To make a function nicer without changing it much, convolve it with an approximate delta function |
06/05/2009 - 12:57 |
*11 years 11 weeks* ago |

To optimize a sum try making the terms roughly equal in size |
24/04/2009 - 19:48 |
*11 years 17 weeks* ago |

To prove convergence, find a rapidly converging subsequence |
25/04/2009 - 17:06 |
*11 years 15 weeks* ago |

To prove facts about Borel sets, use closure properties |
05/05/2009 - 14:47 |
*11 years 14 weeks* ago |

To prove facts about finite groups, use induction on the order |
19/04/2009 - 15:28 |
*11 years 16 weeks* ago |

To prove that a number is irrational, show that it is almost rational |
05/05/2009 - 10:44 |
*10 years 27 weeks* ago |

To prove that a sequence converges, find one or more convergent subsequences |
25/04/2009 - 17:04 |
*11 years 17 weeks* ago |

To prove that a set is open or closed, use basic theorems rather than direct arguments |
13/05/2009 - 23:48 |
*11 years 14 weeks* ago |

To prove that two objects are equal show that in enough circumstances they behave in the same way |
19/04/2009 - 14:51 |
*11 years 18 weeks* ago |

To prove that two real numbers are equal, prove that neither is greater than the other |
07/12/2008 - 20:47 |
*11 years 16 weeks* ago |

To represent one object as combinations of another, try averaging the latter object using the symmetries of the former |
22/05/2009 - 19:44 |
*11 years 13 weeks* ago |

To show that a group element is non-trivial, show that it has a non-trivial action or image |
30/04/2009 - 19:31 |
*11 years 15 weeks* ago |

To simplify a closed subset of the plane, approximate it using a grid of squares |
08/05/2009 - 12:46 |
*10 years 3 weeks* ago |

To understand an object, consider treating it as one of a family of objects and analysing the family |
25/04/2009 - 18:39 |
*11 years 17 weeks* ago |

To work out powers mod n, use repeated squaring |
10/05/2009 - 16:43 |
*11 years 15 weeks* ago |

Transfinite induction |
02/01/2009 - 01:44 |
*5 years 44 weeks* ago |

Transform equation to reach a solved pattern |
06/07/2009 - 18:42 |
*11 years 1 week* ago |

Treat an explicit but messy function abstractly |
21/04/2009 - 00:15 |
*11 years 18 weeks* ago |

Try to prove a stronger result |
25/11/2011 - 02:27 |
*8 years 39 weeks* ago |

Turn sets into functions |
14/12/2008 - 11:55 |
*10 years 18 weeks* ago |

Universal constructions |
08/12/2008 - 14:50 |
*11 years 11 weeks* ago |

Unusual choices of probability distribution |
29/03/2009 - 22:37 |
*11 years 21 weeks* ago |

Use an appropriate series expansion |
24/04/2009 - 15:57 |
*11 years 15 weeks* ago |

Use an approximation as if it were exact |
11/05/2009 - 14:25 |
*11 years 15 weeks* ago |

Use analytic expressions of constraints in sums or integrals |
05/04/2009 - 10:29 |
*11 years 20 weeks* ago |