Cellular Boundary Formula

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

Explores the homology of Riemann surfaces, including singular homology and the standard n-simplex.

Covers Riemann surfaces as complex manifolds of dimension 1, including transition maps and holomorphic functions.

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

Explores the definition of connections for smooth vector fields on manifolds.

Covers the classification of compact p-adic manifolds using the C.o.V-formula and explores smooth algebraic varieties and Hensel's lemma.

Covers the creation of a study area using ArcGIS for mapping population concentration and public transport in Switzerland.

Covers projects on deciphering handwriting, mapping, and recreating Venice in 3D.

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Explores strategies for sustainable technology use in mapping projects.