Tangent Spaces in Algebraic Geometry

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Tangent to Graph of a Function

Explores finding the equation of the tangent line to a function's graph at a point.

Derivability Conditions

Explores conditions for non-differentiability in multivariable calculus and the implications of the differentiability theorem.

Ideals and Representations

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Variety Defined as the Closure of VCA

Explores the concept of variety defined as the closure of VCA and its applications in algebraic geometry.

Adjunctions and Applications

Covers adjunctions, projective varieties, regularity, and valuative criteria in algebraic geometry.

Dimension Theory of Rings

Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.

Dedekind Rings and Fractional Ideals

Explores Dedekind rings, fractional ideals, integrally closed properties, prime ideal factorization, and the structure of fractional ideals as a commutative group.

Differentiability of Functions of Several Variables

Covers the differentiability of functions of multiple variables and the significance of directional derivatives and gradients.

Differential of a Morphism

Introduces the concept of the differential of a morphism and its applications in algebraic treatments.

Lie Algebras: Introduction and Structure

Introduces Lie algebras, vector spaces with a special bracket operation.