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.
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.