Modern Algebraic GeometryCovers modern algebraic geometry, including algebraic sets, morphisms, and projective algebraic sets.
Affine VarietiesIntroduces affine varieties and covers morphisms between them and their coordinate rings.
Compact Manifolds ClassificationCovers the classification of compact p-adic manifolds using the C.o.V-formula and explores smooth algebraic varieties and Hensel's lemma.
Dimension of Algebraic VarietyExplores the dimension of algebraic varieties, including the (Krull)-dimension of rings and computing dimensions using tools from commutative algebra.
Tangent Spaces InsightsExplores the relationships between tangent spaces, dimensions, and sub-varieties in algebraic geometry.
Signal RepresentationsCovers matrix operations, Fourier transformations, Gaussian models, and signal representations using algebraic methods.
