Lectures related to Local Degrees: Calculating Maps

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.

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

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

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

Introduces hypergraphs, generalizing graphs by allowing subsets of nodes to form edges and exploring their applications in various fields.

Covers the concept of degree in homotopy theory and the structure of complexes with two simplices.

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

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.

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

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

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

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Explores the properties and applications of finite fields, including isomorphism and cyclic properties.

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

Covers graphical models for probabilistic distributions using graphs, nodes, and edges.

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

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

Covers the concept of orientation and degrees in topology, focusing on assigning orientations to manifolds.