Abel's Theorem in Problems and Solutions
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Vladimir Arnold famously taught a proof of the insolubility of the Quintic to Moscow Highschool students in the 1960s using a concrete, low-prerequisite approach. His lectures were turned into a book Abel’s Theorem in Problems and Solutions by V.B. Alekseev which is available online here: https://webhomes.maths.ed.ac.uk/~v1ranick/papers/abel.pdf. He doesn't consider Galois theory in full generality, but instead gives a more concrete topological/geometric…
on “There is No Quintic Formula [video]” ↗Is there any Category Theory tutorial that illustates that we need this apparatus to solve some real problem? For example, for Group Theory there is an excellent book 'Abel's theorem in problems and solutions' that does exactly that.
on “From Sets to Categories (2023)” ↗This was published as: Abel's Theorem in Problems and Solutions by VB Alekseev if you are interested in taking a look. https://link.springer.com/book/10.1007/1-4020-2187-9
on “The Quintic, the Icosahedron, and Elliptic Curves [pdf]” ↗