June 1st
Today I learned about the Mahler measure, from here . (continue reading...)
June 2021
June 2nd
Today I learned a proof that $e^q$ is irrational for any $q\in\QQ\setminus\{0\},$ following Hermite. (continue reading...)
June 3rd
Today I learned an example of spectral graph theory doing something of number-theoretic interest, from THE BOOK. (continue reading...)
June 5th
Today I learned about the difficulty generalizing the result from yesterday to arbitrary dimensions. (continue reading...)
June 6th
Today I learned that a number of geometric concepts can be defined purely formally from an arbitrary distance metric, from the ARML Power Round. (continue reading...)
June 6th
Today I learned the classification of primes in polynomial rings over principal ideal domains, from Undergraduate Commutative Algebra. (continue reading...)
June 7th
Today I learned a truly clever proof to the Spectal theorem, from THE BOOK of course. (continue reading...)
June 8th
Today I learned about the semi-failure of function extensionality for polynomials. (continue reading...)
June 9th
Today I learned a little about group homology and chain complexes, from Napkin . (continue reading...)
June 10th
Today I learned a proof to Sperner's theorem, from THE BOOK. (continue reading...)
June 11th
Today I learned about the P\'olya-Vinogradov inequality, from Joni and Tao . (continue reading...)
June 12th
Today I learned about representing numbers as sums of distinct squares, from a bunch of places. (continue reading...)
June 13th
Today I learned a few ways to evaluate $\zeta$ at even integers, from THE BOOK, and some consequences. (continue reading...)
June 14th
Today I learned more formally about the association between points in $k^n$ and maximal ideals of $k[x_1,\ldots,x_n],$ from Undergraduate Commutative Algebra. (continue reading...)
June 15th
Today I learned the start of some group cohomology. (continue reading...)
June 16th
Today I learned finish to the proof that any $G$-module can be embedded into an injective $G$-module. (continue reading...)
June 17th
Today I learned that group cohomology is well-defined. (continue reading...)
June 18th
Today I learned an algebraic proof of the Cayley-Hamilton theorem. (continue reading...)
June 19th
Today I learned a more thorough version of the Snake Lemma to set up for the long exact sequence of cohomology. (continue reading...)
June 20th
Today I learned some stuff around the Cauchy-Schwartz inequality, from THE BOOK. (continue reading...)
June 21st
Today I learned a proof of Nakayama's lemma as a corollary of the determinant trick. (continue reading...)
June 22nd
Today I learned some stuff about short exact sequences. (continue reading...)
June 23rd
Today I learned (and reviewed) some proofs of the Sylow theorems that I like. (continue reading...)
June 24th
Today I learned about the Wronskian. (continue reading...)
June 25th
Today I learned a little more about polynomial statistics over finite fields. (continue reading...)
June 26th
Today I learned a proof of the Hilbert basis theorem. (continue reading...)
June 27th
Today I learned about Artinian rings. (continue reading...)
June 28th
Today I learned a toy model for schemes, as more or less the opposite category of commutative algebras. (continue reading...)
June 29th
Today I learned more about the Zariski topology. (continue reading...)
June 30th
Today I learned more formally about integral elements and closures. (continue reading...)