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How to Win at Risk: Exact Probabilities

The classic board game Risk involves conquering the world by winning battles that are played out using dice. There are lots of places on the web where you can find out the odds of winning a battle given the number of armies that each player has. However, all the ones that I have seen do this by Monte Carlo simulation, and so are innately approximate. The Wolfram Language makes it so easy to work out the exact values that I couldn't resist calculating them once and for all.
Jon McLoone, Director, Technical Communication & Strategy
Best of Blog

What Is a Computational Essay?

A Powerful Way to Express Ideas People are used to producing prose—and sometimes pictures—to express themselves. But in the modern age of computation, something new has become possible that I’d like to call the computational essay. I’ve been working on building the technology to support computational essays for several decades, but it’s only very recently […]

Stephen Wolfram
Education & Academic

What Is a Computational Essay? (Russian)

Высокоэффективный способ выражения идей

Люди привыкли к созданию прозы, а иногда изображений, для самовыражения. Но в современную эпоху вычислений появилось нечто новое, что я хотел бы назвать вычислительным эссе.

Я работаю над созданием технологии для поддержки вычислительных эссе уже в течение нескольких десятилетий, но только совсем недавно я понял, насколько вычислительные эссе могут быть важны как для формы обучения людей, так и для их формы обмена фактами и идеями. Профессионалы будущего будут регулярно предоставлять результаты и отчеты как вычислительные эссе. Педагоги будут регулярно объяснять концепции, используя вычислительные эссе. Студенты будут регулярно создавать вычислительные эссе в качестве домашней работы для своих классов.

Вот очень простой пример вычислительного эссе:

Stephen Wolfram
Education & Academic

Limits without Limits in Version 11.2

Here are 10 terms in a sequence: And here's what their numerical values are: But what is the limit of the sequence? What would one get if one continued the sequence forever? In Mathematica and the Wolfram Language, there's a function to compute that: Limits are a central concept in many areas, including number theory, geometry and computational complexity. They're also at the heart of calculus, not least since they're used to define the very notions of derivatives and integrals. Mathematica and the Wolfram Language have always had capabilities for computing limits; in Version 11.2, they've been dramatically expanded. We've leveraged many areas of the Wolfram Language to achieve this, and we've invented some completely new algorithms too. And to make sure we've covered what people want, we've sampled over a million limits from Wolfram|Alpha.
Devendra Kapadia, Manager of Calculus and Algebra, Algorithms R&D
Announcements & Events

What Can You Say in One Line of the Wolfram Language? The 2017 One-Liner Competition

The One-Liner Competition is a tradition at our annual Wolfram Technology Conference, which took place at our headquarters in Champaign, Illinois, two weeks ago. We challenge attendees to show us the most impressive effects they can achieve with 128 characters or fewer of Wolfram Language code. We are never disappointed, and often surprised by what they show us can be done with the language we work so hard to develop—the language we think is the world's most powerful and fun. This year's winning submissions included melting flags, computer vision and poetry. Read on to see how far you can go with just a few characters of Wolfram Language code...
Christopher Carlson, Senior User Interface Developer, User Interfaces
Computation & Analysis

Building the Automated Data Scientist: The New Classify and Predict

Automated Data Science

Imagine a baker connecting a data science application to his database and asking it, "How many croissants are we going to sell next Sunday?" The application would simply answer, "According to your recorded data and other factors such as the predicted weather, there is a 90% chance that between 62 and 67 croissants will be sold." The baker could then plan accordingly. This is an example of an automated data scientist, a system to which you could throw arbitrary data and get insights or predictions in return. One key component in making this a reality is the ability to learn a predictive model without specifications from humans besides the data. In the Wolfram Language, this is the role of the functions Classify and Predict. For example, let's train a classifier to recognize morels from hedgehog mushrooms:
Etienne Bernard, Lead Architect, Machine Learning
Best of Blog

Notebooks in Your Pocket—Wolfram Player for iOS Is Now Shipping

Ten months ago, I announced the beginning of our open beta program for Wolfram Player for iOS. The beta is over, and we are now shipping Wolfram Player in the App Store. Wolfram Player for iOS joins Wolfram CDF Player on Windows, Mac and Linux as a free platform for sharing your notebook content with the world. Wolfram Player is the first native computational notebook experience ever on iOS. You can now take your notebooks with you and play them offline. Wolfram Player supports notebooks running interfaces backed by Version 11.1 of the Wolfram Language---an 11.2 release will come shortly. Wolfram Player includes the same kernel that you would find in any desktop or cloud release of the Wolfram Language.
John Fultz, Director of User Interface Technology
Design & Visualization

Computational Microscopy with the Wolfram Language

Microscopes were invented almost four hundred years ago. But today, there's a revolution in microscopy (as in so many other fields) associated with computation. We've been working hard to make the Wolfram Language a definitive platform for the emerging field of computational microscopy. It all starts with getting an image of some kind---whether from a light or x-ray microscope, transmission electron microscope (TEM), confocal laser scanning microscope (CLSM), two-photon excitation or a scanning electron microscope (SEM), as well as many more. You can then proceed to enhance images, reconstruct objects and perform measurements, detection, recognition and classification. At last month's Microscopy & Microanalysis conference, we showed various examples of this pipeline, starting with a Zeiss microscope and a ToupTek digital camera.
Shadi Ashnai, Manager of Sound & Vision, Algorithms R&D Markus van Almsick, Algorithms R&D
Announcements & Events

It’s Another Impressive Release! Launching Version 11.2 Today

Our Latest R&D Output I’m excited today to announce the latest output from our R&D pipeline: Version 11.2 of the Wolfram Language and Mathematica—available immediately on desktop (Mac, Windows, Linux) and cloud. It was only this spring that we released Version 11.1. But after the summer we’re now ready for another impressive release—with all kinds […]

Stephen Wolfram
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