Lectures related to Digital Integration: Accuracy and Formulas

Explores linear dependence of vectors, demonstrating examples and conditions for collinearity.

Introduces vector definitions, displacement, addition, and applications in geometry.

Covers orthogonal projections, rectors, norms, and geometric observations in vector spaces.

Introduces the basics of analytical geometry, emphasizing vector representation, operations, and applications in geometry.

Covers coordinates, midpoints, and abscissa in analytical geometry, providing practical problem-solving examples.

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 concept of symmetry in parallelograms and the properties of their diagonals.

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

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

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.

Explores vector equations, observation points, and normal equations in a plane.

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

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.

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

Explores the process of division euclidienne in polynomials, emphasizing the importance of polynomial degrees during operations.