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I am relatively new to the world of academical mathematics, but I have noticed that most, if not all, mathematical textbooks that I've had the chance to come across, seem completely oblivious to the existence of lambda notation.

More specifically, in a linear algebra course I'm taking, I found it a lot easier to understand "higher order functionals" from the second dual space, by putting them in lambda expressions. It makes a lot more sense to me to put them in the neat, clear notation of lambda expressions, rather than in multiple variable functions where not all the arguments are of the same "class" as some are linear functionals and others are vectors. For example, consider the canonical isomorphism - $$A:V \rightarrow V^{**}$$

It would usually be expressed by $$Av(f) = f(v)$$ This was a notation I found particularly difficult to understand at first as there are several processes taking place "under the hood", that can be put a lot more clearly, in my opinion, this way:

$$A = \lambda v \in V. \lambda f \in V^{*}. f(v)$$

I agree that this notation may become tedious and over-explanatory over time, but as a first introduction of the concept I find it a lot easier as it makes it very clear what goes where.

My question is, basically, why isn't this widespread, super popular notation in the world of computer science, not as popular in the field of mathematics? Or is it, and I'm just not aware?