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Related lectures (30)

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Tangent vectors without embedding space: Making tangent spaces linear

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.

Linear Applications: Matrices and Transformations

Covers linear applications, matrices, injectivity, surjectivity, and matrix multiplication properties.

Algebraic Curves: Normalization

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

Group Morphisms: Injectivity and Conjugation

Explores group morphisms, injectivity criteria, and conjugation concepts within groups.

Linear Algebra: Rank Theorem

Covers the Rank Theorem in linear algebra, focusing on vector spaces and linear applications.

Real Functions: Definitions and Properties

Explores real functions, covering parity, periodicity, and polynomial functions.

Isometries: Transformations Preserving Distances in the Plane

Introduces isometries as transformations preserving distances in the plane, focusing on symmetry and geometric relationships.

Coordinate Application: Components and Bases

Covers components and bases in vector spaces, demonstrating linearity and injectivity.

Injective Morphisms in Mathematics

Introduces injective morphisms and vector spaces with examples and verification methods.

Sets and Functions

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