Lectures related to Implicit Functions Theorem

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Covers the joint equidistribution of CM points in algebraic structures and quadratic forms.

Covers the (log n) approximation algorithm for the sparsest cut problem, presenting the mathematical theorems and proofs.

Explores Taylor's formula, uniqueness of Taylor series, Mean Value Theorem, inflection points, and convexity.

Covers the application of Cauchy equations and integral decomposition, addressing questions related to holomorphic functions and Jacobian matrices.

Covers indeterminate forms, logarithmic functions, and the 'role of the gendarmes' theorem.

Explores the applications of Green's Theorem in 2D, emphasizing the importance of regular domains for successful integration.

Explores the Cauchy-Lipschitz theorem for differential equations and its proof.

Covers the Stokes theorem, extending the Green theorem to surfaces in R3 and explaining its application.

Explores the Intermediate Values Theorem for continuous functions on closed intervals.

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Explores the application of the Gauss/Green theorem to calculate curve integrals along simple closed curves.

Explores closed curves in topological spaces, emphasizing their properties and significance in mathematics.

Covers the basics of formal logic, focusing on logical expressions and mathematical proofs.

Explores elastic and inelastic collisions, kinetic energy conservation, and work principles with practical examples.

Covers the Fourier inversion formula, exploring its mathematical concepts and applications, emphasizing the importance of understanding the sign.

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Covers the basics of Coq, focusing on arithmetic expressions, evaluation, and proof techniques.