As a PhD econ student, the mathematics just comes down solving constrained optimization problems. Figuring out what to consider as an optimand and the associated constraints is the real kicker.
It depends on what you’re doing. That is accurate for, say, describing the training of a neural network, but if you want to prove something about generalization, for example (which the book at least touches on from my skimming), you’ll need other techniques as well
Most economists (who write these sort of textbooks) have some sort of math background. The push to find the most general "math" setting has been an ongoing topic since the 50's and so you can probably find what you are looking for. It's not part of undergraduate textbooks since adding generality gives better proofs but often adds "not that much" to insight.
Nevertheless, the standard micro/macro models are just applications of optimization theory (lattice theory typically for micro, dynamical systems for macro). Game theory (especially mechanism design) is a bit of different topic, but I suppose that's not what you are looking for.
E.g., micro models are just constrained optimization based on the idea of representing preference relations over abstract sets with continuous functions. So obviously, the math is then very simple. This is considered a feature. You can also use more complex math, which helps with certain proofs (especially existence and representation).
You could grab some higher level math for econ textbooks, which typically include the models as examples, where you skip over the math.
For example, for micro, you can get the following:
https://press.princeton.edu/books/hardcover/9780691118673/an...
I think it treats the typical micro model (up to oligopoly models) via the first 50 or so pages while explaining set theory, lattices, monotone comparative statics with Tarski/Topkis etc.
