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I think it is a matter of perspective. The book covers stuff you learn in the first two semesters when studying maths. So for someone who studied maths (probably the author) these are the basics.

You were learning spectral theorem applications in the second semester of math?

I learned the spectral theorem with a couple applications in the first semester of my electrical engineering graduate studies. First year graduate material is commonly called basics in my experience. Compared to the state of the art, it is. Compared to what an undergraduate freshman knows, not so much.

Right, it's material I covered in my senior year of undergrad taking hpc grad courses. If it were covered anywhere in the second semester of undergrad I would be shocked.

This is more like the first two years of mathematics course in the French Preparatory Classes for Great engineering schools Program.

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