News, Views & Insights
Today we celebrate the arrival of the 36th (x.x) version of the Wolfram Language and Mathematica: Version 14.1. We’ve been doing this since 1986: continually inventing new ideas and implementing them in our larger and larger tower of technology. And it’s always very satisfying to be able to deliver our latest achievements to the world.
Today we celebrate a new waypoint on our journey of nearly four decades with the release of Version 14.0 of Wolfram Language and Mathematica. Over the two years since we released Version 13.0 we’ve been steadily delivering the fruits of our research and development in .1 releases every six months. Today we’re aggregating these—and more—into Version 14.0.
Over the last few days, I’ve been asked how ChatGPT (particularly allied to Wolfram|Alpha) will affect education, how it relates to “computational literacy for all” and the computer-based mathematics education that my book The Math(s) Fix provides a blueprint for.
Wolfram is involved in Edtech in many other ways too; it will be great seeing how the full range of powerful integrations emerge that can deliver better education.
It’s always amazing when things suddenly “just work”. It happened to us with Wolfram|Alpha back in 2009. It happened with our Physics Project in 2020. And it’s happening now with OpenAI’s ChatGPT.
I’ve been tracking neural net technology for a long time (about 43 years, actually). And even having watched developments in the past few years I find the performance of ChatGPT thoroughly remarkable. Finally, and suddenly, here’s a system that can successfully generate text about almost anything—that’s very comparable to what humans might write. It’s impressive, and useful. And, as I’ll discuss elsewhere, I think its success is probably telling us some very fundamental things about the nature of human thinking.
Wolfram Language has a wealth of built-in functions that require little or no programming, but there are special cases that require additional skill and knowledge to get the code to do things that go beyond those built-in capabilities. Wolfram U is pleased to announce a new free interactive course by veteran Wolfram programmer and instructor Dave Withoff that offers a collection of useful tips and instruction for intermediate-level programmers. This course will expand your understanding of Wolfram Language and help you to write more complex programs for custom results.
Let me start by saying that for beginners to the language, the free interactive course An Elementary Introduction to the Wolfram Language continues to be the best way to start learning how to write programs with Wolfram Language. A Guide to Programming with Wolfram Language is intended as a follow-on course for users who are ready to delve deeper into the language.
If you’re already familiar with the language and prepared to dive in to more advanced topics, you can explore the interactive course by clicking the following image before reading the rest of the blog post.
To introduce Wolfram Language and modern computational thinking to the world, Stephen Wolfram published An Elementary Introduction to the Wolfram Language in 2015. Functionality gains for the Wolfram Cloud soon made it possible to turn the book into a full interactive online course that includes videos, exercises and a scratch notebook in an easy-to-use interface, available to anyone with an internet connection. Indeed, lessons from the introductory course have been viewed over a million times on computers, tablets and smartphones around the globe since its launch.
The new intermediate-level programming course grew out of user interest for more advanced lessons and a desire to address questions from experienced users related to topics such as assignments and evaluation rules, patterns, program interfaces and plotting. Dave Withoff has been using Wolfram Language since the release of Mathematica 1.2 in 1989. Dave was a developer of packages and internal code for early versions of Mathematica and is an experienced instructor in the world of academia and with Wolfram U. He has used his expertise with the language to create the new course lessons, sharing tips and techniques he has developed over the years.
Students should have some knowledge of Wolfram Language programming before they begin the course, which includes intermediate-level topics, such as the structure of expressions, variable localization and other details about the basic design of the system. Later sections include lessons on speed and memory efficiency, construction of interactive user interfaces, data visualization and debugging.
Here is a quick look at some of the lessons included in the course (shown in the table of contents in the left-hand column):
Even though the content goes beyond the introductory level, it should not take very long to complete this course. You should be able to finish the 22 short videos and eight quizzes in about four hours. The course tracks your progress automatically and generates your personalized certificate of course completion when you finish.
The next few sections of the blog post describe the different interactive course components in detail.
The body of the course is a set of 22 lessons, starting with “Multiparadigm Programming.” This introductory lesson uses hands-on examples to illustrate different programming styles, followed by dedicated lessons on functional and rule-based programming that demonstrate different ways of writing programs in Wolfram Language.
Course sections include "Basic Language Structure," "Values and Variables," "Common Special Expressions," "Program Interfaces," "Plotting," "Analyzing and Optimizing Programs" and "Selected Applications." Each section has two or three lessons and an auto-graded quiz to test your understanding.
The videos range from 6 to 15 minutes in length, and each video is accompanied by a lesson notebook displayed on the right-hand side of the screen. There is an embedded scratch notebook where you can copy and paste Wolfram Language input directly from the lesson so you can try the examples for yourself.
Each lesson comes with a set of exercises to practice the concepts. A detailed solution is provided for every exercise because the course is designed for independent study. The following shows an example from the lesson on knowledge representation, from the "Program Interfaces" section:
The notebooks with the exercises are interactive, so students can try variations of each problem in the Wolfram Cloud. In particular, they are encouraged to change the variables in examples and investigate the documentation and options available for built-in functions.
At the end of each section is a short, multiple-choice quiz with 10 problems. The quiz problems are at roughly the same level as those shown in the lessons, and a student who reviews the section thoroughly should have no difficulty in doing well on the quiz.
