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njwildberger.com | ||
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micromath.wordpress.com
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| | | | | Continuing the theme of alternative approaches to teaching calculus, I take the liberty of posting a letter sent by Donald Knuth to to the Notices of the American Mathematical Society in March, 1998 (TeX file). Professor Anthony W. Knapp P O Box 333 East Setauket, NY 11733 Dear editor, I am pleased to see so... | |
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math.andrej.com
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| | | | | [AI summary] The discussion revolves around the philosophical and methodological pluralism in mathematics, emphasizing that mathematics is a human-made construct with historical developments rather than an absolute, universal truth. Key points include the idea that different mathematical frameworks (e.g., classical vs. intuitionistic logic, paraconsistent logic) represent distinct 'worlds' of mathematics, each with its own standards and validity. The conversation highlights the importance of acknowledging these pluralistic perspectives without assuming a single, unifying foundation. It also touches on the role of context, the evolution of mathematical concepts, and the implications of relativism for the future of mathematics. The discussion underscores that ... | |
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www.quantamagazine.org
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| | | | | Number theorist Andrew Granville on what mathematics really is - and why objectivity is never quite within reach. | |
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divisbyzero.com
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| | | In my next real analysis lecture, we'll be discussing the Bolzano-Weierstrass theorem. (It says that any bounded sequence of real numbers contains a convergent subsequence.) I'll be showing my class this video in which Steve Sawin(AKA Slim Dorky) raps the complete proof of the theorem. https://www.youtube.com/watch?v=dfO18klwKHg You can read the lyrics here. He has some... | ||
