Proof Techniques: Direct, Contraposition, Cases

Related lectures (27)

Page 2 of 3

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

Explores the composition of applications in mathematics and the importance of understanding their properties.

Explores optimal transport in heat equations and metric spaces.

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

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

Covers the long exact sequence of relative homology groups and chain complexes.

Explores the concept of universal coating through detailed proofs and examples, emphasizing uniqueness and significance.

Explores the proof of measure concentration using Laplace transform methods and demonstrates its application through examples and propositions.

Explores differentiating under the integral sign and continuity of functions in integrals.

Explores Newtonian potential in bounded domains, discussing its conditions and properties.