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micromath.wordpress.com | ||
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jiggerwit.wordpress.com
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| | | | | What follows are the opening paragraphs of a pdf document giving an argument for controlled natural languages in mathematics. At the recent Big Proof 2 conference in Edinburgh, I realized that a case must be made for developing a controlled natural language for mathematics. There is little consensus on this issue, and mathematicians and computer... | |
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mathscholar.org
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| | | | | [AI summary] The text presents a detailed, self-contained proof of the Fundamental Theorem of Calculus (FTC) using basic principles of calculus and real analysis. It breaks the proof into two parts: Part 1 establishes that the integral of a continuous function defines a differentiable function whose derivative is the original function, and Part 2 shows that the definite integral of a continuous function can be computed as the difference of an antiderivative evaluated at the endpoints. The proof relies on lemmas about continuity, differentiability, and the properties of integrals, avoiding advanced techniques. The text is structured to provide a clear, step-by-step derivation of the FTC for readers familiar with calculus fundamentals. | |
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njwildberger.com
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| | | | | Modern mathematics is enormously complicated and sophisticated. It takes some courage, and perhaps some foolishness, to dare to suggest that behind the fancy theories lie serious logical gaps, and indeed error. But this is the unfortunate reality. Around the corner, however, is a new and more beautiful mathematics, a more honest mathematics, in which everything... | |
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ssir.org
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| | | How can we transform the university research enterprise to enhance its social impact? | ||
