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matheuscmss.wordpress.com | ||
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terrytao.wordpress.com
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| | | | | Many modern mathematical proofs are a combination of conceptual arguments and technical calculations. There is something of a tradeoff between the two: one can add more conceptual arguments to try ... | |
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almostsuremath.com
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| | | | | Continuing on from the previous post, I look at cases where the abstract concept of states on algebras correspond to classical probability measures. Up until now, we have considered commutative real algebras but, before going further, it will help to look instead at algebras over the complex numbers $latex {{\mathbb C}}&fg=000000$. In the commutative case,... | |
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qchu.wordpress.com
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| | | | | (Part I of this post ishere) Let $latex p(n)$ denote the partition function, which describes the number of ways to write $latex n$ as a sum of positive integers, ignoring order. In 1918 Hardy and Ramanujan proved that $latex p(n)$ is given asymptotically by $latex \displaystyle p(n) \approx \frac{1}{4n \sqrt{3}} \exp \left( \pi \sqrt{ \frac{2n}{3}... | |
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austinmorlan.com
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| | | It took me longer than necessary to understand how a rotation transform matrix rotates a vector through three-dimensional space. Not because it's a difficult concept but because it is often poorly explained in textbooks. Even the most explanatory book might derive the matrix for a rotation around one axis (e.g., x) but then present the other two matrices without showing their derivation. I'll explain my own understanding of their derivation in hopes that it will enlighten others that didn't catch on right away. | ||
