The Wolfram Language is utilized across a variety of fields for many different purposes. We’re proud of our products’ broad applications in multiple disciplines and are excited to share seven of the latest books by Wolfram Language users. These draw upon topics ranging from social networks and communications to computational origami to the biosciences. We also had the privilege of speaking to two authors about their projects and experiences with Mathematica and the Wolfram Language.

Analyzing Narratives in Social Networks »

Dr. Zvi Lotker, author of Analyzing Narratives in Social Networks, is an associate professor in the Faculty of Engineering at Bar-Ilan University, Israel. He has a double bachelor’s degree in mathematics and computer science and another bachelor’s degree in industrial engineering, all from Ben-Gurion University, and a master’s degree in mathematics and a doctorate in distributed algorithms, both from Tel Aviv University. His main research areas are communication networks, online algorithms, sensor networks and social networks. In 2018, he was awarded the SIROCCO Prize for Innovation in Distributed Computing.

Book publisher Springer says that Analyzing Narratives in Social Networks emphasizes the storytelling aspect of social networks, as well as the connection between narrative and social networks by incorporating narrative, dynamic networks and time. It constructs a bridge between literature, digital humanities and social networks and attempts to express social and philosophic constructs in mathematical terms. By using literature networks and their accompanying narratives, this book allows for a novel approach to social network analysis.

We caught up with Dr. Lotker to discuss his latest book, his experience with the Wolfram Language and his innovative and interdisciplinary approach to social network analysis.

Q: How did you first encounter Mathematica and the Wolfram Language?

A: I am a long-devoted user of Mathematica. I have been using it since Version 2.0 back in 1992. A childhood friend recommended the program to me, and I have been closely following it since. Mathematica has accompanied me throughout my career. I used it back when I was a student and use it today in my research. It has a significant influence on my work, as I tend to get inspired to research in different directions when there are new versions to work with. I can definitely say that my book would not have been written without Mathematica.

Q: How does your book contribute to the literature on social network analysis?

A: There are a lot of new concepts in my book, such as subjective clocks, social rationality, conflict functions and high-dimensional time frames. It is also, in my opinion, the first to differentiate between frequency graphs and distance graphs in the context of social networks. But the most significant contribution my book makes is connecting social networks to narrative. Allowing machines to work with narrative gives us tools to examine philosophical questions and interact with the humanities in ways that the computer sciences have not been able to as of yet. It allows us to expand the scope of questions we can investigate using social networks.

Q: How does your book diverge from other works on social network analysis?

A: Usually, social network analysis takes social networks and analyzes them. Instead, I have tried to develop tools and definitions to allow others to go and analyze narrative networks. I have explored questions such as: What is a story? When does a story start or end? How do we define and compute conflict? How do we represent good and evil in a narrative, and what does that say about the morality of man and machine?

These literary questions have not been asked in the context of social networks yet, but doing so can enrich the field greatly, as it frames any data we have within its context. For example, I have found that community detection does not work on narrative due to freedom of interpretation, which is essential in narrative. My book addresses this using anchors and new conflict functions which expand the definition of community detection by allowing for freedom of interpretation.

Q: You take a unique approach in this book. Tell us more about how you use literature to study social networks.

A: In the sciences, we aim for the one true answer. In literature, there is an acceptance of, and even a call for, a spectrum of interpretations and answers. This is that freedom of interpretation that we addressed in the previous question. Combining the two perspectives was difficult for me, as I too come from the deterministic attitude of computer sciences.

I navigated this dissonance by having the human engage in a dialogue with the machine. The key to this process was to define concepts that both humans and machines could understand: concepts such as anchors, clocks and conflicts that could be expressed both mathematically and conversationally. Machines love to count and process, while humans love to categorize and ask questions. Combining the strengths of both sides in a dialogue between the two enriches everyone in the interaction and allows us to see things in narrative that we would otherwise not be able to. An example I like in the book is the analysis of Coppola’s The Godfather, which reveals new feminist aspects in the struggles between Connie and Michael.

Q: How might readers use the content and conclusions in your book in their everyday lives?

