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Napkin Folding — mathematics

How can I use non-constructive proofs in data analysis?

Posted by Cameron Davidson-Pilon at

In mathematics, there are two classes of proof techniques: constructive and non-constructive. Constructive proofs will demonstrate how to build the object required. Its construction proves its existence, hence you are done. An example of this is proving that prime numbers are infinite using Euclid's argument: to find a prime number, you multiply together all the prime numbers seen thus far and add 1.  On the other hand, a non-constructive proof does not detail how to build the object, just states that it must...

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Evolutionary Group Theory - or what happens when algebraic groups have sex.

Posted by Cameron Davidson-Pilon at

And now for something totally different. This is not data related. It's a paper I wrote about an intersection between group theory and evolutionary dynamics. Basically, what happens when groups have sex. Interested? Read on!   TLDR: You can find analogous group theory axioms in dynamical systems. Population Dynamics of Algebraic Groups We construct a dynamical population whose individuals are assigned elements from an algebraic group \(G\) and subject them to sexual reproduction. We investigate the relationship between the dynamical...

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