your study?

A: I’m lucky in that I’ve never really worried about career life balance, so to speak. I know that if, for whatever reason, I wasn’t able to be a president tomorrow, I would still do my research and I would still be involved because I love what I do. I actually know that if I retire someday, I’ll be doing this stuff because I love it.

I even have another book in mind, and I’d like to do it a similar way. My goal is to make the barrier for entry very low, meaning I want to make the information accessible and inviting. A lot of this kind of information ends up being very exclusive, so only those who have a preexisting dedication seek it out. With this book, I want people to feel inspired to do more. Without barriers, people can become imaginative and creative with what they’re doing.

I’m thinking of a book on partial and differential equations, which is pretty austere stuff, and yet it drives the world and it should be accessible to more people. So I’d like to work on that because it’s not really as daunting or as frightening as it seems when you’re faced with the full theoretical aspects of partial differential equations. For example, if you had to know how your car works in detail down to the radical reactions that are occurring during combustion in your engine, you’d never turn the key on. You’d never drive anywhere but you’re perfectly capable of driving and using your car, and so forth, and getting enormous pleasure and gain from it. And I see math the same way.

The computer now does all that for you much better than you would ever do it, so why try? Why not focus on the part of the problem that’s the most important? Like, why is it a problem? How can a human brain digest this differently than a computer? So, let’s try to create a word statement, a picture for what it is, so that we really understand it, and let’s build some equations that describe it. Let the computer solve it, and then let’s try to see how it behaves. Does our model accurately describe the behavior? And if not, okay, what can we do to make it more sophisticated? So you also believe in starting with small learning models and then working your way up to progressively more accurate, serious models. That’s something I’m not sure I’ll ever see in practice, but making advanced technologies more accessible is amazing work.

Natural Resource Economics: Analysis, Theory, and Applications »

Written by Dr. Jon M. Conrad and Dr. Daniel Rondeau and released in 2020, this new book brings computation to resource management and economics. Publisher Cambridge calls it “foundational to advanced research, as it presents required mathematical methods, classic dynamic models for non-renewable and renewable resources, and explores several contemporary problems.” Moreover, students are given resources to use Mathematica in studies such as the transition from fossil fuels to clean energy, as well as over-fishing and deforestation. Natural Resource Economics: Analysis, Theory, and Applications also allows those interested in environmental studies to access information through advanced technology.

Multivariable Calculus with Mathematica »

This textbook, written by Dr. Robert P. Gilbert, Dr. Michael Shoushani and Dr. Yvonne Ou, is unique because it encourages students to learn the ins and outs of Mathematica so the program can be utilized to its fullest extent as a resource. Moreover, the book is described by publisher Routledge as “a textbook addressing the calculus of several variables. Instead of just using Mathematica to directly solve problems, the students are encouraged to learn the syntax and to write their own code to solve problems.” Multivariable Calculus with Mathematica also provides questions to test students’ ability at the end of each chapter, as well as an online component that aims to increase students’ understanding of real-life applications to their study.

Analysis with Mathematica »

Galina Filipuk and Andrzej Kozłowski have released the third volume of their series Analysis with Mathematica. This series tackles concepts ranging from single-variable calculus to differential geometry and special functions. Each volume, while varying in subject, is unified by the organization of the text. Publisher DeGruyter says that Mathematica is constantly integrated with examples so students are better able to understand the concepts. This organization provides students with numerous practice problems, allowing them to learn the concepts from their own calculations with Mathematica. Additionally, each textbook in the series is a continuation of the last, meaning that they assume that the reader has prior knowledge, making this series perfect for more experienced users of Mathematica.

If you would like to preview Dr. Filipuk and Dr. Kozłowski’s trilogy, you can find sample chapters of each textbook and converse with the authors on Wolfram Community.

Mathematics, Physics & Chemistry with the Wolfram Language »

S. M. Blinder’s 2022 textbook holds a vast wealth of knowledge ranging from special functions to black holes. Additionally, Mathematics, Physics & Chemistry with the Wolfram Language utilizes interactive learning, as it comes with all of its code written in Wolfram Notebooks. This allows the reader to work through practice problems with full control and the ability to experiment, ensuring full understanding of the concepts. World Scientific, the book’s publisher, writes, “This book should be a valuable resource for researchers, educators and students in science and computing who can profit from a more interactive form of instruction.”

A Quantum Computation Workbook »

This accessible textbook from author Dr. Mahn-Soo Choi provides students not only instruction on quantum computation, but also tools to best use Mathematica to that end. Springer, the publisher, calls this textbook “an organization of all the subjects required to understand the principles of quantum computation and information processing in a manner suited to physics, mathematics, and engineering courses as early as undergraduate studies.” Additionally, A Quantum Computation Workbook is praised because it helps students to develop their understanding of Mathematica and quantum computation by encouraging them to alter the code within the textbook.

Graph and Network Theory: An Applied Approach Using Mathematica »

Published in 2022 and written by Dr. Michael A. Henning and Dr. Jan H. van Vuuren, this new book hones in on application. Springer depicts the textbook as “covering a diversity of topics in graph and network theory, both from a theoretical standpoint, and from an applied modelling point of view.” This dynamic approach to teaching graph theory makes Graph and Network Theory a valuable resource for those interested in learning fundamental and advanced concepts. The textbook also provides students with multiple approaches to the material, meaning that there are different study tracks depending on students’ prior knowledge, with demonstrations and real-life applications to motivate any student.

Computer Modeling and Simulation of Dynamic Systems Using Wolfram SystemModeler »

In 2020, a full team of educators worked together to bring readers this new text: Dr. Kirill Rozhdestvensky, Dr. Vladimir Ryzhov, Dr. Tatiana Fedorova, Dr. Kirill Safronov, Dr. Nikita Tryaskin, Dr. Shaharin Anwar Sulaiman, Dr. Mark Ovinis and Dr. Suhaimi Hassan. This textbook serves as both a brief introduction into model theory and an advanced look at creating computer models. With its special attention given to Wolfram System Modeler, Computer Modeling and Simulation of Dynamic Systems Using Wolfram System Modeler is perfect for those who wish to become more familiar with Wolfram technology and computer modeling. Moreover, Springer recommends it to “students and professionals in the field,” writing “the book serves as a supplement to university courses in modeling and simulation of dynamic systems.”

If you’re interested in finding more books that use the Wolfram Language, check out the full collection at Wolfram Books. If you’re working on a book about Mathematica or the Wolfram Language, contact us to find out more about our options for author support and to have your book featured in an upcoming blog post!