Has this been updated since 1977? Because the field and tools and even the view points have changed a ton.
The original posting is about new tools and algorithms, with some more analysis. Well beyond my background from undergrad courses in LP and OR, but probably more relevant and insightful to you.
For example all of the "hard" leetcode problems can be casted as math programming ones. But the interviewers will not appreciate this solution approach lol.
Once you conquer the logic/language then learning the tools is the easy part.
I once witnessed a programmer with a PhD in Maths find closed form formulas for a lot of questions where it was expected to write some code with loops building/accumulating a result. As a simple example, to explain what was going on, if the question would be "calculate the 100th fibonacci number", she would just use Binet's formula to do so (as opposed to using a loop). I was rather impressed how often that happened.
The astonishment doesn't get less, but it shifts from Binet's single formula to the exponential map, and maybe the fundamental theorem of algebra (or generalisations).
For evaluating the Fibonacci numbers (as with any other integer linear recurrence), I'd generally prefer the matrix-exponentiation-by-squaring approach, or one of the simplified formulas based on it. Those don't need anything more complicated than bigint multiplication. [And from there, taking the ratio between two values gives you a quick way to approximate the golden ratio!]
If you want to beat the O(n^2) runtime of the trivial iteration, you pretty much have to use Newton's method for φ, exponentiation by squaring on the matrix form, or another method with faster-than-linear convergence.
If they’re writing a compartmentalized library specific to their domain, it’s fine. I’ve worked with a Stats PhD doing that.
If you’re dropping them into a shared codebase, the comprehensibility of their code to the other people on their team is essential. Great code that depends on knowledge no one else on the team has is not great. You end up with “That’s going to take forever to change, Steve wrote it”.
„Learning how to formulate problems as integer/linear programming ones“, as another commenter put it, works great if it‘s a natural fit and sure is fun for idk 7th grade math text problems I guess but OTOH squeezing realistic problems into systems of hundreds of equations (or more if dealing with linearizations of inherently non-linear/concave/multi-step problems) to satisfy tool idiosyncracies calls for additional tools in your arsenal.