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micromath.wordpress.com | ||
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almostsuremath.com
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| | | | | The aim of this post is to motivate the idea of representing probability spaces as states on a commutative algebra. We will consider how this abstract construction relates directly to classical probabilities. In the standard axiomatization of probability theory, due to Kolmogorov, the central construct is a probability space $latex {(\Omega,\mathcal F,{\mathbb P})}&fg=000000$. This consists... | |
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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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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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myinnermishmash.wordpress.com
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| | | Hey guys! :) For today, I chose to share with you quite a short Celtic harp piece played by Scottish harpist Rachel Newton, called Beinn an Eoin, which is the name of a mountain in the Scottish Highlands. https://www.youtube.com/watch?v=dULpviNMW88 | ||
