Ask a Tech Teacher

OCTOBER 14, 2019

A strong mathematical background is crucial; algebra, statistics, and probability are all going to play a huge role in an architect’s ability to do their job. A student can flourish on a math test, for example, but have struggled to remember certain steps of the mathematical processes that they’re using.

Architecture 170

Architecture Schooling Mathematics Algebra 170

Stephen Wolfram

SEPTEMBER 27, 2024

Just like in our original f [0] = 1 case, we can construct “blue graph trees” rooted at each of the initial conditions. 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 ]. are also primitive recursive.

Computer 106

Computer Mathematics Argumentation Sciences 106

User Generated Education

MARCH 12, 2023

Estimating Dimensions of New Planets Possible Vegetation and Creatures via Math Snacks’ Agrinautica This app allows students to terraform planets by adding gorgeous plants, animals, fungi and minerals, each representing a unique mathematical expression. Standards Addressed Next Generation Science Standards ETS1.C:

Sciences 62

Sciences Science Algebra Mathematics 62

Stephen Wolfram

MARCH 5, 2024

Three centuries ago science was transformed by the idea of representing the world using mathematics. A lot of science—and technology—has been constructed specifically around computationally reducible phenomena. And that’s for example why things like mathematical formulas have been able to be as successful in science as they have.

Sciences 115

Sciences Science Computer Mathematics 115

Stephen Wolfram

NOVEMBER 10, 2021

It’s yet another surprising construct that’s arisen from our Physics Project. 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.) In some ways it’s a bit like our efforts to construct the ruliad.

Physics 116

Physics Mathematics Computer Construction 116

Stephen Wolfram

DECEMBER 11, 2023

But here we want to think not about what’s “mathematically describable”, but instead about what in general is actually implemented —say by our senses, our measuring devices, or our ways of analyzing things. How Observers Construct Their Perceived Reality Our view of the world is ultimately determined by what we observe of it.

Physics 112

Physics Computer Mathematics Communications 112

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 110

Physics Computer Biology Mathematics 110

Stephen Wolfram

JUNE 28, 2023

They’re mathematically more complex, but each one we successfully cover makes a new collection of problems accessible to exact solution and reliable numerical and symbolic computation. It’s the end of a long journey, and a satisfying achievement in the quest to make as much mathematical knowledge as possible automatically computable.

Computer 119

Computer Calculus Construction Mathematics 119

Stephen Wolfram

SEPTEMBER 9, 2021

Its key idea is to think of things in the world as being constructed from some kind of simple-to-describe elements—say geometrical objects—and then to use something like logical reasoning to work out what will happen with them. In the mathematical paradigm one imagines having a mathematical equation and then separately somehow solving it.

Physics 65

Physics Sciences Science Mathematics 65

Stephen Wolfram

SEPTEMBER 9, 2021

Its key idea is to think of things in the world as being constructed from some kind of simple-to-describe elements—say geometrical objects—and then to use something like logical reasoning to work out what will happen with them. In the mathematical paradigm one imagines having a mathematical equation and then separately somehow solving it.

Sciences 59

Sciences Science Physics Mathematics 59

Stephen Wolfram

MAY 25, 2021

Presumably it’s that we can sample space without having to think about time, or in other words, that we can consistently construct a stable notion of space. Fast numbers-based ways to do particular computations are often viewed as representing “ exact solutions ” to corresponding mathematical problems. But which axioms should these be?

Mathematics 52

Mathematics Physics Computer Algebra 52

Stephen Wolfram

MARCH 23, 2023

There’s a big example of this historically, in mathematics. But then mathematical notation was invented, and math took off—with the development of algebra, calculus, and eventually all the various mathematical sciences. Back before about 500 years ago, pretty much the only way to “express math” was in natural language.

Computer 145

Computer Mathematics Math Achievement 145

Futurum

SEPTEMBER 12, 2023

Biology is often combined with engineering, medicine, psychology, sociology, chemistry, physics or mathematics, so that scientists can tackle complex, real-world problems. If you have the option, take a statistics course and mathematics courses beyond algebra,” says Barbara. Do you have a question for Barbara or Olivia?

Biology 81

Biology STEM Chemistry Critical Thinking 81

Stephen Wolfram

OCTOBER 7, 2021

And the involvement of numbers will often allow us to make immediate use of traditional mathematical methods. This structure is very dependent on the algebraic properties of. If we combine multiplication with addition, we get different forms—and we can make some interesting mathematical connections. For we get. &#10005.

Physics 52

Physics Mathematics Algebra Construction 52

Stephen Wolfram

MAY 16, 2022

My original goal in A New Kind of Science was to take a step beyond the mathematical paradigm that had defined the state of the art in science for three centuries—and to introduce a new paradigm based on computation and on the exploration of the computational universe of possible programs. But there’s more.

