April 1st
Today I learned that the matrix exponential can be used to solve systems of linear differential equations, from 3Blue1Brown of course. (continue reading...)
April 2021
April 2nd
Today I learned how to show that $A\times B:\equiv\prod_{(x:2)}\op{rec}_2(\UU,A,B)(x)$ behaves the way that it should. (continue reading...)
April 3rd
Today I learned generalized Fourier series. (continue reading...)
April 4th
Today I learned (finally) why the norm-$1$ idele-class group $\AA^\times_{K,1}/K^\times$ is compact, from here . (continue reading...)
April 5th
Today I learned a relatively clean proof of the fact that\[\sum_{n\in\FF_p^\times}n^k\equiv0\pmod p\]provided that $p-1\nmid k,$ from here . (continue reading...)
April 6th
Today I learned the proof that $L(s,\chi)$ is non-vanishing along $\op{Re}s=1,$ for unitary Hecke characters $\chi.$ (continue reading...)
April 7th
Today I learned about "wild'' automorphisms of $\CC,$ from here . (continue reading...)
April 8th
Today I learned how to construct wild automorphisms of $\CC$ via Zorn's lemma. (continue reading...)
April 9th
Today I learned the proof of Chebotarev's theorem in the abelian case. (continue reading...)
April 10th
Today I learned a fun example of a telescoping product, from the Purple Comet. (continue reading...)
April 11th
Today I learned a fun application of Chebotarev's theorem, from here . (continue reading...)
April 12th
Today I learned the proof of the general case of Chebotarev's theorem, from here . (continue reading...)
April 13th
Today I learned about characters of finite fields, from here . (continue reading...)
April 14th
Today I learned about path-connectedness, from Keith Conrad . (continue reading...)
April 15th
Today I learned Sierpinski's proof that all measurable solutions to Cauchy functional equation are linear, from here . (continue reading...)
April 16th
Today I learned about Kummer series acceleration, from Keith Conrad of course. (continue reading...)
April 17th
Today I learned the proof of the functional equation for the Dedekind zeta function $\zeta_K,$ mostly from here . (continue reading...)
April 18th
Today I learned about adjoints in category theory, from Vakil . (continue reading...)
April 19th
Today I learned (finally) the proof of the fundamental correspondence in Galois theory, from Marcus (say). (continue reading...)
April 20th
Today I learned a little about the relationship between localizing a global field and localizing a ring. (continue reading...)
April 21st
Today I learned about the different in the monogenic case.\todo{} (continue reading...)
April 22nd
Today I learned an example of contour integration, to build towards the Prime Number Theorem. (continue reading...)
April 23rd
Today I learned how to extract the Dirichlet series coefficients from a Dirichlet series function, from here . (continue reading...)
April 24th
Today I learned about line bundles. (continue reading...)
April 25th
Today I learned about Pratt primality certificates. (continue reading...)
April 26th
Today I learned the proof of function extensionality from the existence of the interval type. (continue reading...)
April 27th
Today I learned that some self-contained calculus can be done over the $p$-adics, from here . (continue reading...)
April 28th
Today I learned that the Fourier transform for finite fields behaves as it does in local fields, from here . (continue reading...)
April 29th
Today I learned the definition of the wedge product, from the Napkin . (continue reading...)
April 30th
Today I learned the Kuratowski closure-complement theorem, from here . (continue reading...)