Explores making tangent spaces linear, defining tangent vectors without an embedding space and their operations, as well as the equivalence of different tangent space notions.

Isomorphism of Groups

Covers bijections between automorphisms and equivariant bijections in group isomorphisms.

Algebraic Curves: Normalization

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Sets and Functions

Introduces sets, functions, and their properties, including injective and surjective functions, composition, and inverse functions.

Linear Algebra: Main Theorem and Injectivity

Covers the main theorem of linear algebra and the conditions for injectivity.