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peterbloem.nl | ||
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jaydaigle.net
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| | | | | We continue our exploration of what numbers are, and where mathematicians keep finding weird ones. In the first three parts we extended the natural numbers in two ways: algebraically and analytically. Those approaches gave overlapping but distinct sets of numbers. This week we combine them to get the complex numbers, and see some hints of why the complex numbers are so useful-and so frustrating. | |
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jmanton.wordpress.com
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| | | | | The following hints atwhy the quintic equation cannot be solved using radicals. It follows the approach in the first part of Ian Stewart's book "Galois Theory". If time permits, a future post will summarise the approach in V. B. Alekseev's book "Abel's Theorem in Problems and Solutions". Another candidate is Klein's book "Lectures on the... | |
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thenumb.at
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rjlipton.com
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| | | Newman's theorem on rational approximations and complexity theory Donald Newman was not a theorist, but was a mathematician who worked on many topics during his career. One of his results is a lovely theorem that shows that the approximation of continuous functions by rational functions can be very different from the approximation by polynomials. Today... | ||
