Projective Geometry: Tangent Lines

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Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.

Covers the definitions and properties of projective algebraic sets and their applications in algebraic geometry.

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Covers modern algebraic geometry, including algebraic sets, morphisms, and projective algebraic sets.

Explores Bézout's theorem and Cayley-Bacharach, discussing intersection multiplicities and linear combinations in projective geometry.

Explores the applications of Serre duality in Enriques-Severi-Zariski lemma, foliations, and Riemann-Roch theorem.

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

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

Explores the Isoclines Method and solutions of differential equations with tangents.

Explains tangent vectors of curves and the construction and applications of Bézier curves in computer graphics.