Articles

• A

  • A non-trivial circular argument can often be usefully perturbed to a non-circular one

• B

  • Bijections and counting

• I

  • If a parameter is generating undesirable boundary terms, try averaging over many choices of that parameter
  • If your problem can be expressed in terms of convolutions and inner products then take the Fourier transform

• K

  • Keep parameters unspecified until it is clear how to optimize them

• S

  • Some useful examples of graphs

• T

  • To compute probabilities of unions and intersections, use the inclusion-exclusion formula
  • To compute the probability that exactly k of n events occur, use generalized inclusion-exclusion
  • To increase the occurrence of a property in a set, try randomly refining that set in a way that favors the property

• U

  • Use the compactness and contradiction method to derive finitary quantitative results from infinitary qualitative ones