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At the University of Pittsburgh at Greensburg in the US, biologists Barbara Barnhart and Dr Olivia Long are using their Science Seminar programme to ease this transition for first year students studying biology, chemistry and biochemistry degrees. What do students learn from studying this?
As I teach my Linear Algebra and Differential Equations class this semester, which uses more computing than ever, I'm thinking even more about these topics. The computer is a tool for studying mathematical ideas in the same sense that a microscope is for studying biology and a telescope is for studying astronomy.
The fall of 2021 involved really leaning into the new multicomputational paradigm , among other things giving a long list of where it might apply : metamathematics, chemistry, molecular biology, evolutionary biology, neuroscience, immunology, linguistics, economics, machine learning, distributed computing.
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.
The function Map takes a function f and “maps it” over a list: Comap does the “mathematically co-” version of this, taking a list of functions and “comapping” them onto a single argument: Why is this useful? But we wanted to be able to compute hundreds of different functions to arbitrary precision for any complex values of their arguments.
In 2000 I was interested in what the simplest possible axiom system for logic (Boolean algebra) might be. of what’s now Wolfram Language —we were trying to develop algorithms to compute hundreds of mathematical special functions over very broad ranges of arguments. Back in 1987—as part of building Version 1.0
Events are like functions, whose “arguments” are incoming tokens, and whose output is one or more outgoing tokens. Chemistry / Molecular Biology. But in thinking about molecular computing it may be crucial—and perhaps it’s also necessary for understanding molecular biology. There are many.
Events are like functions, whose “arguments” are incoming tokens, and whose output is one or more outgoing tokens. Chemistry / Molecular Biology. But in thinking about molecular computing it may be crucial—and perhaps it’s also necessary for understanding molecular biology. There are many.
The global structures of metamathematics , economics , linguistics and evolutionary biology seem likely to provide examples—and in each case we can expect that at the core is the ruliad, with its unique structure. And we can trace the argument for this to the Principle of Computational Equivalence. But that’s not all there is to it.
Then McCarthy started to explain ways a computer could do algebra. It was all algebra. And the only conclusion we can arrive at is that a person can’t do this much algebra with the hope of getting it right.” Richard Feynman and I would get into very fierce arguments. And he says “There’s a problem. It’s just my nature.
In the basic definition of a standard cellular automaton, the rule “takes its arguments” in a definite order. But what kind of integro-differential-algebraic equation can reproduce the time evolution isn’t clear. RandomGraph[{20, 40}, EdgeStyle -> Gray, VertexStyle -> Table[i -> (RandomInteger[] /. {0
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