What Is Wolfram Mathematica? Programming Language For Math

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Here you will find useful and interesting information about Wolfram Alpha, In general you will discover Wolfram Mathematica is a program useful in Mathematics and other contexts.

We will see that engineers, scientist from diverse fields, economists and many professionals use Mathematica as an option for making applications in a kind environment for the amateur user. In this article we will explain how to use Mathematica for simple applications as calculator or for analysing bid amounts of data using graphs and networks to measure and see the information available from a set of data, this is a basic operation for many data scientist, and other applications that we will explore.

In your reading you will learn what is Mathematica, how to run scripts, furthermore you will learn how to do a Mathematica notebook through a short tutorial with pictures created in Mathematica 10.1. We hope we can help you to improve your skills in programming and use well-known software for diverse applications, welcome to Prograp and thanks for reading in advance!

A Short Tutorial in Mathematica

Now it's time to learn some basic commands of Mathematica! This is an introduction to Mathematica and it's algorithms, our beginner's guide will show you some basic functions of Mathematica that you can use for different contexts, since performing arithmetic to optimize your travel in diverse countries and analyze data.

Now let's begin with the Arithmetic, as first step you have to get Mathematica, you can read our article about How To Download Wolfram Mathematica For Free Trial. Please remember that Mathematica needs to put Shift + Enter at the last of all your commands line.

Here you can find some simple commands that you can use for performing the basics operations like sum, subtraction, multiplication and division. Now let's try them, at first you need to open a Notebook Mathematica

Push New Document and you will see the following window

For example if we introduce 5+2 and you push Shift+Enter at the same time then we will get 7. It's time to Try new possibilities! Put what you want to calculate in the line and you will see in, after you push Shift+Enter you will see the result immediately behind the line.

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It's time to come back to the classics, maybe most of use met this kind of mathematics objects in our high school or university, the trigonometric functions and the integrals, here you can see how to do them using Mathematica.

At first the Cos[x] (use [] to introduce the argument of the function) will be studied, we define the domain of this function from -2Pi to 2Pi, remember pi is 3.1415.... until infinite, Use the general format shown in orange.

The presentation is an essential part of the work, now you can see well-known functions of mathematics, physics and engineering, Bessel´s Functions, here you can find an illustrative video for understand their role in physical applications. Now our goal it to plot them using Mathematica, we put the function depending of n and x, where n is the degree of the Bessel function and can be considered as an index for all the Bessel's functions. Furthermore our domain goes from 0 to 15, you are free to set your own domain.

Add the line command Filling->Axis as shown in the picture and the colours will be part of your presentation, this will help you to see the behaviour of the particular given functions.

Mathematica can be used too for creating figures and objects, in this case we can see two spheres with defined radius equal to 1 by defect.The set of points (2,1,1) represent the center of the spheres. Try to see them using your mouse. Adding color can be an interesting option for using this kinds of graphs to design and present such geometrical shapes.

It's interesting to study the evolution of a given function dependent of a set of parameters, especially we wanna consider the continuous dependence of the functions to that set of parameters without analyzing part by part then the command Manipulate is suitable for you, we will manipulate here a function with constrained parameter a which lies between 0 and 2. The domain of the function will be [0,6].

At first you have to click the option Evaluation, then you will choice Dynamic Updating Enabled to activate this feature. You can manipulate continuous and discrete parameters as well.

3D objects can be manipulated too, try the following command and change the values of a using the bar, then you will observe different shapes related to a similar algebraic equation and witnessing the transition from diverse geometries.

The following option can be useful for your presentation if you deal with a task related to understand and show the geography of a region. You only need to use the command GeoGraphics[] and if you provide your actual position then you will be able to see a map of the area around you, in my case I was in Medellin-Colombia so the map you are watching now is from this place.

Now let's analyze an important application, a graph is a mathematical object which resumes the relationship between points called objects, such relationship is a symmetric relation between the points (nodes) of the graph. But, what does it mean? A simple example is the following: consider the relationship friendship, if Alice has a friend called Bob then Bob will say Alice is his friend, it means symmetry. Now if we consider to Alice and Bob as points in the graph, then they are connected because they are friends. Using the information of your Facebook account for example we can produce such patterns and analyze the relationships between your list of friend with themselves.

A mathematical object which can summarise such information is a graph, in this case you can see the following network (graph), it explains how complex can be such relationships.

At the final the option CommunityGraphPlot will help you to understand the principal links between the set of points of the graph, this option can be used widely in Market Analysis to understand the dynamics of a set of individuals and the links of information between them.

In the context of image manipulation you can see the following art application of Mathematica, a common picture transformed in a pop art picture using the command ImageForestingComponents. This seems to be just for fun but the Image Analysis is fundamental to be able to apply transformation to a given image.

The following is an interesting application of complex variable analysis, the Mandelbrot Set and the Julia Set, you can find such structures called Fractals in the analysis of Craters, Lightning bolts, Trees, Algae, Earthquakes, Blood vessels, DNA,, Snowflakes, the rings of Saturn and much more. Type the command as shown and you will see the fractals generation in front of you.

