949 reputation
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visits member for 3 years, 9 months
seen 14 mins ago

Feb
11
awarded  Nice Question
Feb
11
asked Where does the word “torsion” in algebra come from?
Jan
16
answered Applications of category theory and topoi/topos theory in reality
Jul
20
awarded  Yearling
Feb
29
comment Is there an algorithm that can tell whether the power of two rational numbers is rational?
4^0.5 is most certainly rational. But you raise an excellent point. When discussing problems about exact real numbers it's a good idea not to use decimal notation because it suggests you're talking about approximations.
Feb
16
answered How can we find the values that a (divergent!) series tends to?
Feb
15
comment Is learning haskell a bad thing for a beginner mathematician?
It's not quite fair to say that with Haskell you are learning about one specific category. At the core of Haskell is a lambda calculus that is precisely the internal language of cartesian closed categories. Anything you prove about Haskell programs within this core using CCC language will apply to any CCC. More generally, the applicability of what you prove about Haskell programs is a function of the generality of your argument and many proofs about Haskell programs are easy to generalise to various classes of category (eg. by writing them in point free form.)
Nov
17
comment Numerical optimisation in presence of fast algorithm for some axes
That seems pretty nice. It ought to be in the text books. It does look you may need to fully invert C though, which isn't always convenient.
Nov
17
awarded  Scholar
Nov
17
accepted Numerical optimisation in presence of fast algorithm for some axes
Nov
17
comment How to write a functional fold in mathematics?
Any description that mathematicians understand is good enough. But if you really want to go formal, fold can be nicely expressed using the language of category theory. This is what Lambek's lemma is about. See, for example, here: cs.nott.ac.uk/~vxc/mgs/MGS2011_categories.pdf (You need to do a tiny bit of massaging because foldr is more natural for lists than foldl, but it's not a big deal.)
Oct
17
comment Do We Need the Digits of $\pi$?
It's not a good test for randomness tests because we lack a proof that π has the properties we want to test.
Oct
8
comment Seemingly simple system of equations
If you know that 6 is a root then divide x-6 into your cubic (en.wikipedia.org/wiki/Polynomial_long_division) You'll be left with a quadratic that's easy to solve.
Oct
6
awarded  Student
Oct
6
asked Numerical optimisation in presence of fast algorithm for some axes
Jul
21
awarded  Yearling
Jan
18
comment Probability of picking a random natural number
This is more a question for a psychologist than for a mathematician. Humans tend to pick certain numbers more often than other numbers. For example 7, 17, 35 and 37 are quite popular. No amount of mathematics would allow you to predict such a distribution without some facts from psychology. See here for some more details: scienceblogs.com/cognitivedaily/2007/02/…
Jan
18
comment Odds of Winning the Lottery Using the Same Numbers Repeatedly Better/Worse?
@afilbert It's a bad idea to play pet numbers. Pet numbers are numbers that are special to you for some reason. The set of numbers that are special to people is much smaller than the set of all possible numbers. (Eg. people often pick dates which means 19 comes up often in people's pet numbers.) The net effect is that you are more likely to choose the same combination as someone else and have to share the prize. Pick randomly instead. And don't just pick numbers as people often pick the same 'random' numbers (eg. 37 is popular).
Dec
11
awarded  Quorum
Aug
13
awarded  Commentator