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When districts slot students into math classes based on ability they send conspicuous messages to those on the lower track that they are not smart enough, says Ho Nguyen, who was a K-12 math and computerscience program administrator in San Francisco during the district's detracking attempt. Nevertheless, the attempt was tense.
My argument is that computerscience was originally invented to be taught to everyone, but not for economic advantage. I see the LSA effort and our Teaspoon languages connected to the original goals for computerscience. In 1961, the MIT Sloan School held a symposium on “Computers and the World of the Future.”
If anything, over the past seven years, my feelings about the centrality of computing in the mathematics major have gotten even more entrenched. First, I know more computerscience and computer programming now than I did in 2007. These days the computer plays a front-and-center role in all of my classes.
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 ].
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. As the Version 1.0
At the level of individual events, ideas from the theory and practice of computation are useful. Events are like functions, whose “arguments” are incoming tokens, and whose output is one or more outgoing tokens. And the same issue arose for Alonzo Church’s lambda calculus (introduced around 1930).
At the level of individual events, ideas from the theory and practice of computation are useful. Events are like functions, whose “arguments” are incoming tokens, and whose output is one or more outgoing tokens. And the same issue arose for Alonzo Church’s lambda calculus (introduced around 1930).
Because it implies that whatever “computational parametrization” or “computational description language” one uses for the ruliad, one will almost always get something that can be viewed as “computationally equivalent”. But what about other models of computation—like cellular automata or register machines or lambda calculus?
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. and zero arguments: α[ ]. From a computerscience perspective, we can think of it as being like a type hierarchy.
In the end—after all sorts of philosophical arguments, and an analysis of actual historical data —the answer was: “It’s Complicated”. And there are also foundational questions in computerscience. Lots of college students these days say they want to study “computerscience”. OK, so that’s a lot of projects.
Sometimes textbooks will gloss over everything; sometimes they’ll give some kind of “common-sense-but-outside-of-physics argument”. Once one has the idea of “equilibrium”, one can then start to think of its properties as purely being functions of certain parameters—and this opens up all sorts of calculus-based mathematical opportunities.
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). “Lick” Licklider —who persuaded Ed to join BBN to “teach them about computers”. Nowadays we’d call it the trie (or prefix tree) data structure. But his name shows up from time to time.
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