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qchu.wordpress.com | ||
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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.daniellitt.com
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www.jeremykun.com
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| | | | | The First Isomorphism Theorem The meat of our last primer was a proof that quotient groups are well-defined. One important result that helps us compute groups is a very easy consequence of this well-definition. Recall that if $ G,H$ are groups and $ \varphi: G \to H$ is a group homomorphism, then the image of $ \varphi$ is a subgroup of $ H$. Also the kernel of $ \varphi$ is the normal subgroup of $ G$ consisting of the elements which are mapped to the identity under $ \varphi$. | |
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4gravitons.com
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| | | Merging quantum mechanics and gravity is a famously hard physics problem. Explaining why merging quantum mechanics and gravity is hard is, in turn, a very hard science communication problem. The more popular descriptions tend to lead to misunderstandings, and I've posted many times over the years to chip away at those misunderstandings. Merging quantum mechanics... | ||
