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live-simons-blog.pantheonsite.io | ||
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ptreview.sublinear.info
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mycqstate.wordpress.com
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| | | | | Last Spring I took part in the Simons Institute's semester on Quantum Hamiltonian Complexity. The semester was a great success, with an excellent batch of long-term participants and many fruitful interactions. The Institute asked me to write a short "Research Vignette" presenting, to a broad audience, an example scientific outcome of the programme. You can... | |
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algassert.com
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| | | | | Craig Gidney's computer science blog | |
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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. | ||
