Lectures related to Homotopy: Degree

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Covers the bar construction method, homology groups, classifying space, and the Hopf formula.

Covers the cup product on cohomology, acyclic models, and the universal coefficient theorem.

Explores directed networks with asymmetric relationships and hypergraphs that generalize graphs by allowing edges to connect any subset of nodes.

Explores irreducible polynomials, focusing on their degree and roots in different fields.

Explores the Stein algorithm for polynomial identity testing and the minimization of a cut problem.

Explores the homotopy theory of chain complexes over a field, focusing on closure properties and decomposition.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Covers the theory and applications of elliptic curves in cryptography and number theory.

Covers the fixed points of the Ruelle-Thurston operator and its applications in complex analysis.

Explores polynomial equations, their degree, solutions, and domain definition.

Introduces the basics of polynomials on a field, focusing on definitions, operations, and properties.

Delves into local degrees of continuous maps from the sphere, showcasing their role in calculating map degrees.

Explores infinity category theory, covering ABB, Kao-cosmos, homotopy, categories, and equivalences.

Covers numerical integration methods, focusing on trapezoidal rules, degree of exactness, and error analysis.

Explores the homotopy theory of chain complexes, focusing on model categories, weak equivalences, and the retraction axiom.

Explores error analysis and limitations in interpolation on evenly distributed nodes.

Covers the functional equation of zeta function and Jensen's formula in complex analysis.

Covers the structure of topological spaces with A-complexes and chain complexes.

Shows the equivalence between the index of a covering space's fundamental group and the degree of the covering space.