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devyn.ca | ||
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codethrasher.com
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| | | | | To qualify as a vector space, a set \(V\) and its associated operations of addition (\(+\)) and multiplication/scaling (\(\cdot\)) must adhere to the below: Associativity # \begin{equation} \mathbf{u}+(\mathbf{v}+\mathbf{w}) = (\mathbf{u} + \mathbf{v}) + \mathbf{w} \end{equation} Commutivity # \begin{equation} \mathbf{u} + \mathbf{v} = \mathbf{v} + \mathbf{u} \end{equation} Identity of Addition # There exists and element \(\mathbf{0}\,\in\,V\), called the zero vector, such that \(\mathbf{v} + \mathbf{0} ... | |
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djalil.chafai.net
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| | | | | The logarithmic potential is a classical object of potential theory intimately connected with the two dimensional Laplacian. It appears also in free probability theory via the free entropy, and in partial differential equations e.g. Patlak-Keller-Segel models. This post concerns only it usage for the spectra of non Hermitian random matrices. Let \( {\mathcal{P}(\mathbb{C})} \) be the set of probability measures... | |
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algorithmsoup.wordpress.com
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| | | | | The ``probabilistic method'' is the art of applying probabilistic thinking to non-probabilistic problems. Applications of the probabilistic method often feel like magic. Here is my favorite example: Theorem (Erdös, 1965). Call a set $latex {X}&fg=000000$ sum-free if for all $latex {a, b \in X}&fg=000000$, we have $latex {a + b \not\in X}&fg=000000$. For any finite... | |
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mathagogy.wordpress.com
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| | | This is part of a series offering my views onsome problems with and solutions for UK maths education.The first part looked at the state of affairs with regards to GCSE and PISA results, thesecond part looked at my attempt at a diagnosis, thethird part looked at pre-existing maths education success stories, the fourth partlookedathow textbooks... | ||
