Mathematica beyond Mathematics

Mathematica Beyond Mathematics: The Wolfram Language in the Real World. 2nd Edition. Chapman and Hall/CRC.

Second Edition:

ISBN 9781032004839
December 19, 2022 Forthcoming by Chapman & Hall
458 Pages 353 Color Illustrations

First Edition

by José Guillermo Sánchez León (Author). May 22, 2017.

Reference – 450 Pages – 431 Color & 9 B/W Illustrations. ISBN 9781498796293 – CAT# K30366.

Why a new book about Mathematica?

For the past 30 years I’ve been conducting Mathematica seminars and teaching students how to develop applications using the program in a wide variety of campuses.  These experiences have taught me several things:

i.             A majority of both experienced users and newcomers, still think erroneously that Mathematica is mostly a language for solving symbolic math problems.

ii.            Plenty of long-term users are not aware of many of the new capabilities that that have been added to the program over the years.

iii.           The number of functions available has grown enormously and now there are more than 6,000. With so many functions, it very time consuming to learn about them using the extensive Wolfram documentation.

In this book, I have decided to address these issues and show that the program has capabilities that go beyond math calculations (that’s the reason behind the book title). Throughout the text, Mathematica’s features, including of course the latest ones, are introduced while solving problems in many different fields such as: astronomy, biology, chemistry, economics, finance, geography, linguistics and nuclear physics among many others (See Contents) . When choosing the problems, I have relied on my own experience and also modified a few selected examples from Wolfram Research vast information resources. At the end of each chapter there’re also additional sources to further explore the topics. I have also strived to avoid writing too complicated programs and except in a reduced number of cases, all the examples contain just a few lines of code.

Basically, this is the book that I wish I had had when I started learning Mathematica. A book that without the help of my colleague Ruben Garcia Berasategui would not have been possible to publish in English.

The entire text, including the table of contents and index, have been written exclusively using Mathematica (edited in Math 13.0.1 and 13.1, tested with Math 13.2).  Since the book not only aims at introducing the reader to Mathematica but also to the technical and scientific fields covered, it could be read without being in front a computer. However, to be able to take full advantage of it, access to a local or cloud version of the software is required.

If you have some comment about the book send to me an e-mail (guillermo2046(at), with Subject: Mathematica beyond)


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 including its natural language capabilities, curated datasets and entities. 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. Examples that strike a balance between relevance and difficulty in terms of Mathematica syntax allowing readers to incrementally build up their Mathematica skills as they go through the chapters.

The book shows how a newcomers can start to use the language without  knowing any function (using the natural language).  However some knowledge is recommended, even advanced users can find useful the examples used . When the book is finished, the user will know about 1000 functions, and the most important: the user will have learnt how to browse to find an appropriate function.

Click MBM2Ed Supplementary Materials (2nd Ed. Updated 2022-12-05) and  here (1st Ed. Updated 2018-03-17) to download the supplementary materials where it is included some files to replicate a few examples described in the books and Comments and Corrections.


Preface IX
1. Getting Started 1
1.1 Mathematica, an Integrated Technical Computing System 1
1.2 First Steps 3
1.3 Editing Notebooks 12
1.4 Basic Ideas 19
1.5 From Graphics to Machine Learning 29
1.6 Additional Resources and Supplementary Materials 40

2. Programming: The Beauty and Power of the Wolfram Language 41
2.1 Mathematica’s Programming Language: The Wolfram Language 41
2.2 Lists Operations 46
2.3 Association and Dataset 50
2.4 Matrix Operations 52
2.5 Set, SetDelayed, and Dynamic Variables 55
2.6 Functional vs. Procedural Programming 57
2.7 Apply, Map, and Other Related Functions 60
2.8 Iterative Functions 63
2.9 Pure Functions 64
2.10 Global and Local Variables 70
2.11 Conditional Expressions and Conditions 72
2.12 Accuracy and Precision 79
2.13 Choosing the Method of Computation 82
2.14 Optimizing the Computation Time 84
2.15 Cloud Deployment 86
2.16 Package Development 87
2.17 Additional Resources 90

