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Students Are Busy but Rarely Thinking, Researcher Argues. Do His Teaching Strategies Work Better?

ED Surge

That’s the argument of Peter Liljedahl, a professor of mathematics education at Simon Fraser University in Vancouver, who has spent years researching what works in teaching. These are the students who end up hitting a wall when math courses move from easier algebra to more advanced concepts in, say, calculus, he argues. “At

Research 362
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The Physicalization of Metamathematics and Its Implications for the Foundations of Mathematics

Stephen Wolfram

One can view a symbolic expression such as f[g[x][y, h[z]], w] as a hierarchical or tree structure , in which at every level some particular “head” (like f ) is “applied to” one or more arguments. So how about logic, or, more specifically Boolean algebra ? We’ve looked at axioms for group theory and for Boolean algebra.

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LLM Tech and a Lot More: Version 13.3 of Wolfram Language and Mathematica

Stephen Wolfram

And, yes, when you try to run the function, it’ll notice it doesn’t have correct arguments and options specified. 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 And now in Version 13.3 But in Version 13.3

Computer 120
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The Story Continues: Announcing Version 14 of Wolfram Language and Mathematica

Stephen Wolfram

In addition to whole courses, we have “miniseries” of lectures about specific topics: And we also have courses —and books—about the Wolfram Language itself, like my Elementary Introduction to the Wolfram Language , which came out in a third edition this year (and has an associated course, online version, etc.): is PositionSmallest.

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The Concept of the Ruliad

Stephen Wolfram

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. And we can trace the argument for this to the Principle of Computational Equivalence.

Physics 117
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Five Most Productive Years: What Happened and What’s Next

Stephen Wolfram

In the end—after all sorts of philosophical arguments, and an analysis of actual historical data —the answer was: “It’s Complicated”. I’m particularly interested in how people develop through their lives—leading me recently, for example, to organize a 50-year reunion for my elementary school class.) OK, so that’s a lot of projects.

Physics 112
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Even beyond Physics: Introducing Multicomputation as a Fourth General Paradigm for Theoretical Science

Stephen Wolfram

Events are like functions, whose “arguments” are incoming tokens, and whose output is one or more outgoing tokens. In physics, those “topological phenomena” presumably correspond to things like elementary particles , with all their various elaborate symmetries. One is so-called Böhm trees.

Physics 66