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ianwrightsite.wordpress.com | ||
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peterbloem.nl
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| | | | | [AI summary] The text provides an in-depth explanation of the Fundamental Theorem of Algebra, which states that every non-constant polynomial of degree $ n $ has exactly $ n $ roots in the complex number system, counting multiplicities. It walks through the proof by first establishing that every polynomial has at least one complex root (using the properties of continuous functions and the complex plane), then using polynomial division to factor the polynomial into linear factors, and finally addressing the nature of roots (real vs. complex) and their multiplicities. The text also touches on the conjugate root theorem, which explains why complex roots of polynomials with real coefficients come in conjugate pairs. | |
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rjlipton.com
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| | | | | "If I were to awaken after having slept a thousand years, my first question would be: has the Riemann Hypothesis been proven?" --- David Hilbert Steklov Institute memorial page Sergei Voronin was an expert in number theory, who studied the Riemann zeta function, but who sadly died young over twenty years ago. We discussed his... | |
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terrytao.wordpress.com
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| | | | | Many modern mathematical proofs are a combination of conceptual arguments and technical calculations. There is something of a tradeoff between the two: one can add more conceptual arguments to try ... | |
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rjlipton.com
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| | | How confident should we be that the Riemann Hypothesis is true? Composite of src1, src2 Andrew Odlyzko and Herman te Riele, in a 1985 paper, refuted a once widely believed conjecture from 1885 that implies the Riemann Hypothesis. The belief began a U-turn in the 1940s, and by the late 1970s the community was convinced... | ||