3. Interactive Applications, Image Processing, and More 91
3.1 The Manipulate Function 91
3.2 Creating Demonstrations 97
3.3 Image Processing 100
3.4 Image Manipulation 105
3.5 Graphs and Networks 110
3.6 Application: Finding the Period of a Pendulum 113
3.7 Additional Resources 116

4. Accessing Scientific and Technical Information 117
4.1 The Wolfram Data Framework: Introducing Entities 117
4.2 Computable Data Functions 123
4.3 The Wolfram Data Repository 127
4.4 Weather Data in Real Time 129
4.5 Chemical and Physical Properties of Elements and Compounds 132
4.6 Life Sciences and Medicine 136
4.7 Earth Sciences and Geographic Data 142
4.8 Additional Resources 151

5. Data Analysis and Manipulation 153
5.1 Importing/Exporting 153
5.2 Statistical Analysis 162
5.3 Probability Distributions 169
5.4 Exploratory Data Analysis 181
5.5 Bootstrapping and Confidence Estimates 189
5.6 Curve Fitting 194
5.7 Time Series Analysis 203
5.8 Spatial Statistics 204
5.9 Additional Resources 208

6. Machine Learning and Neural Networks 207
6.1 What is Machine Learning 207
6.2 Classification 212
6.3 Prediction 221
6.4 Working with Neural Networks 225
6.5 Additional Resources 230

7. Calculating π and Other Mathematical Tales 231
7.1 The Origins of π 231
7.2 Archimedes’ Approximation 232
7.3 π with More Than One Billion Decimals 235
7.4 Buffon’s Method 240
7.5 Application: Are the Decimal Digits of π Random? 242
7.6 The Strange Connection 246
7.7 The Riemann Hypothesis 248
7.8 Looking for the Magic Prime Formula 252
7.9 Additional Resources 254

8. Looking at the Sky 255
8.1 A Short Astronomical Walk 255
8.2 Solar Analemma 259
8.3 Stargazing 260
8.4 Application: Determining the Color of the Stars 279
8.5 The Measurement of Distances Across the Universe 283
8.6 Application: Binary Systems and the Search for Exoplanets 287
8.7 Light Curves 291
8.8 Additional Resources 300

9. Nuclei and Radiations 301
9.1 Nuclear and Particle Physics 301
9.2 What are Isotopes? 302
9.3 Decay Constants, Decay Periods and Half-Lives 304
9.4 Decay Chains 308
9.5 Application: Modeling the Evolution of a Chain of Isotopes Over Time 313
9.6 Application: Dating the History of Humankind 316
9.7 Application: Calculating Binding Energies 321
9.8 Radiation Attenuation 328
9.9 Additional Resources 330

10. Modeling: Applications in Biokinetics, Epidemiology and More 331
10.1 Compartmental Modeling 331
10.2 Epidemiological Models 342
10.3 Physiological Modeling 346
10.4 Fitting a Model 351
10.5 Optimal Experimental Designs (OED) 355
10.6 BIOKMOD: The New Iodine OIR Model (ICRP 137) 360
10.7 Additional Modeling Examples 364
10.8 Modeling Using PDEs 366
10.9 System Modeler 369
10.10 Additional Resources 370

11. Economic, Financial and Optimization Applications 371
11.1 Accessing Economic Information 371
11.2 Financial Information 374
11.3 Financial Functions 381
11.4 Optimization 392
11.5 The Shortest Path Problem 403
11.6 Optimum Flows 407
11.7 Blockchains 410
11.8 Additional Resources 412

12. Faster, Further 415
12.1 Parallel Computing 413
12.2 Parallel Programming 414
12.3 The Mandelbrot Set 422
12.4 Comparing Organisms Genetically 427
12.5 Software Development with Wolfram Workbench 431
12.6 Compute Unified Device Architecture (CUDA) 434
12.7 Connecting with Other Programs and Devices 434
12.8 Additional Resources 435

Index 437

Una entrevista (en español) en la Radio Universidad de Salamanca sobre el libro Mathematica beyond Mathematics  puede escucharla AQUÍ.

Note: Mejora y actualiza la version en español  Mathematica más allá de las matemáticas. 2ª Edición marzo 2015 disponible en Google Play. Pulse aquí para descargar material suplementario utilizado en algunos ejemplos del libro. Una entrevista sobre el libro en la SER Salamanca puede escucharla aquí

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