While Computer Science, Computer Engineering, and Software Engineering are similar in many ways, they also have many differences. Computer Science is probably the most theoretical of the three majors that you mentioned, and involves programming, algorithm development and analysis, data structures, math, and possibly physics, in addition to your general education requirements. Computer Engineering is more focused on the hardware side of computers and other devices, and may involve learning how to program, but a good deal of information will probably relate to designing and building computer and other types of hardware.
You will probably also have to take a decent number of math classes, including Calculus, and perhaps physics. You may also have to take some programming classes, as well, in addition to classes possibly on electrical engineering and other hardware related topics. Software Engineering is a major that may be more based on actually developing computer software and programs, so you'll probably have to take classes on programming, algorithm development and analysis, data structures, as well as math, in addition to your general education requirements.
Computer Science and Software Engineering may seem similar, but computer science puts more of an emphasis on the theoretical aspects of computing and programming, and will probably involve a decent amount of math, including Calculus and possibly more advanced math-related topics, as well. If you would like to go to graduate school for Computer Science or Computer Engineering, you would probably want to go with CS or CE, rather than Software Engineering, though SE isn't a bad major, either! In terms of which major will end up getting you the best paying job, all three of these majors can lead to jobs that pay fairly well, such as computer programmers, software architects, computer engineers, IT analysts, etc. I would suggest that you check out the websites of various colleges and universities and see what the requirements are for these three degree programs, in order to get a better idea of what is required of students that are in these majors.
You could also arrange a meeting with an admissions representative or faculty member in one of the departments that you have an interest in, in order to learn more about what the major is actually like. Some schools or professors may even allow you to sit in on a class, if you're interested in doing so. Best of luck and I hope I helped you!
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