Guillermo Sánchez León
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Mathematica Beyond Mathematics: The Wolfram Language in the Real World.1st Edition. Chapman and Hall/CRC.

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 25 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 11.0, tested with Math 11.1, 11.2 and 11.3).  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 here (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.


1. Getting Started 1
1.1 Mathematica, an Integrated Technical Computing System 1
1.2 First Steps 4
1.3 The Help System 11
1.4 Basic Ideas 13
1.5 Computational Capabilities 28
1.6 Utilities 34
1.7 Editing Notebooks 38
1.8 Sharing Notebooks 42
1.9 The Wolfram Cloud 43
1.10 Additional Resources 44

2. Data Analysis and Manipulation 45
2.1 Lists 45
2.2 Importing/Exporting 48
2.3 Descriptive Statistics 57
2.4 Application: Analysis of the Evolution of Two Cell Populations 61
2.5 Application: Global Energy Consumption Analysis 62
2.6 Database Access with Open Database Connectivity (ODBC) 69
2.7 Additional Resources 74

3. Programming: The Beauty and Power of the Wolfram Language 75
3.1 Mathematica’s Programming Language: The Wolfram Language 75
3.2 Functional vs. Procedural Programming 77
3.3 Set vs. SetDelayed 79
3.4 Matrices and Lists Operations 81
3.5 How Mathematica Works Internally 84
3.6 Apply, Map and Other Related Functions 86
3.7 Iterative Functions 89
3.8 Pure Functions 89
3.9 Global and Local Variables 93
3.10 Conditional Expressions 95
3.11 Accuracy and Precision 100
3.12 Choosing the Method of Computation 103
3.13 Optimizing the Computation Time 105
3.14 Cloud Deployment 107
3.15 Package Development 108
3.16 Advanced Programming Tools 113
3.17 Additional Resources 114

4. Interactive Applications, Image Processing, and More 115
4.1 Manipulate 115
4.2 Creating Demonstrations 125
4.3 Image Processing 131
4.4 Graphs and Networks 141
4.5 Mazes 144
4.6 Application: Finding the Period of a Pendulum 145
4.7 Advanced Calculus 148
4.8 Additional Resources 152

5. Accessing Scientific and Technical Information 153
5.1 Computable Data: Doing Computations with Data from Different Fields 153
5.2 Astronomy 159
5.3 Nuclear and Particle Physics 160
5.4 Engineering 161
5.5 Chemical and Physical Properties of Elements and Compounds 162
5.6 Genomics and Proteomics 166
5.7 Meteorology 169
5.8 Combining Data and Graphics 172
5.9 Geodata 173
5.10 Some Recommendations 182
5.11 Additional Resources 182

6. Probability and Statistics 183
6.1 The Latest Features 183
6.2 Statistics Data 184
6.3 Probability Distributions 187
6.4 Application: Fitting Experimental Data 207
6.5 Time Series Analysis 210
6.6 Cluster Analysis 212
6.7 Stochastic Processes 220
6.8 Reliability and Survival Analysis 220
6.9 R Integration with RLink 222
6.10 Application: Predicting Outputs Using Machine Learning Methods 222
6.11 Application: Development of a Package for Quality Control 223
6.12 Additional Resources 228

7. Calculating Π and Other Mathematical Tales 229
7.1 The Origins of Π 229
7.2 Archimedes’ Approximation 230
7.3 Π with More Than One Billion Decimals 234
7.4 Buffon’s Method 238
7.5 Application: Are the Decimal Digits of Π Random? 240
7.6 The Strange Connection 244
7.7 The Riemann Hypothesis 246
7.8 Additional Resources 252

8. Looking at the Sky 253
8.1 A Short Astronomical Walk 253
8.2 Stargazing 256
8.3 Application: Determining the Color of the Stars 273
8.4 The Measurement of Distances Across the Universe 276
8.5 Application: Binary Systems and the Search for Extrasolar Planets 280
8.6 Light Curves 283
8.7 Additional Resources 292

9. Nuclei and Radiations 293
9.1 What are Isotopes? 293
9.2 Decay Constants, Decay Periods and Half-Lives 295
9.3 Decay Chains 299
9.4 Application: Modeling the Evolution of a Chain of Isotopes Over Time 303
9.5 Application: Dating the History of Humankind 306
9.6 Application: Calculating Binding Energies 311
9.7 Additional Resources 316

10. Modeling: Applications in Biokinetics 317
10.1 Compartmental and Physiological Modeling 317
10.2 Application: Fitting a Model 333
10.3 Optimal Experimental Designs (OED) 337
10.4 Biokmod: Applications to ICRP Models 342
10.5 Radiation Attenuation 352
10.6 Additional Resources 353
11. Economic and Financial Applications 355
11.1 Financial Information 355
11.2 Financial Functions 362
11.3 Optimization 373
11.4 The Shortest Path Problem 387
11.5 Optimum Flows 392
11.6 Additional Resources 394

12. Faster, Further 395
12.1 Parallel Computing 395
12.2 Parallel Programming 396
12.3 Application: The Mandelbrot Set 403
12.4 Application: Comparing Organisms Genetically 408
12.5 Grid Computing with Wolfram Lightweight Grid Manager (WLGM) 411
12.6 Compute Unified Device Architecture (CUDA) 418
12.7 Mathematica for the Web: webMathematica 419
12.8 Software Development with Wolfram Workbench 427
12.9 New Applications and Functionality Integrated in Mathematica 432
12.10 Additional Resources 433

Index 435

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

Note: Este libro actualiza y mejora  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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