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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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Is a College Degree the Worst Investment You Can Make — or the Best?

ED Surge

Universities generally cover a wide range of subjects, focused on an academic field, say mathematics or computer science. And the argument is that if a university degree is a good investment, it ought to be substantially more valuable than the opportunity cost. My argument is that the risk is too high, and the returns too low.

educators

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Should universities use differential treatment to admit students?

Futurum

The idea that exam results should be assessed differently based on a student’s socio-economic background is known as differential treatment, and Emil is investigating whether such policies can improve equality and efficiency in education and labour markets. As you can imagine, there are many arguments both for and against these ideas.

Economics 111
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How Did We Get Here? The Tangled History of the Second Law of Thermodynamics

Stephen Wolfram

But by the end of the 1800s, with the existence of molecules increasingly firmly established, the Second Law began to often be treated as an almost-mathematically-proven necessary law of physics. There were still mathematical loose ends, as well as issues such as its application to living systems and to systems involving gravity.

Energy 88
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Nestedly Recursive Functions

Stephen Wolfram

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 ].

Computer 107
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Don’t Give Up on Algebra: Let’s Shift the Focus to Instruction

National Science Foundation

In its current form, school algebra serves as a gatekeeper to higher-level mathematics. Researchers and policy makers have pushed to open that gate—providing more students access to algebra, focusing in particular on those students historically denied access to higher-level mathematics. Berry & Larson, 2019; Levitt, 2019).

Algebra 76
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How can first-year STEM university students be better supported?

Futurum

Library and research skills cover areas such as knowing how to reference and cite authors properly, being able to discern between reliable and unreliable sources of information, accessing scientific literature and giving accurate evidence-based arguments when writing scientific essays and reports. What do students learn from studying this?

Biology 81