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mattbaker.blog | ||
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lucatrevisan.wordpress.com
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| | | | | In which we show how to find the eigenvalues and eigenvectors of Cayley graphs of Abelian groups, we find tight examples for various results that we proved in earlier lectures, and, along the way, we develop the general theory of harmonic analysis which includes the Fourier transform of periodic functions of a real variable, the... | |
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www.jeremykun.com
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| | | | | Last time we defined and gave some examples of rings. Recapping, a ring is a special kind of group with an additional multiplication operation that "plays nicely" with addition. The important thing to remember is that a ring is intended to remind us arithmetic with integers (though not too much: multiplication in a ring need not be commutative). We proved some basic properties, like zero being unique and negation being well-behaved. | |
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qchu.wordpress.com
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| | | | | In this post we'll describe the representation theory of theadditive group scheme$latex \mathbb{G}_a$ over a field $latex k$. The answer turns out to depend dramatically on whether or not $latex k$ has characteristic zero. Preliminaries over an arbitrary ring (All rings and algebras are commutative unless otherwise stated.) The additive group scheme $latex \mathbb{G}_a$ over... | |
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mappingignorance.org
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| | | [AI summary] This post summarizes a scientific study comparing the productivity of Microsoft Word and LaTeX for academic writing, finding Word superior for general text and tables while LaTeX excels with complex equations. | ||
