I'm a math major who has recently graduated and I will be starting full time work in 'data analysis'.
Having finished with decent marks and still being incredibly interested in mathematics, I was thinking of pursuing graduate study/research at some point in the future. I was reading up about possible areas of study for this when I came across topological data analysis, which (as I understand it) is an application of algebraic topology to data analysis.
Given my situation, I was intrigued by the concept and I would like to do some self study so I can have a working understanding of the subject. I have only done basic undergraduate abstract algebra, analysis and point set topology, and I am currently reading Munkres' Topology (Chapter 9 onwards). How do I get from where I am now to understanding the theory behind TDA and being able to apply it?
My knowledge on further mathematics is far from extensive and I would appreciate any advice on links/texts which I could use to learn the relevant material.