Students will receive instant feedback about their answers to the quiz questions, and they are encouraged to try hand and computer calculations to solve them.
Students are encouraged to watch all the lessons and attempt the quizzes in the recommended sequence because course topics may rely on earlier concepts and techniques. When you complete the course, you can download a personalized certificate of completion. You will earn a course certificate after watching all the lessons and passing all the quizzes. Your progress is tracked automatically for you within the course using your Wolfram ID, making it easy to just pick up where you left off if you exit and return to the course later. A course certificate adds value to your professional resume, school and job applications or social media profile. This course provides useful preparation for the Wolfram Language Level I certification exam, and students are encouraged to take the exam and earn a proficiency certification.
Wolfram U offered a sneak peek of the course lessons and quizzes to Daily Study Group participants this spring, and we received some valuable feedback. Here is what participants said:
“This course improves efficiency by enabling me to keypunch less and giving me the knowledge to reduce computer run time.” “[Exercises] are always helpful and fun.” “Multiple Choice questions are adequate to test one’s knowledge. The best exercises were those when we were asked to program a solution for a problem with a specific outcome. It shows the versatility of Wolfram Language.” “I refer to the various notebooks included in the course to serve as examples and demonstrations of concepts applicable to the task on which I am working. Those dealing with symbolic computation are most helpful.” “The programming guide was very helpful, provided insights into the language.”I think you’ll find this new interactive course to be an enjoyable learning experience on your journey to become a more advanced and skilled user of Wolfram Language, just like our Daily Study Group cohort did. I hope you’ll reach out to let us know about the ways you find the course helpful and to share stories about your results. As always, we welcome any comments or suggestions for future courses and certifications.
I’m grateful to Andre Kuzniarek at Wolfram for suggesting the course concept; to the author, Dave Withoff, for answering the call to create this collection of programming topics; and to the Wolfram U staff who contributed to making it a reality. I would specifically like to acknowledge Cassidy Hinkle, Laura Crawford and Mariah Laugesen of the Wolfram U team.
| Want more help? Register for one of Wolfram U’s Daily Study Groups. |
In 2020 it was Versions 12.1 and 12.2; in 2021 Versions 12.3 and 13.0. In late June this year it was Version 13.1. And now we’re releasing Version 13.2. We continue to have a huge pipeline of R&D, some short term, some medium term, some long term (like decade-plus). Our goal is to deliver timely […]
Last year we released Version 13.0 of the Wolfram Language. Here are the updates in trees since then, including the latest features in 13.1.
In Version 12.3 we introduced Tree as a new fundamental construct in the Wolfram Language. In Version 13.0 we added a variety of styling options for trees, and in Version 13.1 we’re adding more styling as well as a variety of new fundamental features.
An important update to the fundamental Tree construct in Version 13.1 is the ability to name branches at each node, by giving them in an association:
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All tree functions now include support for associations:
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In many uses of trees the labels of nodes are crucial. But particularly in more abstract applications one often wants to deal with unlabeled trees. In Version 13.1 the function UnlabeledTree (roughly analogously to UndirectedGraph) takes a labeled tree, and basically removes all visible labels. Here is a standard labeled tree
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and here’s the unlabeled analog:
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In Version 12.3 we introduced ExpressionTree for deriving trees from general symbolic expressions. Our plan is to have a wide range of “special trees” appropriate for representing different specific kinds of symbolic expressions. We’re beginning this process in Version 13.1 by, for example, having the concept of “Dataset trees”. Here’s ExpressionTree converting a dataset to a tree:
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And now here’s TreeExpression “inverting” that, and producing a dataset:
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(Remember the convention that *Tree functions return a tree; while Tree* functions take a tree and return something else.)
Here’s a “graph rendering” of a more complicated dataset tree:
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The new function TreeLeafCount lets you count the total number of leaf nodes on a tree (basically the analog of LeafCount for a general symbolic expression):
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Another new function in Version 13.1 that’s often useful in getting a sense of the structure of a tree without inspecting every node is RootTree. Here’s a random tree:
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RootTree can get a subtree that’s “close to the root”:
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It can also get a subtree that’s “far from the leaves”, in this case going down to elements that are at level –2 in the tree:
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In some ways the styling of trees is like the styling of graphs—though there are some significant differences as a result of the hierarchical nature of trees. By default, options inserted into a particular tree element affect only that tree element:
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But you can give rules that specify how elements in the subtree below that element are affected:
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In Version 13.1 there is now detailed control available for styling both nodes and edges in the tree. Here’s an example that gives styling for parent edges of nodes:
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Options like TreeElementStyle determine styling from the positions of elements. TreeElementStyleFunction, on the other hand, determines styling by applying a function to the data at each node:
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This uses both data and position information for each node:
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In analogy with VertexShapeFunction for graphs, TreeElementShapeFunction provides a general mechanism to specify how nodes of a tree should be rendered. This named setting for TreeElementShapeFunction makes every node be displayed as a circle:
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Thanksgiving is a special day to celebrate family, friends and food. Preparation is key to a safe and delicious Thanksgiving dinner. Wolfram Language can help lower the stress and up the ease of your Thanksgiving Day preparations.
Last year we released Version 13.0 of the Wolfram Language. Here are the updates in visual effects and beautification since then, including the latest features in 13.1.
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