A: Storytelling is a cornerstone of the human experience. Any narrative can be looked at with these new tools—even customer service interactions or bedtime stories. My book is a toolbox that gives new methodologies to interact with our narratives. Some, such as my work with clocks in chapter 14, are simple enough to be used in a high-school literature classroom, whereas others can be used in academic research to grant more quantitative qualities to the humanities. It allows scientists, mathematicians and engineers to use the tools that they are most comfortable with to interact with the arts on their own terms. My goal was to expand and bridge both sides of digital humanities, and I share the delight of those that get to cross that bridge.

Q: Your book draws upon a variety of fields. Tell us more about how mathematics, literature, digital humanities and the social sciences intersect in your work.

A: The book is located in an intersection of fields: computer science, artificial intelligence, psychology, sociology and philosophy. Narrative is an interdisciplinary and complicated matter which has touched on all these subjects—yes, even computer science. The technology that takes part in narrative is often ignored, especially in the humanities, but it’s always been there, whether as fire to tell stories around, paper to put writing on or printing machines to bring books to the masses.

Now that the technology of intelligent machines has become more intertwined with our lives and narratives in the age of big data, it is important to merge it with our narrative analysis. Subjective clocks are an example of this merging. They were inspired by psychology, taking into account the human experience of forgetting unimportant time spans and remembering critical moments in the narratives of our personal lives. Introduced to social networks, these subjective clocks have turned into an important tool to understanding humans and our social interactions.

Q: How are Mathematica and the Wolfram Language used in this book?

A: My research process relies heavily on Mathematica. I usually start with an idea or a research question and gather relevant data. In the case of my book, it was typically canonical plays and movie scripts. I then use Mathematica to process the data and, at the end, produce images that summarize the process. Using the images, I can verify the soundness of the process and discard illogical conjectures. When I have the final images, I write. That’s how the book was born.

All the algorithms and graphs in my book were coded using Mathematica, and the program has saved me much time in both my researching and writing processes. I have also used Mathematica when teaching from my book over these past three years. The students who study the book are introduced to Mathematica and enjoy using it in their work. Machine learning especially is loved by students, who have great fun when exploring it within the context of narrative.

Q: Tell us more about your career as a professor at Bar-Ilan University and how you became interested in writing about social networks.

A: I am dyslexic, but I have always loved stories. When I was a child, I had a dream of developing a machine that would write and read stories to me. I also had a passion for cinema, mathematics and books—even with my difficulties with them. When I went on a sabbatical later in life, I wanted to revisit those childhood dreams. I wanted to see if I could have machines understand stories. I started to play with the idea and saw that it was possible and not just science fiction.

My book is the result of that dream, made actionable by social networks and computer science. Dynamic social networks are the perfect model for the relationships found between characters in narratives and are discrete objects that computers can manipulate and understand. My current dream is that people, even those with reading difficulties, will use the tools from my book to teach and discuss literature, and that doing so will open a door for others to develop new ways to read and appreciate stories.

Matemática discreta con apoyo de software (Discrete Mathematics with Software Support) »

Enrique Vílchez Quesada, the author of Matemática discreta con apoyo de software (Discrete Mathematics with Software Support), is a full professor at the Computer Science School of the National University of Costa Rica (UNA). He possesses a bachelor’s degree in mathematics teaching from UNA and a master’s degree in educational technology and informatics from the UNA School of Informatics. Vílchez Quesada is an international lecturer at multiple conferences related to the fields of educational mathematics, educational computing and applied mathematics.

His book Matemática discreta con apoyo de software addresses essential content related to discrete mathematics through classical theory, the development of examples and the didactic application of the free-use package VilCretas. Created by the author, VilCretas adds over 230 commands to the Wolfram Language and allows students to interact with mathematical objects, favoring classroom processes based on experimentation and analysis.

We had the opportunity to talk with Vílchez Quesada about his experience with the Wolfram Language, his latest book, the VilCretas package and his pedagogical philosophy.

Q: How did you first encounter Mathematica and the Wolfram Language?

