nhaliday + math.nt   40

Diophantine approximation - Wikipedia
- rationals perfectly approximated by themselves, badly approximated (eps~1/q) by other rationals
- irrationals well-approximated (eps~1/q^2) by rationals: https://en.wikipedia.org/wiki/Dirichlet%27s_approximation_theorem
nibble  wiki  reference  math  math.NT  approximation  accuracy  levers  pigeonhole-markov  multi  tidbits  discrete  rounding 
august 2017 by nhaliday
254A, Supplement 4: Probabilistic models and heuristics for the primes (optional) | What's new
among others, the Cramér model for the primes (basically kinda looks like primality is independently distributed w/ Pr[n is prime] = 1/log n)
gowers  mathtariat  lecture-notes  exposition  math  math.NT  probability  heuristic  models  cartoons  nibble  org:bleg  pseudorandomness  borel-cantelli  concentration-of-measure  multiplicative 
february 2017 by nhaliday
nt.number theory - Is $x^{2k+1} - 7x^2 + 1$ irreducible? - MathOverflow
Here is a proof, based on a trick that can be used to prove that x^n+x+1 is irreducible when n≠2 mod 3.
q-n-a  overflow  math  algebra  tidbits  math.NT  contradiction  polynomials  nibble  multiplicative 
january 2017 by nhaliday
The Mathematician Ken Ono’s Life Inspired By Ramanujan | Quanta Magazine
This intellectual crucible produced the desired results — Ono studied mathematics and launched a promising academic career — but at great emotional cost. As a teenager, Ono became so desperate to escape his parents’ expectations that he dropped out of high school. He later earned admission to the University of Chicago but had an apathetic attitude toward his studies, preferring to party with his fraternity brothers. He eventually discovered a genuine enthusiasm for mathematics, became a professor, and started a family, but fear of failure still weighed so heavily on Ono that he attempted suicide while attending an academic conference. Only after he joined the Institute for Advanced Study himself did Ono begin to make peace with his upbringing.
profile  math  people  career  popsci  hmm  news  org:mag  org:sci  giants  math.NT  nibble  org:inst 
may 2016 by nhaliday

bundles : academeframemath

related tags

aaronson  accretion  accuracy  acm  additive  additive-combo  alg-combo  algebra  algebraic-complexity  algorithms  AMT  announcement  approximation  bayesian  better-explained  big-list  big-picture  big-surf  binomial  bio  blowhards  books  boolean-analysis  borel-cantelli  business  career  cartoons  characterization  chart  checklists  chemistry  circuits  clarity  clever-rats  coding-theory  cog-psych  commentary  communication  communication-complexity  complexity  concentration-of-measure  concept  conceptual-vocab  confluence  contradiction  convexity-curvature  cool  counterexample  course  criminal-justice  crypto  cs  curiosity  curvature  data-science  database  decision-making  decision-theory  definition  differential  discrete  discussion  DP  dynamic  economics  electromag  embeddings  epistemic  erdos  ethics  examples  exposition  extratricky  feynman  fields  film  finiteness  formal-values  fourier  game-theory  geometry  giants  gowers  graph-theory  graphs  greedy  ground-up  growth  GT-101  hamming  harvard  heuristic  hi-order-bits  history  hmm  hn  homepage  ideas  identity  idk  impro  induction  info-foraging  information-theory  init  insight  integral  interview  intuition  iteration-recursion  knowledge  language  lecture-notes  lens  lesswrong  letters  levers  linear-algebra  linear-programming  links  list  logic  machine-learning  macro  magnitude  markov  math  math.AG  math.CA  math.CO  math.CV  math.DS  math.FA  math.GR  math.NT  math.RT  mathtariat  measure  mental-math  metabuch  metameta  michael-nielsen  micro  mit  models  monte-carlo  mostly-modern  motivation  multi  multiplicative  music-theory  naturality  nature  neuro  news  nibble  nitty-gritty  numerics  objektbuch  occam  oly  open-problems  org:bleg  org:inst  org:mag  org:mat  org:sci  orourke  overflow  p:**  p:someday  people  philosophy  physics  pigeonhole-markov  polynomials  popsci  pre-2013  prioritizing  probabilistic-method  probability  prof  profile  proofs  pseudorandomness  psychology  q-n-a  qra  quantum  questions  rand-approx  random  rationality  ratty  reading  rec-math  recommendations  reference  reflection  relativity  research  review  rhetoric  rigor  rigorous-crypto  rounding  s:*  s:***  salil-vadhan  skeleton  social-science  soft-question  space-complexity  spectral  stanford  stat-mech  stats  stories  street-fighting  structure  subculture  summary  synthesis  tcs  tcstariat  techtariat  the-trenches  thermo  thinking  tidbits  time-complexity  top-n  topics  topology  tricki  tricks  trivia  unit  vague  valiant  wigderson  wiki  world-war  wormholes  yoga  👳  🤖  🦉 

Copy this bookmark: