Remove Calculus Remove Computer Science Remove Equality Remove Mathematics
article thumbnail

The Physicalization of Metamathematics and Its Implications for the Foundations of Mathematics

Stephen Wolfram

1 Mathematics and Physics Have the Same Foundations. 2 The Underlying Structure of Mathematics and Physics. 3 The Metamodeling of Axiomatic Mathematics. 4 Simple Examples with Mathematical Interpretations. 15 Axiom Systems of Present-Day Mathematics. 21 What Can Human Mathematics Be Like? Graphical Key.

article thumbnail

There is transfer between programming and other subjects: Skills overlap, but it may not be causal

Computing Education Research Blog

They looked at 105 studies and found that there was a measurable amount of transfer between programming and situations requiring mathematical skills and spatial reasoning. We cannot predict that students learning programming will automatically get higher mathematics grades, for example. Those things transfer.

educators

Sign Up for our Newsletter

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

article thumbnail

Contending with the Unintended Consequences of History: Revisiting Brown v. Board of Education and the Need for Systemic Change in K-12 Education

National Science Foundation

The biases are notably stark if schools are divided out by minority enrollment, as public middle and high schools with more than 50 percent White students have only 2 percent of mathematics teachers and 1 percent of science teachers that are Black ( National Center for Science & Engineering Statistics ).

article thumbnail

Grading in my Discrete Mathematics class: a 3x3x3 reflection

Robert Talbert, Ph.D.

Here's the one from Winter 2021 for calculus and here's the one for modern algebra. This semester I taught two sections of Discrete Structures for Computer Science 1, an entry-level course for Computer Science majors on the mathematical foundations of computing.

article thumbnail

Games and Puzzles as Multicomputational Systems

Stephen Wolfram

Imagine that rather than playing a specific game, we instead at each step just make every possible move with equal probability. The setup for tic-tac-toe is symmetrical enough that for most of the game the probability of every possible configuration at a given step is equal. The Icosian Game & Some Relatives. &#10005.

Physics 71
article thumbnail

The Concept of the Ruliad

Stephen Wolfram

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.) For integers, the obvious notion of equivalence is numerical equality. For hypergraphs, it’s isomorphism. Experiencing the Ruliad.

Physics 122
article thumbnail

Computational Foundations for the Second Law of Thermodynamics

Stephen Wolfram

How does one tie all this down with rigorous, mathematical-style proofs? But having seen that the core phenomenon of the Second Law can be reduced to an essentially purely computational statement, we’re now in a position to examine this in a different—and I think ultimately very clarifying—way. Well, it’s difficult.