I studied mathematics as an undergraduate and found that these topics aren't covered in pure math classes typically until students are sufficiently experienced that they can grasp the fully technical definitions.

It's more common for CS courses rather than math courses to rush the definition of Big O out the door to students who will struggle to understand the formal definition.

Likely because the author is a math professor and those concepts are typically only covered in CS department courses.

This isn't true, bounding functions are really useful for many proofs. But see nilkn's response.