Advanced Analysis II: Reciprocal Functions

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Explores iterated integrals, order, domains, and symmetrical roles of variables in 2D space.

Covers graphical models for probabilistic distributions using graphs, nodes, and edges.

Explores automorphisms of graphs, focusing on automorphism groups, Cayley-Abels graphs, and quasi-isometry.

Covers defining topological phases for photonic systems using unitary scattering matrices, transitioning from graphs to networks.

Covers the concept and calculation of directional derivatives in multivariable calculus.

Explores derivatives, tangents, and elementary function rules in general mathematics.

Covers the analysis of temporal summations in bio mechanics.

Covers level curves and graphs of functions in two and three dimensions.

Explains injective, surjective, and bijective functions using examples and graphs.

Covers the concept of renormalization in Algebraic Quantum Field Theory.