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Gödel's incompleteness theorems
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Cauchy Equations and Integral Decomposition
Covers the application of Cauchy equations and integral decomposition, addressing questions related to holomorphic functions and Jacobian matrices.
Intermediate Values Theorem
Explores the Intermediate Values Theorem for continuous functions on closed intervals.
Optimal Transport: Theory and Applications
Explores the theory of optimal transport, focusing on Lipschitz functions and uniqueness of solutions.
Equidistribution of CM Points
Covers the joint equidistribution of CM points in algebraic structures and quadratic forms.
Hitting Probabilities: Markov Chains
Covers hitting probabilities in Markov chains with disjoint subsets, the function h(i), theorems, proofs, and expected time to hit calculations.
Chain Rules: Higher Dimensional Versions
Explores the chain rule for compositions of differential functions in higher dimensions, emphasizing gradients and directional changes.
Derivatives and Limits: Generalization and Indeterminacy
Covers the generalization of the TAF theorem, lateral derivatives, limits of derivatives, and indeterminacy.
Maximum and Minimum Values: Theorems and Continuity
Explores the theorems on maximum and minimum values of functions and their relation to continuity.
Approximation in Sobolev Spaces
Covers the approximation of functions in Sobolev spaces using smooth functions.
Green's Theorem in 2D: Applications
Explores the applications of Green's Theorem in 2D, emphasizing the importance of regular domains for successful integration.