To make a function nicer without changing it much, convolve it with an approximate delta function |
06/05/2009 - 11:57 |
*11 years 33 weeks* ago |

To optimize a sum try making the terms roughly equal in size |
24/04/2009 - 18:48 |
*11 years 39 weeks* ago |

To prove convergence, find a rapidly converging subsequence |
25/04/2009 - 16:06 |
*11 years 37 weeks* ago |

To prove facts about Borel sets, use closure properties |
05/05/2009 - 13:47 |
*11 years 36 weeks* ago |

To prove facts about finite groups, use induction on the order |
19/04/2009 - 14:28 |
*11 years 38 weeks* ago |

To prove that a number is irrational, show that it is almost rational |
05/05/2009 - 09:44 |
*10 years 49 weeks* ago |

To prove that a sequence converges, find one or more convergent subsequences |
25/04/2009 - 16:04 |
*11 years 39 weeks* ago |

To prove that a set is open or closed, use basic theorems rather than direct arguments |
13/05/2009 - 22:48 |
*11 years 37 weeks* ago |

To prove that two objects are equal show that in enough circumstances they behave in the same way |
19/04/2009 - 13:51 |
*11 years 40 weeks* ago |

To prove that two real numbers are equal, prove that neither is greater than the other |
07/12/2008 - 19:47 |
*11 years 38 weeks* ago |

To represent one object as combinations of another, try averaging the latter object using the symmetries of the former |
22/05/2009 - 18:44 |
*11 years 35 weeks* ago |

To show that a group element is non-trivial, show that it has a non-trivial action or image |
30/04/2009 - 18:31 |
*11 years 37 weeks* ago |

To simplify a closed subset of the plane, approximate it using a grid of squares |
08/05/2009 - 11:46 |
*10 years 26 weeks* ago |

To understand an object, consider treating it as one of a family of objects and analysing the family |
25/04/2009 - 17:39 |
*11 years 39 weeks* ago |

To work out powers mod n, use repeated squaring |
10/05/2009 - 15:43 |
*11 years 37 weeks* ago |

Transfinite induction |
02/01/2009 - 00:44 |
*6 years 14 weeks* ago |

Transform equation to reach a solved pattern |
06/07/2009 - 17:42 |
*11 years 23 weeks* ago |

Treat an explicit but messy function abstractly |
20/04/2009 - 23:15 |
*11 years 40 weeks* ago |

Try to prove a stronger result |
25/11/2011 - 01:27 |
*9 years 9 weeks* ago |

Turn sets into functions |
14/12/2008 - 10:55 |
*10 years 40 weeks* ago |

Universal constructions |
08/12/2008 - 13:50 |
*11 years 33 weeks* ago |

Unusual choices of probability distribution |
29/03/2009 - 21:37 |
*11 years 43 weeks* ago |

Use an appropriate series expansion |
24/04/2009 - 14:57 |
*11 years 37 weeks* ago |

Use an approximation as if it were exact |
11/05/2009 - 13:25 |
*11 years 37 weeks* ago |

Use analytic expressions of constraints in sums or integrals |
05/04/2009 - 09:29 |
*11 years 42 weeks* ago |

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