Functional Analysis I: November 18, 2021

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

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

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

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

Explores linear similarities and similitudes, demonstrating their properties and applications in geometry.