Special Topics

Automated Number Theory Automated Number Theory Automated Conjecture

Represent Represent It Conjecture! Hassler Whitney Map It Represented Partial Mapping Partial Mapping, the Program Map That Which Is Not Represented by Math, One Take Take Two, an Example Other Than an Irrational Number Math as Data Concept Plus Calculation More from Terence Tao and Friends Analytic Number Theory Exponent Database Wolfram Data Repository Does Not Compute? Include It Map That Which Math Cannot Represent Error Limitation MUH Map the Connections Map the Answers Automated Conjecture Map the Map Maps A Map The Library of Babel Represented Concept Maps Concept Maps Compute Compute Compute Proof Compute Proof (Understanding It) Numbers as Functions Neurosymbolic Networks A Map of Math Parameterization as a Means of Limiting Applicability Rather than Demonstrating Error Law of Small Numbers Proof as Program Curry-Howard

  Random Permutations  by John Baez Part 0  — What's the average length of the longest cycle in a random permutation of an  n -element set? Part 1  — What is the probability that a randomly chosen permutation of an  n -element set has exactly  k  fixed points? Part 2  — What is the probability that the shortest cycle in a randomly chosen permutation of an  n -element set has length greater than  k ? Part 3  — A large collection of questions about random permutations, with answers. Part 4  — What is the probability that a randomly chosen permutation of an  n -element set has a cycle of length g reater n / 2? Part 5  — What is the average length of a cycle in a randomly chosen permutation of an  n -element set? Part 6  — What expected number of cycles of length  k  in a randomly chosen permutation of an  n -element set? Part 7  — How is the distribution of the number of cycles of lengt...