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Leading Edge

What’s Your Favorite Element?

Judging elements is like choosing a favorite ice cream. Carbon and hydrogen are like vanilla and chocolate, the basis for so many other flavors, but too commonplace to claim as your preferred element. By using the load-on-demand information packages that are readily available in Mathematica, one can better investigate the popularity of the 118 elements available in ElementData by studying how often they occur in the 34,000 chemicals featured in ChemicalData. Of all the elements, hydrogen and carbon unsurprisingly occur most frequently, respectively in 94 and 93 percent of the chemicals. As an organic chemist, my focus has traditionally been on carbon-containing molecules, so I cannot help but view the periodic table from a carbon-centered perspective: how will certain elements affect the behavior of molecules to which they are bonded, and how will they interact with other molecules?
Kristen Aramthanapon, Scientific Information Group
Announcements & Events

Mathematica Immersion: Coming This Summer…

Last year, we had the first ever Advanced Mathematica Summer School (AMSS). I am pleased to report it was a great success. We saw a large number of applications in all areas and fields, and a select few made it into the program. And we had a real blast doing what we know best—working with Mathematica and using it to make projects happen! We are ready to invite you all to immerse in Mathematica for two weeks this summer during the AMSS 2009. The philosophy of the Summer School is to help people take their projects and implement them in incredible ways with Mathematica. Heading the Technical Services Group has given me the firsthand experience of interacting with our user base and talking about their projects. Since last year's Summer School, I thought on several occasions, "Wow! This would be a really cool Summer School project!"
Onkar Singh, Project Director, Consulting
Education & Academic

College Calculus with Mathematica

Calculus has occupied a central position in scientific thought ever since its discovery by Newton and Leibniz more than 300 years ago. The combination of elegance, utility, and rigor that characterize this subject have led to its extensive use in theoretical approaches to diverse fields such as economics, finance, and biology. Indeed, calculus is one of the greatest intellectual achievements of humankind, which explains its important role in the training of students all over the world. It has been my privilege to present a "College Calculus with Mathematica" talk as part of a series of free online seminars organized by the Wolfram Education Group. Today, I would like to give you a glimpse of the seminar's topics and write about the advantages of online instruction.
Devendra Kapadia, Manager of Calculus and Algebra, Algorithms R&D
Computation & Analysis

Interactive Angle Measurement with Mathematica

Consider the typical infographics found on the internet, many of which are only slightly less silly than this one by Jamie Schimley: If you want to regenerate a chart such as this in Mathematica using the PieChart function, you need hard data: the relative areas of the slices. You could eyeball the values and get an approximation, but since I deal with user interfaces I was immediately interested in creating one that would allow me to measure the angle of each sector of a pie chart. The following code creates locators that can be positioned to calculate the angle of any sector. Buttons let you record the angles as you measure them, and reproduce the chart at the end. (This could be done with less code, but I wanted a more complete interface with finishing touches like disabling the Print Chart button if you haven’t measured any angles yet, and showing the current angle with a tooltip.)
Faisal Whelpley, User Interface Developer, User Interface Group
Education & Academic

Splines Come to Mathematica

One of the areas I contributed to Mathematica 7 was support for splines. The word “spline” originated from the term used by ship builders referring to thin wood pieces. Over the last 40 years, splines have become very popular in computer graphics, computer animation and computer-aided design fields. From containers for household goods to state-of-the-art airplanes, it is hard to find any industrial product without spline surfaces. Also, they are widely used in other mathematical studies, such as interpolation and approximation. Through its integration of numerics, symbolics and graphics, Mathematica has the opportunity to go much further with splines than has ever been possible before. Mathematica has had basic spline packages for a long time. But in Mathematica 7 we decided to make highly general spline support a core feature of the system. Splines give another way to represent classes of functions. For decades, mathematicians had been using polynomials for numerical analysis. In the early 20th century, with advances in approximation theory, spline functions were beginning to emerge. The basic idea is simple. In essence, they consist of piecewise polynomials with local supports. Since Version 5.1, Mathematica has offered general support for piecewise functions, both numerically and symbolically. In Mathematica 7, the B-spline functions can be expanded using PiecewiseExpand. For example, a uniform cubic B-spline basis function can be expanded to the following.
Yu-Sung Chang, Technical Communication & Strategy Group
Announcements & Events

