February 1st
Today I learned the definition of a natural transformation. (continue reading...)
February 2021
February 2nd
Today I learned about the principal congruence modular subgroup of level $N.$ (continue reading...)
February 3rd
Today I learned that $\lnot\lnot$ has the required operators to be a monad. (continue reading...)
February 4th
Today I learned a little more about decidability of symbolic algebra series convergence. (continue reading...)
February 5th
Today I learned a concrete example of a monad, courtesy of Alexander Burton. (continue reading...)
February 6th
Today I learned how to recover the modulus of a linear congruential pseudorandom number generator, from here . (continue reading...)
February 7th
Today I learned that random play in two-pile Nim give each player a $\frac12$ probability of winning if one pile has at least $2$ stones. (continue reading...)
February 8th
Today I learned some deeper type-theoretic significance to currying. (continue reading...)
February 9th
Today I learned the baby-step giant-step algorithm to solve the discrete log problem in general finite cyclic groups. (continue reading...)
February 10th
Today I learned that the Eisenstein series are modular forms, from here . (continue reading...)
February 11th
Today I learned (finally) the proof that $[0,1]$ is compact in the standard topology on $\RR.$ (continue reading...)
February 12th
Today I learned the definition of support in topology. (continue reading...)
February 13th
Today I learned some basic results in topological group theory. (continue reading...)
February 14th
Today I learned some basic facts about Artin $L$-functions. (continue reading...)
February 15th
Today I learned the statement of Artin reciprocity, which we use with some auxiliary results to derive Hilbert class fields and Kronecker-Weber, from here . (continue reading...)
February 16th
Today I learned that the ray class groups are finite assuming that the normal class group is finite, from here . (continue reading...)
February 17th
Today I learned Ostrowski's theorem for function fields, from here . (continue reading...)
February 18th
Today I learned an example of representation theory in the service of combinatorics, from Artin 10.6.5. (continue reading...)
February 19th
Today I learned about the topology of profinite groups. (continue reading...)
February 20th
Today I learned about the Mellin transformation, from here mostly. (continue reading...)
February 21st
Today I learned the proof of the functional equation for the Riemann $\zeta$ function, from here . (continue reading...)
February 22nd
Today I learned about the $p$-adic Gaussian from Terrence Tao . (continue reading...)
February 23rd
Today I learned about the Zariski topology. (continue reading...)
February 24th
Today I learned about the $p$-adic Gaussian to derive the completed Riemann $\xi$ function, from Terrence Tao . (continue reading...)
February 25th
Today I learned about the Lesbegue measure. (continue reading...)
February 26th
Today I learned how to show intervals $[a,b]$ have Lebesgue measure $b-a.$ (continue reading...)
February 27th
Today I learned about the adeles of $\CC(t),$ which provides some nice analogy to the situation with number fields. (continue reading...)
February 28th
Today I learned the classification of characters over $\QQ_p$ as $\QQ_p\cong\widehat{\QQ_p},$ from Keith Conrad as usual. (continue reading...)