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Asked by anon-277281 to William on 20 Jan 2021.
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William Smith answered on 20 Jan 2021:
I love this question 🙂
Day to day, I make use of: Matrices, vectors, transformations, projections, Newton’s method, Gauss-Newton, least squares, Normal distribution, Riemannian manifolds, statistics on manifolds, spherical geometry, differential geometry, chain rule, multi variable calculus, statistical models, probabilistic models and much more!
It’s usually gets crazy when I try to solve multivariable calculus by hand on my white board. This means 1. you have lots of values you need to find the best value for, 2. you have a measure of how good your solution is and 3. you know how this measure changes if you change one unknown value. Then you have to try to simultaneously find the best combination of values for the unknowns…
Also, it turns out that there are lots of ways to do a multiplication. You will have only used the standard one in maths so far but there are others such as matrix multiplication, Hadamard product and Kronecker product. Often I use all of these in one equation which makes doing any kind of manipulation crazily complicated!
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Comments
Will commented on :
Mostly I let software do the computations, but I like to try and understand the concepts I’m using anyway. A recent example of this is Bessel functions – something I hadn’t heard of before:
Used in all sorts of wave examples, but here it was used to predict heat loss.
Will commented on :
Link was missing – should be “https://en.wikipedia.org/wiki/Bessel_function”
Amy commented on :
Wow Will, you do use a lot of maths. I do adding, subtracting, multiplication and division. Sometimes I rearrange equations!