With that title and reception I can imagine people bookmarking this for „later“ and feeling good about it. But who reads that stuff really?
To each their own, but 700+ pages for material that is done in my experience in the first 2-3 weeks of undergraduate math is more disheartening than empowering for a student, in my opinion.
If you can open a math book anywhere in the last 20% of pages and just start reading, you are looking at pop science and not lecture notes.
If you are interested in this kind of role, it is usually called Executive Assistant in the corporate world. Had the fortune to support my CEO and attend e.g. all board meetings (because I did the minutes). This is at a >10$ bn revenue established company. Very rewarding, but experience depends very much on the style of your boss.
A map between algebraic curves is defined by polynomials. That the map is defined over K means you can find a coordinate system such that the equations of the curves and the equations of the morphisms have coefficients in K and not some larger ring, eg the complex numbers or a large extension field of F_p(field of p elements)
Good question, no there is no difference for elliptic curves, which you can think of as 1-dimensional geometric objects (curves) which posses group structure. A good map in this category should respect the geometry (be a so called rational map, ie defined by polynomials in a suitable coordinate system) and the group structure. Interestingly all these maps are either constant (map everything to 0) or surjective.
For higher dimensional geometric groups (abelian surfaces etc) one usually wants to make a distinction and calls the surjective homomorphisms with finite preimage isogenies.
To each their own, but 700+ pages for material that is done in my experience in the first 2-3 weeks of undergraduate math is more disheartening than empowering for a student, in my opinion.
If you can open a math book anywhere in the last 20% of pages and just start reading, you are looking at pop science and not lecture notes.