I came from a Chemical Engineering and Math degree, but ended up teaching myself programming while I was in university. I saw my freshman year roommate getting offered more for an internship than chemical engineers were making after they graduated and put 2 and 2 together.
I think there is a huge benefit to having had some sort of extremely rigorous quantitative background. When I talk with people who are self taught who haven't come from a hard (where that is an extremely hand wavey concept) can get started in engineering and often can be productive, but really struggle when things break or get difficult. There's a sharpening of the mind that comes with extreme analytic rigour, and I think that's more important than whether you get it in a real analysis class or in a CS class.
I think there is a huge benefit to having had some sort of extremely rigorous quantitative background. When I talk with people who are self taught who haven't come from a hard (where that is an extremely hand wavey concept) can get started in engineering and often can be productive, but really struggle when things break or get difficult. There's a sharpening of the mind that comes with extreme analytic rigour, and I think that's more important than whether you get it in a real analysis class or in a CS class.