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To prove facts about finite groups, use induction on the order 19/04/2009 - 15:28 11 years 16 weeks ago
To prove facts about Borel sets, use closure properties 05/05/2009 - 14:47 11 years 14 weeks ago
To prove convergence, find a rapidly converging subsequence 25/04/2009 - 17:06 11 years 15 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 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 make a function less variable without changing it much, compare it with less variable functions 10/06/2009 - 19:36 11 years 10 weeks ago
To increase the occurrence of a property in a set, try randomly refining that set in a way that favors the property 28/05/2009 - 18:02 11 years 12 weeks ago
To find the value of a coefficient, do something that kills all the other terms 07/05/2009 - 20:32 11 years 15 weeks ago
To find a rational with low denominator near a given real, use continued fractions 12/05/2009 - 22:32 11 years 15 weeks ago
To find a factor of n, find some m such that (m,n) is not 1 10/05/2009 - 16:13 11 years 15 weeks ago
To factorize n, find a non-trivial square root of 1 mod n 10/05/2009 - 16:23 11 years 15 weeks ago
To evaluate an integral, differentiate under the integral sign 24/04/2009 - 16:15 11 years 17 weeks ago
To establish that n is composite, show that Fermat's little theorem does not hold for n 10/05/2009 - 15:58 11 years 15 weeks ago
To construct exotic sets, use limiting arguments 15/05/2009 - 14:32 11 years 14 weeks ago
To construct exotic functions, use limiting arguments 25/03/2009 - 18:24 11 years 14 weeks ago
To construct a function with several local constraints, start with simple cases and build from there 24/05/2009 - 09:02 11 years 13 weeks ago
To compute the probability that exactly k of n events occur, use generalized inclusion-exclusion 12/05/2009 - 22:55 10 years 18 weeks ago
To compute probabilities of unions and intersections, use the inclusion-exclusion formula 12/05/2009 - 16:37 10 years 18 weeks ago
To compute covariance, use bilinearity 26/04/2009 - 03:52 11 years 17 weeks ago
To calculate an infinite sum exactly, try antidifferencing 27/04/2009 - 22:23 11 years 17 weeks ago
To calculate a contour integral, use theorems rather than direct calculation 01/05/2009 - 18:21 11 years 16 weeks ago
Think axiomatically even about concrete objects 26/04/2009 - 13:55 10 years 11 weeks ago
Think about the converse 25/03/2009 - 12:13 11 years 22 weeks ago
The van der Corput lemma for oscillatory integrals 21/04/2009 - 00:42 11 years 17 weeks ago
The van der Corput lemma for equidistribution 21/04/2009 - 00:32 11 years 17 weeks ago