Elliptic Curves: Theory and Applications

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Related lectures (32)

Page 3 of 4

Covers the definition and operations of polynomials, including addition and multiplication, degree, coefficients, and their role in algebraic systems.

Bar Construction: Homology Groups and Classifying Space

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

Error Analysis and Interpolation

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

Curves in Space: Parametric Equations and Surfaces

Covers the equations for curves and surfaces in space, including parametric and particular surfaces.

Numerical integration: continued

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

Acyclic Models: Cup Product and Cohomology

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

Analyse 2: Division euclidienne

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

Curvature and Osculating Circle

Covers curvature, osculating circles, and the evolute of plane curves, with examples and equations.

Elliptic Curves and Lattices

Explores Elliptic Curve Discrete Logarithm Problem, lattice-based cryptography, and cryptographic schemes like ECDSA.

Curves and Surfaces

Covers the representation of plane curves and the nature of obtained curves.