CSTEM

JULY 30, 2024

Elementary students rarely encounter computer science or engineering, and advanced science courses in high school favor higher-income, non-minority students. In middle schools offering algebra, white students make up 50% of the attendees, but 58% of those enrolled in algebra classes. Changing placement policies.

Algebra 52

Algebra Education Education Economics 52

Stephen Wolfram

MARCH 7, 2022

In more explicit form we could write this as Equal [f[x_, y_], f[f[y_, x_],y_]] —where Equal ( ) has the “known meaning” of representing equality. and at t steps gives a total number of rules equal to: &#10005. So how about logic, or, more specifically Boolean algebra ? &#10005. &#10005.

Mathematics 114

Mathematics Physics Computer Algebra 114

Stephen Wolfram

MAY 25, 2021

Instead, what happens is that the universe evolves by virtue of lots of elementary updating events happening throughout the network. The same is true of axioms for areas of abstract algebra like group theory—as well as basic Euclidean geometry (at least for integers). But at the lowest level in our models, time doesn’t work that way.

Mathematics 52

Mathematics Physics Computer Algebra 52

Stephen Wolfram

JUNE 28, 2023

As an example, here’s a small piece of code (from my An Elementary Introduction to the Wolfram Language ), shown in the default way it’s rendered in notebooks: But in Version 13.3 But what if we ask a question where the answer is some algebraic expression? But in Version 13.3 Sometimes that’s easy to determine.

Computer 119

Computer Calculus Construction Mathematics 119

Stephen Wolfram

DECEMBER 11, 2023

In observing the metamathematical universe the analogy is basically different possible kinds of theories or abstractions—say, algebraic vs. geometrical vs. topological vs. categorical, etc. With our concept of “elementary equivalencings” we have a way to measure both in terms of computational operations.

Physics 112

Physics Computer Mathematics Communications 112

Stephen Wolfram

OCTOBER 7, 2021

or ) must for example be equal to 1 mod 2, 3 and 6. This structure is very dependent on the algebraic properties of. A few additional results are (where the decimals are algebraic numbers of degree 6, and a is a real number): &#10005. How should we decompose that into “elementary events”? &#10005. &#10005.

Physics 52

Physics Mathematics Algebra Construction 52

Stephen Wolfram

NOVEMBER 10, 2021

For integers, the obvious notion of equivalence is numerical equality. For example, we know (as I discovered in 2000) that (( b · c ) · a ) · ( b · (( b · a ) · b )) = a is the minimal axiom system for Boolean algebra , because FindEquationalProof finds a path that proves it.

Physics 116

Physics Mathematics Computer Construction 116