I found out I can pick up a second major in math should I elect to take a two semester sequence in abstract algebra. My first major is in chemical engineering. Right now, I plan on taking a two semester sequence in either: 1) probability with measure theory, 2) abstract algebra (Dummit and Foote), or 3) undergrad partial differential equations (Strauss). If I choose abstract algebra, I would be able to pick up a degree in math, without adding a semester. However, abstract algebra seems to be the most useless of the three. Of course, I would have to guess that PDE would be the most useful, but the fact that the undergrad version probably lacks rigor deters me from taking it. Instead, after finishing senior year (in which I would be taking probability with measure theory as well as graduate real analysis), I would self study functional analysis and then PDE, with the more rigorous book by Evans. However, I am not sure if functional analysis, ironically, would then require abstract algebra. If I elect to skip abstract algebra I and II, I will have had no college exposure to algebra other than that contained in the Differential equations/linear algebra introductory combined course. While I like "beautiful math," I am more interested in learning beautiful math that is necessary to rigorously understand math that can be applied to engineering/physics. As an aside, I will have already taken a senior level probability class before graduation, so this could devalue taking the graduate probability class. I am interested in the the measure-theoretic proability because I am under the impression that probability is one of the more useful math classes one could take, and the rigor in measure theory is fundamental to deeply understand statistics (which I could either self study, or learn through a senior level class during senior year); it seems like statistics would have practical benefits in industry or academia and would also help in understanding subjects such as statistical mechanics. Would it be valuable to pick up that second degree in math if I plan to either work as an engineer or go to grad school in engineering? Is a 2-course sequence in abstract algebra necessary for developing a deep understanding of applied math as it relates to engineering/physics? Is abstract algebra useless?