What about the 'nuts and bolts' of integration, differentiation, etc. Why is linear algebra covered but no calculus? Even if calculus is covered in real analysis, I think calc needs its own course, and is the most important one by far as a building block before you dive into the other stuff. Otherwise, you will be stuck and not knowing any of the notation. No mention of partial differential equations either, which is also very important. You need to learn how to master change of variables and substitution--those come up constantly in advanced concepts.
Linear Algebra courses in pure math degrees are typically used as a gentle introduction to theoretical math, different from the applied linear algebra courses that engineers and the likes would take.
Just based on my experience with UCLA's pure math undergraduate program (which I assume is similar to other top tier math departments), the listed subjects in the video cover the "core/required" courses of a solid pure math degree. PDE's and differential equations in general are optional electives (edit: usually taken by the applied variants of math degrees).
It should also be noted that calculus is a pre-req for even declaring the major, and hope the video should list that as a pre-req for self-study as pure math.