A: I began using Wolfram technologies as a mathematics education student at UNA about 25 years ago. In principle, my use of it had a mainly technical focus, learning to use basic commands with certain applications in an educational context. After that, as a professor at different universities in Costa Rica, such as the Technological Institute of Costa Rica (ITCR), the University of Costa Rica and UNA, at which I am a tenured professor. I have been doing different teaching innovation processes using Mathematica in basic mathematics, calculus, linear algebra, statistics and discrete mathematics courses. These projects, after many years of development and various extensions, have had a direct impact on the improvement of academic work inside and outside UNA, demonstrating the didactic quality of the Wolfram Language in multiple content areas.

Q: Tell us more about your development process with VilCretas.

A: In the course EIF–203 Discrete Structures for Computer Science, a subject that is part of the study plan of the information systems engineering program at UNA, there was development of a research project in teaching called “VilCretas: A Didactic Resource through the Use of Mathematica Software for the EIF–203 Course.” The main objectives of the project were to design a software package aimed at the Mathematica program that would serve as a didactic resource to teach in discrete mathematics courses and to analyze the strengths and weaknesses of a computer-assisted strategy implemented through the use of said package, with the intention of evaluating its teaching effectiveness.

The software package called VilCretas integrates 233 functions oriented to didactic work in the context of the contents of the course and any other subject with similar properties. The development cycle of each of the commands included their design, programming, integration into the package, implementation and testing. VilCretas focuses on the following content areas: recursion, recurrence relationships, algorithm analysis, binary relationships, graph theory, tree theory, machines and finite-state automata, and languages and grammars. Its effectiveness from an educational point of view was verified through a case study.

For more information, you can consult “Estudio de caso: Estrategia de enseñanza y aprendizaje asistida por computadora para un curso de matemática discreta a través del uso del paquete VilCretas en el software Wolfram Mathematica.”

Q: How do the new commands from VilCretas aid and enhance Mathematica?

A: VilCretas is a library that adds 233 functions to Mathematica and enhances the software in the following aspects. The commands of the VilCretas package transform arid themes into possibilities for visualization and conceptual manipulation through the generation of dynamic objects, where a student, through simple slides or changing values in text fields, can visually experience the meaning of definitions, properties and theorems in different thematic axes of finite mathematics.

It also provides user-friendly commands without requiring in-depth knowledge of the Wolfram Language. This aspect is very important because usually in mathematics courses at the university level, the task of addressing the theoretical-practical content and simultaneously teaching the student population to program in the language of interest becomes very complex. VilCretas provides instructions that facilitate the generation of objects with real magnitudes through the use of geographic data already integrated within the features of Mathematica.

It is a package designed for educational purposes, so it provides the student with self-learning tools. By simply invoking certain commands, students can automatically receive step-by-step the detail of the execution of certain classic discrete mathematics algorithms, allowing them to review what they have previously solved with more traditional resources.

Q: What type of audience would benefit most from the content of your book?

A: This book is aimed at students and teachers of a generic course in discrete mathematics based on the use of software, recognizing in the use of educational technology a pedagogical mechanism that can contribute favorably to the achievement of more participatory and educational approaches and a more constructive nature by discovery.

Q: How do you envision this book being used in the classroom?

A: This book highlights the objective of creating a mathematics education centered on an innovative pedagogical design, through which teaching is oriented towards learning processes of a heuristic nature, stimulating the visualization, manipulation and autonomous construction of discrete mathematical knowledge. The effort made in this work is a reflection of a search for methodological change in an area of knowledge that is difficult to understand, responsibly assuming the substantial challenge caused by the uncertainty of a pioneering didactic transformation.

Q: How does your book contribute to the literature on discrete mathematics?

A: This book provides its readers with a nontraditional vision of discrete mathematics. It is focused on exploring new teaching and learning opportunities where the active participation of the student in the classroom laboratory is highlighted: valuing, investigating and arguing, all circumscribed within the framework of a pedagogical practice where educational technology occupies a preponderant place. After many years of classroom experience, I provide in this book a disruptive exposition by incorporating a propitious combination between classical theory, the development of a relevant number of examples and the use of software as a fundamental didactic resource.

Q: Tell us more about the relationship between VilCretas and discrete mathematics.

