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What should mathematics majors know about computing, and when should they know it?

Robert Talbert, Ph.D.

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. In the original article, I gave a list of what computing skills mathematics majors should learn and when they should learn them.

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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.

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How can first-year STEM university students be better supported?

Futurum

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?

Biology 81
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Can AI Solve Science?

Stephen Wolfram

Three centuries ago science was transformed by the idea of representing the world using mathematics. And that’s for example why things like mathematical formulas have been able to be as successful in science as they have. In 2000 I was interested in what the simplest possible axiom system for logic (Boolean algebra) might be.

Science 122
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Even beyond Physics: Introducing Multicomputation as a Fourth General Paradigm for Theoretical Science

Stephen Wolfram

Many would say that modern exact science was launched in the 1600s with the introduction of what we can call the “ mathematical paradigm ”: the idea that things in the world can be described by mathematical equations—and that their behavior can be determined by finding solutions to these equations.

Physics 65
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Multicomputation: A Fourth Paradigm for Theoretical Science

Stephen Wolfram

Many would say that modern exact science was launched in the 1600s with the introduction of what we can call the “ mathematical paradigm ”: the idea that things in the world can be described by mathematical equations—and that their behavior can be determined by finding solutions to these equations.

Science 64
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Remembering the Improbable Life of Ed Fredkin (1934–2023) and His World of Ideas and Stories

Stephen Wolfram

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. So what happened is Marvin [Minsky] and I basically fleshed out the idea of a mathematical thing.