Sciences 64

Sciences Science Mathematics Physics 64

Futurum

OCTOBER 4, 2022

They developed a ‘peeling technique’, whereby the electronic components are constructed on conventional fabrication substrates that can withstand high temperatures and corrosive chemicals but can then be thinly peeled off and transferred elsewhere. HOW DID CHI HWAN BECOME A BIOMEDICAL ENGINEER?

Biomedical Engineering 107

Biomedical Engineering Engineering Research Research 107

Stephen Wolfram

JANUARY 9, 2024

Then for each function (or other construct in the language) there are pages that explain the function, with extensive examples. One new construct added in Version 13.1 —and And now there’s a way to specify that, using Threaded : In a sense, Threaded is part of a new wave of symbolic constructs that have “ambient effects” on lists.

Computer 95

Computer Calculus Construction Accessibility 95

Stephen Wolfram

SEPTEMBER 29, 2023

And if we treat these as equivalent and merge them we now get: (The question of “state equivalence” is a subtle one, that ultimately depends on the operation of the observer, and how the observer constructs their perception of what’s going on. It’s a new kind of fundamentally multiway construct.

Physics 100

Physics Computer Argumentation Construction 100

Stephen Wolfram

NOVEMBER 3, 2023

But the general concept of a multiway system, with its discrete branching at discrete steps, depends on a level of fundamental discreteness that’s quite unfamiliar from traditional statistical mechanics—though is perfectly straightforward to define in a computational, or even mathematical, way.

Physics 82

Physics Construction Equality Sciences 82

PCS Edventures

MARCH 4, 2020

Whether you agree with the theory that mathematics exists for humans to discover or that it is a man-made tool, numeric systems designed to measure the world around us serve as the foundation for scientific and technological advancement. Algebra , which incorporates unknown variables into arithmetic equations. What is Math?

Mathematics 52

Mathematics Energy Architecture Government 52

Robert Talbert, Ph.D.

APRIL 15, 2022

Those assessments can take on various forms, and in well-constructed courses they do have varying forms, corresponding to different levels of Bloom's Taxonomy. But no matter the form, they are are typically one-and-done: Students turn them in, and the work is graded, and that's that. Limit the frequency of reassessments.

Academic Standards 52

Academic Standards Communications Calculus Algebra 52

Futurum

AUGUST 11, 2022

Raja was part of the team that created the first ever digital photo mosaic of the Andromeda galaxy, constructed by stitching together 57 images taken by a ground-based telescope. I work with the Project for Inmate Education programme at UCSC, where I teach algebra and astronomy in Santa Cruz jail facilities.

Astronomy 98

Astronomy Equality Research Research 98

Stephen Wolfram

AUGUST 22, 2023

He was going for what he saw as the big prize: using them to “construct the universe”. It explains that III has four divisions: Mathematical and Programming Services, Behavioral Science, Operations, and “New York”. Then McCarthy started to explain ways a computer could do algebra. It was all algebra.

Computer 69

Computer Physics Science Sciences 69

Stephen Wolfram

MAY 17, 2021

And for example in 1978 the following “radius 3” rule (operating on size-7 neighborhoods) was constructed (and we’ll call it the “GKL rule”): &#10005. But in the 1980s a complicated cellular automaton was constructed that it was possible to prove would not show such behavior. But it turns out that this isn’t true.

Computer 52

Computer Achievement Mathematics Physics 52

Stephen Wolfram

DECEMBER 13, 2021

Any integral of an algebraic function can in principle be done in terms of our general DifferentialRoot objects. the same integral could still be done, but only in terms of elliptic integrals : Mathematical Functions: A Milestone Is Reached. has lots of specific mathematical enhancements. we’re delivering another jump forward.

Construction 68

Construction Computer Physics Accessibility 68

Stephen Wolfram

MAY 20, 2021

Having this as a single function makes it easier to use in functional programming constructs like this: &#10005. But sometimes it’s much more convenient to get the subgraph (and in fact in the formalism of our Physics Project that subgraph—that we view as a “ geodesic ball ”—is a rather central construct). So in Version 12.3

Computer 52

Computer Construction Physics Technology 52

User Generated Education

OCTOBER 16, 2015

embers of these subcultures strive to blur the lines between creator and consumer by constructing a social network that ties users and makers close together. One of President Obama’s initiatives has been a call to action for making STEM (science, technology, engineering, mathematics) education a priority in the United States.

Education 110

Education Education Accessibility STEM 110

User Generated Education

JULY 7, 2016

embers of these subcultures strive to blur the lines between creator and consumer by constructing a social network that ties users and makers close together. One of President Obama’s initiatives has been a call to action for making STEM (science, technology, engineering, mathematics) education a priority in the United States.

Education 61

Education Education Accessibility STEM 61