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We have also covered two other forms of calculus over the the last week: Alien calculus [0][1] Matrix Calculus [2][3] Might as well throw in some other gene

We have also covered two other forms of calculus over the the last week: Alien calculus [0][1] Matrix Calculus [2][3] Might as well throw in some other generalizations of the derivative [4] , it is amazing how these concepts apply to all sorts of mathematical structures once you generalize them, whlie you are probably fairly interested in math if you are reading the comments here, but on the offi chance you have not done so, look up measure theory, it is a fun concept that allows you to generalize the integral in neat ways that you'll notice has a lot of application to computer science especially vision related applications. [0] https://news.ycombinator.com/item?id=35476236 https://news.ycombinator.com/item?id=35476236 [1] https://www.quantamagazine.org/alien-calculus-could-save-particle-physics-from-infinities-20230406/ https://www.quantamagazine.org/alien-calculus-could-save-par... [2] https://news.ycombinator.com/item?id=35568311 https://news.ycombinator.com/item?id=35568311 [3] https://www.matrixcalculus.org/ https://www.matrixcalculus.org/ [4] https://math.stackexchange.com/a/1209684 https://math.stackexchange.com/a/1209684

quickthrower2 4y ago
Of course LLMs probably have sparked an interest in calculus. I have dusted of decades old knowledge, relearning the difference between a d and a δ, or what is df/dx ln(x).
- JadeNB 4y ago
  > what is df/dx ln(x). Since this may be a misunderstanding, and it's very common among my students, let me suggest that you almost certainly mean df/dx, where f(x) = ln(x); or d(ln(x))/dx; or (d/dx)(ln(x)). All of these indicate taking the derivative of ln(x) with respect to x (which is 1/x). df/dx ln(x) would be the product of the derivative of some unspecified function f with ln(x).
  - quickthrower2 4y ago
    Yes sorry I was being a bit lazy there
iamwil 4y ago
Is there a calculus for sets or multi sets?
- gylterud 4y ago
  There is the theory of containers (unrelated to the docker kind). They represent functors on sets and the differential operator on them satisfies the usual laws. In short a container is a set of shapes and a set of positions for data in each shape. The derivative of a container is the container you get by removing one position in each shape. An example of a container is the list container, which maps any set to the sets of lists of elements from the set. The derivative of the list is the pair of lists. As for multisets, the bag functor is better defined on groupoids than sets. But there is a generalised notion of container for groupoids, with a similar calculus. The bag functor is special because it is its own derivative, just like the exponential function.
  - iamwil 4y ago
    What do I look up to learn more? Are there online lectures or papers to get an intro on the topic?

quickthrower2 4y ago

Of course LLMs probably have sparked an interest in calculus. I have dusted of decades old knowledge, relearning the difference between a d and a δ, or what is df/dx ln(x).

JadeNB 4y ago
> what is df/dx ln(x). Since this may be a misunderstanding, and it's very common among my students, let me suggest that you almost certainly mean df/dx, where f(x) = ln(x); or d(ln(x))/dx; or (d/dx)(ln(x)). All of these indicate taking the derivative of ln(x) with respect to x (which is 1/x). df/dx ln(x) would be the product of the derivative of some unspecified function f with ln(x).
- quickthrower2 4y ago
  Yes sorry I was being a bit lazy there

iamwil 4y ago

Is there a calculus for sets or multi sets?

gylterud 4y ago
There is the theory of containers (unrelated to the docker kind). They represent functors on sets and the differential operator on them satisfies the usual laws. In short a container is a set of shapes and a set of positions for data in each shape. The derivative of a container is the container you get by removing one position in each shape. An example of a container is the list container, which maps any set to the sets of lists of elements from the set. The derivative of the list is the pair of lists. As for multisets, the bag functor is better defined on groupoids than sets. But there is a generalised notion of container for groupoids, with a similar calculus. The bag functor is special because it is its own derivative, just like the exponential function.
- iamwil 4y ago
  What do I look up to learn more? Are there online lectures or papers to get an intro on the topic?