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jmanton.wordpress.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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jiggerwit.wordpress.com
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| | | | | YBC 7289 Introduction (A pdf version of this post appears at the end of this post.) We propose a one-shot calculation of ?2 using Babylonian mathematics. An Old-Babylonian (OB) tablet YBC 7289 (from around 1800 B.C. to 1600 B.C.) contains the approximation B = 1 + 24/60 + 51/602 + 10/603 = 30547/21600 for ?2.... | |
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njwildberger.com
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| | | | | Our paper "A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode" is now available at Taylor and Francis Online. It will appear next month in print form in the American Mathematical Monthly. Here is the link to the paper: https://www.tandfonline.com/doi/full/10.1080/00029890.2025.2460966 From the Abstract: The Catalan numbers?? ??count the number of subdivisions of a polygon... | |
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stephenmalina.com
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| | | Selected Exercises # 5.A # 12. Define $ T \in \mathcal L(\mathcal P_4(\mathbf{R})) $ by $$ (Tp)(x) = xp'(x) $$ for all $ x \in \mathbf{R} $. Find all eigenvalues and eigenvectors of $ T $. Observe that, if $ p = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + a_4 x^4 $, then $$ x p'(x) = a_1 x + 2 a_2 x^2 + 3 a_3 x^3 + 4 a_4 x^4. | ||
