If you have used Mathematica occasionally or heard of it, you may have the false impression that it is a program for performing complicated calculations, usually for academic purposes. However, this idea is far from the truth. Actually, Mathematica is much more than that. By putting together the computational power and ease of use of the Wolfram Language, Mathematica’s high-level general-purpose programming language, the program can be used in any scientific or technical field: Aerospace engineering, environmental sciences, financial risk management, medical imaging and many others. (You can get an idea by visiting: http://www.wolfram.com/solutions).
Mathematica can be considered a tool that empowers non-professional programmers to develop applications although if you are a professional programmer, you will see that the software provides a development environment similar to the ones available for C++ or FORTRAN. You can even use the program to control external devices.
Although many books have been written about Mathematica, very few of them cover the new functionality added to the most recent versions of the program. This text introduces the new features using real-world examples, based on the experience of the author as a consultant. In the process, you will also learn more about the Wolfram Language and how you can use it to solve a wide variety of problems. Both are the most important objectives of the book. To accomplish that, the author raises questions from a wide range of topics and answers them by taking full advantage of Mathematica’s latest features. For example: What is the hidden image in “The Ambassadors” painting by Holbein? What sources of energy does the world really use? How can we calculate tolerance limits in manufacturing processes? Are our cities getting warmer? Is the novel “El Quijote” written in Pi? How do we know how old our planet is? How can we find planets outside our solar system? How big is our galaxy? And the universe? How do we know it? How can we model the distribution of radioactive isotopes in the human body? And a tsunami? What are and how can we create Mandelbrot fractals? How can we measure the genetic distance between species? How can we perform financial calculations in real time? How do we value financial derivatives? How can we make entertaining simulations for teaching mathematics, physics, statistics, ... ? Why are there no free quarks?
The answers to the previous questions will not only help you master Mathematica, but also to become more familiar with the corresponding topics themselves.
This book will not only be useful to newcomers but also to those familiar with the program and interested in learning more about the new functionality included in the latest versions.
Those readers with minimal or no knowledge of Mathematica are strongly advised to read chapter 1 along with Stephen Wolfram’s book An Elementary Introduction to the Wolfram Language available from within the program documentation: Help ▶ Wolfram Documentation ▶ Introductory Book ≫
This text will also make it easy to start programming using the Wolfram Language and to learn how to take full advantage of its capabilities.
The final objective of Mathematica Beyond Mathematics is to help you avoid feeling overwhelmed by the software’s vast capabilities. The author has explored a significant part of them choosing the most relevant parts and illustrating them with examples from many different sources including the program documentation. Links to additional resources will also be provided. The main aim of all this is to reduce significantly the amount of time required to master the tool. The commands used will be explained using short sentences and simple examples.
Although this book is not a manual, inexperienced readers should at least read the first four chapters in consecutive order to gain a solid understanding of how Mathematica works. Regarding the rest of the chapters, you should keep in mind the following: a) Chapter 5 covers the most innovative features of the program such as how to access data from many different fields and how to use natural language to interact with the software; b) Chapter 6 deals with relatively advanced probability and statistics topics; c) Chapters 7 to 11 explore topics related to a single area of knowledge (mathematics, astronomy, nuclear physics, biokinetic modeling and economics and finance). You can read them according to your preferences; and d) Chapter 12 is for those readers facing problem requiring big computational resources (parallel computing, grid-enabled calculations, etc.) and/or the ones interested in other programs related to Mathematica such as webMathematica for adding computational capabilities to websites or Workbench, a complete software development environment using the Wolfram Language.
The principal theme of each chapter is used as the motivation to illustrate certain features of Mathematica that you may find useful for solving a great variety of problems. For example: Chapter 6 teaches you how to build a Mathematica package; in Chapter 8, related to astronomy, you learn how to create dynamic images; Chapter 10, covering the modeling of biological systems, discusses the resolution of differential equations in Mathematica using concrete examples.
Everything shown in the text has been done using Mathematica, including the access to information sources.
The book has been written using Mathematica 10 and 11 and edited using Mathematica 11, although it should still be useful with future versions of the program as well.
Mathematica Beyond Mathematics is based on Mathematica más allá de las matemáticas, 2ª Edición but its contents have been improved and updated. In this endeavor, Ruben Garcia Berasategui, a lecturer in Jakarta International College, has played a fundamental role, not only by translating the text but also by making insightful comments and suggestions.
The text doesn’t display “In[n]:=” and “Out[n]:=”, the default symbols that Mathematica adds to Input (where the commands are entered) and Output (where the results are shown) cells.
In a few cases, the book uses specific files available for downloading from the author’s website: http://diarium.usal.es/guillermo.
At the end of each chapter there is a section containing additional resources carefully selected that can be accessed most of the time from either Mathematica or through the Internet.
The author would appreciate any comments or suggestions. Please send them to: guillermo2046@gmail.com, with the subject: ‘Mathematica Beyond Mathematics’.
Salamanca (Spain), January 2017
J. Guillermo Sánchez León (http://diarium.usal.es/guillermo). Engineer, physicist and mathematics PhD holder, is an associate professor in the University of Salamanca and works in the energy industry. He has conducted research in a variety of fields: Modeling, optimization, medical physics, astronomy, finance and others. In 1999 he was awarded a research grant at Wolfram Research Inc. headquarters in Champaign (Illinois, USA) after his statistical applications with Mathematica project won a competition sponsored by the company. Since then he has been an active Mathematica and webMathematica alpha and beta tester. He’s also a Wolfram certified instructor and has extensive experience in teaching and developing programs with Mathematica and webMathematica. Some of them are cited as references in Mathematica’s official web page and are available online in both English and Spanish. Among his more than 100 articles, there are several where Mathematica and webMathematica have been used extensively.
Rubén García Berasategui is a math, finance and statistics lecturer in Jakarta International College. He holds a bachelor’s degree in business administration and an MBA. He’s been using Mathematica since 1997 and in 2012 became the first Wolfram certified instructor in Southeast Asia. He has been training hundreds of newcomers to Mathematica and sharing his passion for the program with them ever since.
The author would like to express his gratitude to Sarfraz Khan, Editor of CRC Press (Taylor & Francis Group) for his vision in realizing the need in the market for a book about Mathematica like this one, and for his encouragement and support during the production process.
The author would also like to say thank you to Addlink Software Científico (http://www.addlink.es), sponsor of the first Spanish edition; Antonio Molina and Juan Antonio Rubio for their editorial guidance; and J. M. Cascón (USAL), J. López-Fidalgo (UCLM), S. Miranda (Solventis), R. Pappalardo (US), J. M. Rodríguez (USAL) and C. Tejero (USAL) for their comments and corrections.