- https://oeis.org/ - The On-Line Encyclopedia of Integer Sequences. If you are ever dealing with a sequence of numbers and wondering if there's an underlying structure, this is a great place to start.
- http://ergodic.ugr.es/cphys/LECCIONES/FORTRAN/power_method.pdf - Power method for approximating eigenvalues.
- https://en.wikipedia.org/wiki/List_of_paradoxes - List of paradoxes
- https://en.wikipedia.org/wiki/Potato_paradox - potato paradox
This applies when profiling code. If you have a hotspot that takes 99% of the time and optimize it until your whole program is twice as fast, now that hotspot takes 98% of the time.
- https://en.wikipedia.org/wiki/False_positive_paradox - False positive paradox
- An easier approach to partial fractions decomposition - https://jaydaigle.net/blog/calculus/easier-partial-fractions/ . See the comments also.
- https://en.wikipedia.org/wiki/Horner%27s_method - Useful to divide a polynomial by a monomial
- https://en.wikipedia.org/wiki/Newton%27s_identities#Formulation_in_terms_of_symmetric_polynomials - Useful in solving problems such as https://stackoverflow.com/questions/3492302/easy-interview-question-got-harder-given-numbers-1-100-find-the-missing-numbe?rq=1
The definition of the likelihood function for continuous case:
The left term means “the likelihood of the parameters , given data ”.
Here the notation does not mean the same as the conditional notation. Another representation of the likelihood that is often used is , which is better in the sense that it makes it clear that it’s not a conditional, however, it makes it look like the likelihood is a function of the data and not of the parameters.
average of squares > square of averages
ex:- for [3,4]
average of squares = (3**2 + 4**2) / 2 = 12.5
square of averages = ((3 + 4)/2)**2 = 3.5**2 = 12.25
simplifications I came across
- https://www.youtube.com/watch?v=n2y7n6jw5d0 - A visual explanation of the Laplace Transform and its applications.
- https://www.youtube.com/watch?v=hqOboV2jgVo - shows that the Laplace transform is just a continuous analogue of the summation of a power series.
convert from miles to km
Double four times and divide by ten as soon as possible (i.e. the first time you see a zero on the end, drop it). This amounts to multiplying it by 1.6. Actual formula is 1 mi = 1.60934 km.
Ex:- 30 mph -> 3 (drop the zero) -> 6 -> 12 -> 24 -> 48 kmph.
No need to count how many times you are doubling. Look for something between 1x and 2x of the original number.
Ex:- 135 mph -> 270 -> 27 -> 54 -> 108 (keep going, less than 135) -> 216 kmph (stop here, less than 2* 135 = 270)
pounds to kilos
Divide by 2, less 10%. This amounts to multiplying it by 0.45. Actual formula is 1 lb = 0.453592 kg
Ex:- 160 lbs = 80 - 8 = 72 kg
kilos to pounds
Multiple by 2, add 10%. This amounts to multiplying it by 2.2. Actual formula is 1 kg = 2.20462 lbs