July 26, 2018 — Itai Seggev, Senior Kernel Developer, Algorithms R&D
One of the many beautiful aspects of mathematics is that often, things that look radically different are in fact the same—or at least share a common core. On their faces, algorithm analysis, function approximation and number theory seem radically different. After all, the first is about computer programs, the second is about smooth functions and the third is about whole numbers. However, they share a common toolset: asymptotic relations and the important concept of asymptotic scale.
By comparing the “important parts” of two functions—a common trick in mathematics—asymptotic analysis classifies functions based on the relative size of their absolute values near a particular point. Depending on the application, this comparison provides quantitative answers to questions such as “Which of these algorithms is fastest?” or “Is function 
a good approximation to function g?”. Version 11.3 of the Wolfram Language introduces six of these relations, summarized in the following table.
July 19, 2018 — Devendra Kapadia, Kernel Developer, Algorithms R&D
Asymptotic expansions have played a key role in the development of fields such as aerodynamics, quantum physics and mathematical analysis, as they allow us to bridge the gap between intricate theories and practical calculations. Indeed, the leading term in such an expansion often gives more insight into the solution of a problem than a long and complicated exact solution. Version 11.3 of the Wolfram Language introduces two new functions, AsymptoticDSolveValue and AsymptoticIntegrate, which compute asymptotic expansions for differential equations and integrals, respectively. Here, I would like to give you an introduction to asymptotic expansions using these new functions.
November 9, 2017 — Devendra Kapadia, Kernel Developer, Algorithms R&D
Here are 10 terms in a sequence:
![Table[(2/(2 n + 1)) ((2 n)!!/(2 n - 1)!!)^2, {n, 10}]](https://blog.wolfram.com/data/uploads/2017/11/InOutImg2.png "Table[(2/(2 n + 1)) ((2 n)!!/(2 n - 1)!!)^2, {n, 10}]")
And here’s what their numerical values are:
![N[%]](https://blog.wolfram.com/data/uploads/2017/11/InOutImg3.png "N[%]"){kind=small}
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:
![DiscreteLimit[(2/(2 n + 1)) ((2 n)!!/(2 n - 1)!!)^2, n -> \[Infinity]]](https://blog.wolfram.com/data/uploads/2017/11/InOutImg4.png "DiscreteLimit[(2/(2 n + 1)) ((2 n)!!/(2 n - 1)!!)^2, n -> \[Infinity]]"){kind=small}
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.
July 19, 2017 — Stephen Wolfram
The Philosophy of Chemicals
“We’ve just got to decide: is a chemical like a city or like a number?” I spent my day yesterday—as I have for much of the past 30 years—designing new features of the Wolfram Language. And yesterday afternoon one of my meetings was a fast-paced discussion about how to extend the chemistry capabilities of the language.
At some level the problem we were discussing was quintessentially practical. But as so often turns out to be the case for things we do, it ultimately involves some deep intellectual issues. And to actually get the right answer—and to successfully design language features that will stand the test of time—we needed to plumb those depths, and talk about things that usually wouldn’t be considered outside of some kind of philosophy seminar.
January 3, 2017 — John Moore, Marketing and Technical Content Team Lead, Technical Communications & Strategy Group
It’s been a busy year here at the Wolfram Blog. We’ve written about ways to avoid the UK’s most unhygienic foods, exciting new developments in mathematics and even how you can become a better Pokémon GO player. Here are some of our most popular stories from the year.
November 4, 2016 — Zach Littrell, Technical Content Writer, Technical Communications and Strategy Group
Here are just a handful of things I heard while attending my first Wolfram Technology Conference:
- “We had a nearly 4-billion-time speedup on this code example.”
- “We’ve worked together for over 9 years, and now we’re finally meeting!”
- “Coding in the Wolfram Language is like collaborating with 200 or 300 experts.”
- “You can turn financial data into rap music. Instead, how about we turn rap music into financial data?”
As a first-timer from the Wolfram Blog Team attending the Technology Conference, I wanted to share with you some of the highlights for me—making new friends, watching Wolfram Language experts code and seeing what the Wolfram family has been up to around the world this past year.
August 26, 2016 — Zach Littrell, Technical Content Writer, Technical Communications and Strategy Group
We are constantly surprised by what fascinating applications and topics Wolfram Language experts are writing about, and we’re happy to again share with you some of these amazing authors’ works. With topics ranging from learning to use the Wolfram Language on a Raspberry Pi to a groundbreaking book with a novel approach to calculations, you are bound to find a publication perfect for your interests.
April 16, 2015 — Stephen Wolfram
The Wolfram Cloud Needs to Be Perfect
The Wolfram Cloud is coming out of beta soon (yay!), and right now I’m spending much of my time working to make it as good as possible (and, by the way, it’s getting to be really great!). Mostly I concentrate on defining high-level function and strategy. But I like to understand things at every level, and as a CEO, one’s ultimately responsible for everything. And at the beginning of March I found myself diving deep into something I never expected…
Here’s the story. As a serious production system that lots of people will use to do things like run businesses, the Wolfram Cloud should be as fast as possible. Our metrics were saying that typical speeds were good, but subjectively when I used it something felt wrong. Sometimes it was plenty fast, but sometimes it seemed way too slow.
We’ve got excellent software engineers, but months were going by, and things didn’t seem to be changing. Meanwhile, we’d just released the Wolfram Data Drop. So I thought, why don’t I just run some tests myself, maybe collecting data in our nice new Wolfram Data Drop?
A great thing about the Wolfram Language is how friendly it is for busy people: even if you only have time to dash off a few lines of code, you can get real things done. And in this case, I only had to run three lines of code to find a problem.
First, I deployed a web API for a trivial Wolfram Language program to the Wolfram Cloud:
![In[1]:= CloudDeploy[APIFunction[{}, 1 &]]](https://writings.stephenwolfram.com/data/uploads/2015/04/cloud-bug-hunting-in1.png "In[1]:= CloudDeploy[APIFunction[{}, 1 &]]")
February 9, 2015 — Jenna Giuffrida, Content Administrator, Technical Communications and Strategy Group
We are once again thrilled by the wide variety of topics covered by authors around the world using Wolfram technologies to write their books and explore their disciplines. These latest additions range from covering the basics for students to working within specialties like continuum mechanics.
October 16, 2014 — Jenna Giuffrida, Content Administrator, Technical Communications and Strategy Group
Summer has drawn to a close, and so too have our annual internships. Each year Wolfram welcomes a new group of interns to work on an exciting array of projects ranging all the way from Bell polynomials to food science. It was a season for learning, growth, and making strides across disciplinary and academic divides. The Wolfram interns are an invaluable part of our team, and they couldn’t wait to tell us all about their time here. Here are just a few examples of the work that was done.
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