Now it's time of the Statistics applications, lets compare two set of data, as you can see we can create a PairedHistogram,  in this case we will compare the temperature between New York and Chicago, as we can see we can compare both temperatures for a given time.

Now it's time for a useful application, you can ask to Mathematica to provide a tour In different countries, in our case we wanna see how is the tour in France, In this case the application provides the shortest tour around the principal cities of France with a map of such path.

What is Mathematica software?

Wolfram Mathematica has been for about 30 years a synonymous of development in computer environment for innovators, teachers, students, researchers other people around the world. Mathematica is recognised for its practical and kind use, furthermore Mathematica can be seen as a system in continuous expansion to different fields of the technical computation. You can find it online or in a  version for desktop.

Mathematica has about 5000 integrated functions that cover a wide range of technical computation, all them integrated carefully for function together perfectly and all included in Mathematica. This functions don't relate only to mathematics, they relate too about other topics.  Let's explore these topics, you will discover more about Mathematica!!

What is Wolfram Mathematica used for?

Mathematica is a programming language for Math and which more? This is a common question from users and the people in general who wanna know more about the basics aspects of Mathematica. Wolfram Mathematica has different applications given the high numbers of algorithms developed for this software. The principal features of Mathematica can be summarized in the following list:

• Libraries of mathematical elementary functions (like Sine, Cosine, ...) and special functions (for example Legendre Polynomials, Bessel functions,...)
• Mathematica can perform complex numbers operation with arbitrary precision arithmetic.
• It can perform symbolic computation
• 2D and 3D data visualization and animation tools
• Finite element analysis with 2D and 3D mesh generation
• Constrained and unconstrained optimization (Powell algorithm, steepest descend method, gradient based methods)
• Manipulation of data and matrix
• Solvers for system of equations, diophantine equations, ordinary differential equations (ODE), partial differential equations (PDE), differential algebraic equations (DAE), etc.
• Multivariate statistics libraries including fitting, hypothesis testing, and probability and expectation calculations on over 160 distributions.
• Support for censored data, temporal data, time series, and unit based data
• Supervised and unsupervised machine learning tools for data, images and sounds including artificial neural networks
• Computational geometry in 2D, 3D and higher dimensions
• Tools for 2D and 3D image processing^[11] and morphological image processing including image recognition
• Tools for financial calculations including bonds, annuities, derivatives, options etc.
• Database collection for mathematical, scientific, and socio-economic information and access to Wolfram Alpha data and computations
• Tools for creating and deploying cloud based computational applications and services
• Tools to connect to dynamic-link library (DLL), Structured Query Language (SQL), Java, .NET, C++, Fortran, CUDA, OpenCL, and Hypertext Transfer Protocol (HTTP) based systems
• Parallel programming
• Using  "free-form linguistic input" and Wolfram Language in notebook with Internet connection.

This list was adapted from Wikipedia. You will find a more exhaustive list in the Wikipedia article, our main objective was to provide a short list of applications and uses of Mathematica in order to understand the diverse dynamic and process that can be developed in the Wolfram Mathematica platform.

Who uses Mathematica?

At the beginning of the release of Wolfram Mathematica the main group of users  belonged to the Physics and Mathematics, followed by Engineering and Business Science. Currently Mathematica is not only related to academic fields, the user of engineering have a wide range of professions, such as Engineers, Data scientist, Statistics, Life Science, Social Science, Teachers, Students and people who are interested in the mathematical culture and the learning. From that perspective as the words of Stephen Wolfram suggest, Mathematica has overcome it's initial role as an academic software and it's influence in multiples context is increasing.

Why do you use Mathematica?

I would like to tell my experience with Mathematica, I studied Physics and Mathematics and I use to deal with problems of Mathematics, Physics, Engineering and Statistics, in general I needed to calculate or see integrals, matrix multiplications, convex optimization, plotting graphs, estimate quantities from statistical data and other applications, or just create simple applications in a kind and dynamic environment. I can say from my perspective that Mathematica can be used in a range of contexts and situations, but to improve your programming skills then Mathematica must be accompanied of specific knowledge in programming. The precedent point is important, and I can say that your development as a programmer depends of the tools that you use, that is an advantage and disadvantage of Mathematica because it provides you tools through a simple language that you can learn and use naturally, it allows you to use complex tools with little or not knowledge of the principal aspects of programming.

From the perspective shown we can argue that some ways of Mathematica can be seen as a black-box, so if you wanna use a specific tool and you wanna understand the result of your calculation without further considerations of the internal ways of the computer or machine then Mathematica is a good choice for you, but if your goal is to understand the big picture of the process from the perspective of Computer Science and the intrinsic relationships between the algorithms considered then you have to complement Mathematica with C++ or Python such as, so you can see how to make the algorithm for performing operations from most basic structures.

Remember anyways that from a Computer Science's theorem, any program can run any routine if it is computable, so the main differences between programs lies in specific applications, so you can decide how to use Mathematica with others programming languages for make your learning experience deeper.

Thanks so much for reading us, I hope you can find the information useful, if you wanna learn more about Mathematica please read our article about installation and first steps in Mathematica, click here  How To Download Wolfram Mathematica For Free Trial for more information. Have a nice programming day!! Whatever you are doing for learning to programming keep doing it!