/sci/ - Science & Math

Need recommendations for further self study. Currently pursuing a math major at undergrad. I really love analysis, linear algebra, and differential equations. Functional analysis seems quite interesting, but the textbooks I've been looking at use a lot of topological vocabulary. One of my TAs told me that topology is "the most general mathematics." Is topology the logical next step after a thorough education in analysis? Do I need to familiarize myself with concepts from multivariable analysis before studying topology?

The motivation for this self study is that I would like to be able to convince myself of the concepts I've been told to take on faith in my differential equations course (uniqueness of the inverse laplace transform up to finite discontinuities, fourier convergence, etc)

For reference, I enjoyed studying picrel