The US has different courses at different schools. Sometimes with same name but differences in content or prereqs. It would be more meaningful to sketch this tree for a given school. Or do a few schools. That should give you some feel for the general lay of the land.
And I suggest to sketch it yourself, using a course catalog. You'll learn more doing a little work yourself. Also the course catalog will have course descriptions. Useful since same course may have different names at different schools (or visa versa). Not to say it is totally arbitrary of course. You'll see some stereotypical similarities.
Here is an example: https://www.undergradcatalog.registrar.vt.edu/1920/math.html Note that there are some remedial classes at the beginning which have no prereqs.
Also note that it is possible to have a "corequisite", which means that taking the coreq at same time is adequate (before is fine too). Or to have prereqs that are not just math courses (e.g. department chair permission or interview or placement exam or the like). Furthermore, it's less likely with math but certainly common for other departments to have prereqs that are out of department. IOW calculus before physics. Or physics before physical chemistry. Etc.
Here is another example: https://www.usna.edu/Academics/Majors-and-Courses/course-description/SM.php
You can select a few more on your own. Most schools have this stuff open and online nowadays.
Oh...and one more complexity: there are often a couple or more similar courses (e.g. enriched or specialized in some way) on the same content. So for the last link, if you look at SM 465 Advanced DiffyQs, it has a prereq of "(SM212 or SM222) [different versions of ODE courses] and (SM331 or SM331H or SM333). [different versions of real analysis courses]