Implicit Functions: Introduction and Examples

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Introduces the basics of group theory, defining groups, categories, and groupoids.

Explores the arithmetic of direct sum of abelian groups and the process of turning a monoid into a commutative group.

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.

Covers cyclically monotone sets in optimal transport theory and their properties.

Delves into Fourier series theory, computation, and comparison with functions using the Dirichlet theorem.

Covers exact sequences, torsion, divisibility, and operations on abelian groups.

Covers group quotient, group actions, and functors connecting sets and G-sets.

Explores sequences, integrals, symmetrical functions, differential equations, and the Cauchy problem in advanced analysis.

Covers the analysis and properties of Linear Time-Invariant (LTI) systems.

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