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 |