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terrytao.wordpress.com | ||
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mattbaker.blog
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| | | | | In my last blog post, I discussed a simple proof of the fact that pi is irrational. That pi is in fact transcendental was first proved in 1882 by Ferdinand von Lindemann, who showed that if $latex \alpha$ is a nonzero complex number and $latex e^\alpha$ is algebraic, then $latex \alpha$ must be transcendental. Since... | |
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siddhartha-gadgil.github.io
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rjlipton.com
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| | | | | How to count the number of cycles modulo $latex 2 &fg=000000$ in parallel Gian-Carlo Rota was one the world experts on combinatorics, and helped move the field from a corner of mathematics to become one of its central areas. Rota is famous for many other things, but his book Indiscrete Thoughts is a classic---it is... | |
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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} ... | ||
