Mathematical proof

Related lectures (30)

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

Introduces Coq, covering defining propositions, proving theorems, and using tactics.

Covers the rigorous proof of differential equations, emphasizing accuracy and precision.

Introduces Cartesian product and induction for proofs using integers and sets.

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

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Explores optimal transport in heat equations and metric spaces.

Covers the Zig Zag Lemma and the long exact sequence of relative homology.

Covers the concept of compression and distance boards.

Explores tail bounds, information bounds, and maximal leakage in the context of generalization error.

Covers examples of direct and indirect proofs in mathematics.

Covers proof techniques including direct proof, contraposition, contradiction, cases, and counterexample.

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

Explores the proof of the Central Limit Theorem through Lindeberg's principle and the convergence of random variables.

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.

Covers the concept of outer measure and properties of measurable sets.

Explores distribution and interpolation spaces, showcasing their importance in mathematical analysis and the computations involved.

Introduces modular arithmetic, its properties, and applications in cryptography and coding theory.

Covers the approximation of functions in Sobolev spaces using smooth functions.

Explores convergence in law for random variables, including Kolmogorov's theorem and proofs based on probability lemmas.

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