The reason a university level computer science degree include all the science courses is not just to learn the science of how computers work, but to get a well rounded education in the sciences because many careers in programming are in the sciences. Chemists, physicists, biologists, etc. all use programs to help them in their field of study.

I see a wide divide between "programming" and "software engineering." The former doesn't necessarily include as much creativity and problem solving as the latter.

Choose your path wisely, and be sure to include enjoyment.