A: VilCretas adds commands for specialized use in the area of discrete mathematics, specifically on the topics of recursion, recurrence relations, algorithm analysis, binary relations, graph theory, tree theory, machines and finite-state automata, and languages and grammars. In this sense, the VilCretas package offers the student different tools for conceptual and procedural exploration, giving the possibility of interacting with mathematical objects and favoring classroom processes based on experimentation and analysis under the premise of a guided didactic treatment that will lead to self-learning.

Q: Tell us more about your career as a professor at UNA and how you became interested in writing about discrete mathematics.

A: I am an academic with the category of full professor at the Computer Science School of UNA, teaching the courses of Discrete Structures, Fundamentals of Computer Science and Operations Research. I serve as both a teacher and coordinator. I am a researcher associated with different activities and projects related to the development of software and computerized educational materials. I have been a professor at the Computer Science School of UNA since October 2007. I have been the coordinator of the discrete mathematics chair at UNA for more than 10 years, which is why I have been interested in writing about these topics.

In addition to these two books, here are five more recent books that utilize the Wolfram Language. Click the links to visit websites to purchase them.

Matemática para ingeniería mediante el uso de CDF’s (Mathematics for Engineering Using CDFs) »

In this book, authors Enrique Vílchez Quesada and Juan Félix Ávila Herrera present essential mathematical content for engineering students. Topics include propositional logic, set theory, theory of functions, induction and sequences, and number theory. The authors have incorporated both classical mathematical theory and detailed explanations with examples distributed throughout the book. Teachers and students will also find valuable multimedia resources developed by the authors to enhance the teaching and learning processes. These include 654 examples of code that invite the reader to view different videos with theoretical-practical explanations and around 130 Computable Document Format (CDF) files, developed by the authors, that provide tools for conceptual and algorithmic exploration. Readers are offered a new view of instrumental mathematics in engineering by combining a traditional approach with a computer-assisted one.

Introduction to Communication Systems: An Interactive Approach Using the Wolfram Language »

Author Victor S. Frost provides a unique pedagogical approach to teaching the fundamentals of communication systems by using interactive graphics and inline questions. As noted by the University of Kansas Libraries, this open-access book begins by describing the transformation of bits into digital baseband waveforms. Other topics discussed include binary phase-shift keying (BPSK), quadrature phase-shift keying (QPSK), M-ary quadrature amplitude modulation (M-QAM), M-ary phase-shift keying (MPSK), the basic theory of orthogonal frequency-division multiplexing (OFDM), traditional analog modulation systems and systems tradeoffs, including link budgets.

The topics covered build upon each other and culminate with an introduction to the implementation of OFDM transmitters and receivers, used in WiFi, 4G and 5G communication systems. Students are given interactive graphics and inline review questions that allow them to engage with communication systems concepts and rapidly examine system tradeoffs and design alternatives.

An Introduction to Computational Origami »

According to Springer, origami is treated in this book as a set of basic geometrical objects that are represented and manipulated symbolically and graphically by computers. Author Tetsuo Ida focuses on how classical and modern geometrical problems are solved by means of origami, explaining the methods with both mathematical rigor and an appeal to our scientific intuition, combining mathematical formulas and graphical images to do so.

In turn, the book discusses the verification of origami using computer software and symbolic computation tools. Eos, the binary code for the origami software created by the author, is provided with the book.

Mathematical Models in the Biosciences I »

Author Michael Frame is an award-winning professor who has endeavored to introduce essential concepts of calculus and mathematical modeling to students in the biosciences. As described by Yale University Press, this book explores essential concepts of calculus in the context of biological systems. Frame covers necessary ideas and theories of basic calculus and probability while providing examples of how they apply to subjects like chemotherapy and tumor growth, chemical diffusion, allometric scaling, predator-prey relations and nerve impulses. Based on the author’s calculus class at Yale University, the book makes calculus concepts more relatable for science majors and pre-med students.

Cluster Analysis and Applications »

Springer, the book’s publisher, describes it as intended for graduate students and experts in various fields, such as mathematics, civil and electrical engineering, agriculture and social sciences, that use cluster analysis methods and applications.

Topics covered include representatives, data clustering, searching for optimal partitions, indexes, and fuzzy clustering problems. This book is suitable for an introductory course on cluster analysis or data mining. Each chapter also includes exercises of varying complexity —from simple ones to those suitable for seminar presentations.

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!