Stephen Wolfram

JUNE 28, 2023

Line, Surface and Contour Integration “Find the integral of the function ” is a typical core thing one wants to do in calculus. But particularly in applications of calculus, it’s common to want to ask slightly more elaborate questions, like “What’s the integral of over the region ?”, or “What’s the integral of along the line ?”

Computer 120

Computer Construction Calculus Mathematics 120

Stephen Wolfram

SEPTEMBER 27, 2024

Some involve alternate functional forms; others involve introducing additional functions, or allowing multiple arguments to our function f. But it turns out that the fact that this can happen depends critically on the Ackermann function having more than one argument—so that one can construct the “diagonal” f [ m , m , m ].

Computer 108

Computer Mathematics Argumentation Science 108

National Science Foundation

SEPTEMBER 22, 2021

In its current form, school algebra serves as a gatekeeper to higher-level mathematics. Researchers and policy makers have pushed to open that gate—providing more students access to algebra, focusing in particular on those students historically denied access to higher-level mathematics. Berry & Larson, 2019; Levitt, 2019).

Algebra 76

Algebra Mathematics Flexibility Research 76

Stephen Wolfram

NOVEMBER 10, 2021

And—it should be said at the outset—we’re still only at the very beginning of nailing down those technical details and setting up the difficult mathematics and formalism they involve.) Mathematically this can be thought of as being like decomposing the ruliad structure in terms of fibrations and foliations.). The View from Mathematics.

Physics 117

Physics Mathematics Computer Construction 117

Stephen Wolfram

AUGUST 29, 2024

Pleasantly enough, given our framework, many modern areas of mathematical physics seemed to fit right in.) I had realized that one of the places the ideas of the Physics Project should apply was to the foundations of mathematics, and to metamathematics. And now the responsibility had fallen on us to do this.

Physics 112

Physics Computer Biology Mathematics 112

Stephen Wolfram

JANUARY 9, 2024

So did that mean we were “finished” with calculus? Somewhere along the way we built out discrete calculus , asymptotic expansions and integral transforms. And in Version 14 there are significant advances around calculus. Another advance has to do with expanding the range of “pre-packaged” calculus operations.

Computer 97

Computer Calculus Construction Accessibility 97

Stephen Wolfram

SEPTEMBER 9, 2021

Many would say that modern exact science was launched in the 1600s with the introduction of what we can call the “ mathematical paradigm ”: the idea that things in the world can be described by mathematical equations—and that their behavior can be determined by finding solutions to these equations.

Physics 66

Physics Science Sciences Mathematics 66

Stephen Wolfram

SEPTEMBER 29, 2023

Since the standard Wolfram Language evaluator evaluates arguments first (“leftmost-innermost evaluation”), it therefore won’t terminate in this case—even though there are branches in the multiway evaluation (corresponding to “outermost evaluation”) that do terminate. If you set , then you set , you should get (not ) if you asked for.

Physics 102

Physics Computer Argumentation Construction 102

Stephen Wolfram

SEPTEMBER 9, 2021

Many would say that modern exact science was launched in the 1600s with the introduction of what we can call the “ mathematical paradigm ”: the idea that things in the world can be described by mathematical equations—and that their behavior can be determined by finding solutions to these equations.

Science 60

Science Sciences Physics Mathematics 60

Robert Talbert, Ph.D.

APRIL 15, 2022

An argument for traditional grading goes like this: Sure, a single assessment might have a grade on it that doesn't accurately reflect student understanding. Nobody likes traditional grading because it is so soul-sucking and time-consuming, so why do it more often than necessary? This has a connection with the next point.

Academic Standards 52

Academic Standards Communications Calculus Algebra 52

Stephen Wolfram

FEBRUARY 3, 2023

Sometimes textbooks will gloss over everything; sometimes they’ll give some kind of “common-sense-but-outside-of-physics argument”. How does one tie all this down with rigorous, mathematical-style proofs? But one never quite gets there ; it always seems to need something extra. But the mystery of the Second Law has never gone away.

Computer 91

Computer Energy Physics Construction 91

Stephen Wolfram

AUGUST 22, 2023

It didn’t help that his knowledge of physics was at best spotty (and, for example, I don’t think he ever really learned calculus). It explains that III has four divisions: Mathematical and Programming Services, Behavioral Science, Operations, and “New York”. It says that “From a one-man operation [in 1962], I.I.I.

Computer 69

Computer Physics Science Sciences 69

Stephen Wolfram

JUNE 29, 2022

You can give Threaded as an argument to any listable function, not just Plus and Times : &#10005. we’re adding SymmetricDifference : find elements that (in the 2-argument case) are in one list or the other, but not both. Now we can use the path function to make a “spiralling” tour video: College Calculus. In Version 13.1

Calculus 114

Calculus Construction Computer Argumentation 114

Computing Education Research Blog

NOVEMBER 26, 2021

My argument is that computer science was originally invented to be taught to everyone, but not for economic advantage. Forsythe argued (in a 1968 article) that the most valuable parts of a scientific or technical education were facility with natural language, mathematics, and computer science. It was an amazing event.

Computer Science 139

Computer Science Computer Science Sciences 139