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geoenergymath.com | ||
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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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ai.googleblog.com
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| | | | | [AI summary] Researchers at Google describe a new method using machine learning to improve the simulation of partial differential equations, allowing for faster and more accurate modeling of physical phenomena like climate change and fluid dynamics. | |
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www.jeremykun.com
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| | | | | Finding solutions to systems of polynomial equations is one of the oldest and deepest problems in all of mathematics. This is broadly the domain of algebraic geometry, and mathematicians wield some of the most sophisticated and abstract tools available to attack these problems. The elliptic curve straddles the elementary and advanced mathematical worlds in an interesting way. On one hand, it's easy to describe in elementary terms: it's the set of solutions to a cubic function of two variables. | |
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www.kuniga.me
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| | | NP-Incompleteness: | ||
