A strong background in multivariable calculus, ordinary differential equations, linear algebra, and complex variables is deemed sufficient for learning advanced topics like functional analysis and Hamiltonian dynamics. Recommended resources include Gelfand and Fomin's "Calculus of Variations" and Weinstock's text on applications to physics and engineering. Real analysis is considered essential for effectively engaging with these subjects, as is familiarity with numerical analysis techniques. For those interested in the physics perspective, upper-level classical mechanics books are suggested for a more intuitive understanding. Overall, a solid mathematical foundation will facilitate the study of these complex topics.