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Lecture
Polynomials and Endomorphisms
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Linear Algebra: Abstract Concepts
Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.
Operations in Z
Covers addition properties and operations in the set of integers Z.
System Composition
Explains how systems are composed in parallel or series.
Convolution: Properties and Applications
Covers the concept of convolution and its properties in signal processing.
Linear Combinations and Vector Spaces
Introduces linear combinations in vector spaces, operations, and polynomials of degree 2.
Complex Roots and Polynomials
Explores complex roots, polynomials, and factorizations, including roots of unity and the fundamental theorem of algebra.
Polynomials on a Field: Properties and Applications
Explores the properties and applications of polynomials on a field, including formal derivation and uniqueness.
Cohomology Real Projective Space
Covers cohomology in real projective spaces, focusing on associative properties and algebraic structures.
Elliptic Curves: Group Structure and Isomorphism
Explores the group structure and isomorphism of elliptic curves, including inverses, associativity, and compactification to the torus.
Properties of Rational Multiplication
Covers the properties of rational multiplication through fractions and simple calculations, leading to the resolution of division problems.