Concept

Academic degree

Related lectures (30)

Homotopy: Degree

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

Orientation and degrees

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

Topology of Riemann Surfaces

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

Local Degrees: Calculating Maps

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

Acyclic Models: Cup Product and Cohomology

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

Directed Networks & Hypergraphs

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

Fixed points of the Ruelle-Thurston operator

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

Equations: Degree and Solutions

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

Polynomials, Division, and Ideals

Explores polynomials, their operations, and the concept of ideals in polynomial rings.

Polynomials on a Field: Basics and Operations

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

EPFL Graduation Ceremony 2014

Showcases the EPFL graduation ceremony of 2014, celebrating achievements, innovation, and the evolving education landscape.

Elliptic Curves: Theory and Applications

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

Important Examples: Operations and Multiplication

Covers important examples related to operations and multiplication in real vector spaces.

Projective Plane Curves

Introduces projective plane curves, degrees, components, multiplicities, intersection numbers, tangents, and multiple points, culminating in the statement of Bézout's theorem and its consequences.

Differential Forms Integration

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

Angles: Degrees and Triangle Sum

Introduces measuring angles in degrees and radians, the sum of angles in a triangle, and angle properties.

The Degree of a Covering Space

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

EDIC Open House 2023

Introduces the EDIC Open House 2023 and Parallel track number 1, featuring newly appointed IC faculty members and their labs.

Analyse 2: Division euclidienne

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

Irreducible Polynomials: Degree and Roots

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