Quick-Starting Mathematica with Palettes

I have taught collegiate mathematics for more than 20 years and have used Mathematica for 15 or so of these years to explore, learn and teach. For the last eight years Mathematica has been my primary tool to write all of my exams, handouts, letters, reports, papers, presentations and even a complete electronic textbook. New features introduced recently have been revolutionary in the teaching and learning environment and make possible the creation of materials that integrate text, typeset mathematics and interactive figures, which can be created efficiently and used effectively in ways not possible with other software tools. For faculty and students to benefit from using Mathematica in the teaching and learning process, they must be able to use Mathematica sufficiently well to remain focused on course concepts and not become frustrated by the technology. Without question, the main challenge I face teaching new users how to use Mathematica is helping them master the task of creating syntactically correct commands, followed closely by the challenge of teaching how to use Mathematica to write rich documents that combine text, typeset mathematics and figures. When the use of technology gets in the way of the teaching, learning and writing about content, which should remain the focus of academic learning, then all involved in the teaching and learning process experience frustration! If enough example commands are provided, if the ways of Mathematica are carefully explained, and if patient help is readily available, then some new users are able to work their way up the learning curve and reach a point where they can focus on the subject matter and are able to comfortably use Mathematica to explore, learn, teach and write about the concepts. Members of this group are often able to independently deepen their understanding and use of Mathematica by relying on the Wolfram Mathematica Documentation Center and other resources; but not enough new users reach this level of Mathematica knowledge and thus do not experience firsthand the marvelous capabilities of Mathematica to explore, investigate, learn, teach and write about interesting ideas!
Eric Schulz, User Interface Group
Computation & Analysis

Visualizing Weather Patterns in Mathematica 7

Weather visualizations are very interesting—there are television channels that thrive by showing nothing else. Online, there are several sources for specific maps of current weather conditions. Generally these are produced and maintained by government agencies or other large organizations. But with Mathematica 7, you can easily produce completely customizable weather visualizations on your own computer. As usual, this is made possible by Mathematica’s tight integration of several areas of functionality. Two new features that enable this particular application are powerful new vector visualization functions and built-in weather data. Vector visualization has been present in Mathematica since Version 2. In Mathematica 7 it has been dramatically improved, adding modern techniques in vector data visualization and new algorithms developed at Wolfram Research. Traditional arrow-based vector plots, new methods based on automatic streamline placement, support for vector glyphs and high-resolution images produced using line integral convolutions are all now supported.
Ulises Cervantes-Pimentel, Senior Kernel Developer Andrew Moylan, Technical Content Specialist, Technical Communication and Strategy Group
Computation & Analysis

Mathematica for Web Analytics

Recent versions of Mathematica introduced an innovative way to interact with data. Computable data functions, such as CountryData and WeatherData, provide programmatic access to curated data in a form ready for computation. The idea of computable data has been so useful in Mathematica at large that we’ve been using it internally as well. We’ve packaged some of our internal data as in-house computable data functions, so that all of our colleagues can bring a quantitative edge to their work. I work on one such function: WebsiteData. We host several popular websites at Wolfram Research, so we collect a large volume of web server log data. WebsiteData provides access to our corpus of logs, which we can use to study how visitors interact with our websites. Here’s an example of WebsiteData in action. Let’s find the most popular demonstration from the Wolfram Demonstrations Project this past month: Whenever a visitor surfs to one of our webpages, our webservers (like all webservers) record the page requested, the time of the request, the URL of the page that had linked to our webpage (we call that the referrer) and the value of the visiter’s browser cookie and other incidentals. We’ve built up a rich interface in WebsiteData to provide statistics about these fundamental events aggregated in a variety of ways.
David Howell, Corporate Analysis
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