>>12728549>/g/entooman here , i m tired of being a math brainlet and i want to dedicate my free time to become an autistic math genius .>learning isn't hard so please recommend me some good booksHigh School:
• Euclidean geometry, complex numbers, scalar multiplication, Cauchy-Bunyakovskii inequality. Introduction to quantum mechanics (Kostrikin-Manin). Groups of transformations of a plane and space. Derivation of trigonometric identities. Geometry on the upper half-plane (Lobachevsky). Properties of inversion. The action of fractional-linear transformations.
• Rings, fields. Linear algebra, finite groups, Galois theory. Proof of Abel's theorem. Basis, rank, determinants, classical Lie groups. Dedekind cuts. Construction of real and complex numbers. Definition of the tensor product of vector spaces.
• Set theory. Zorn's lemma. Completely ordered sets. Cauchy-Hamel basis. Cantor-Bernstein theorem.
• Metric spaces. Set-theoretic topology (definition of continuous mappings, compactness, proper mappings). Definition of compactness in terms of convergent sequences for spaces with a countable base. Homotopy, fundamental group, homotopy equivalence.
• p-adic numbers, Ostrovsky's theorem, multiplication and division of p-adic numbers by hand.
• Differentiation, integration, Newton-Leibniz formula. Delta-epsilon formalism.
