>>13825962Oof that's hard. I would say that I have many favorites, but among those favorites, one stands out as the singular most useful. Like it actually blows the others out in terms of use cases and I constantly refer back to the text for my work.
It is pic related. Regression is a fundamental problem in all applied fields. As an an addition, studying interpolation and splining is also beautiful and a very similar problem to regression.
In a linear algebraic sense, regression is when you have more equations than unknowns, interpolation is when you have exactly the same number of equations and unknowns and splining is a special interpolation that allows you to go 'beyond' interpolation and create additional free unknowns for a problem (i.e. an infinite number of solutions). These all have numerous use cases and ramifications across fields and disciplines and are essentially the best tools we have for solving problems numerically.
The problems are beautiful and the methods are exact (if based around polynomials). Regression is the backbone of every scientific discovery ever, the interpolating spline is the best method we have for solving PDEs (it is finite element analysis), and the beyond interpolating spline (with additional unknowns) has ramifications in neural networks (it's essentially why the Double Descent phenomenon exists).
