Computer science majors study how data is processed, stored, and communicated. They learn how to create software that allows computers and machines to run more efficiently, process more data, do more tasks, and otherwise be more useful for either business or commercial users. A computer science major might study algorithms, statistical modeling, programming languages, and app development.
Computer engineering majors bring computer science and electrical engineering together. While computer engineering students also learn how to create and work with software, the focus of computer engineering programs is hardware -- designing and building new chips and machines and wedding those new systems with functional software.
Like computer scientists, computer engineers can design for either business users or commercial users. A computer engineer might design a new microprocessor or a new supercomputer, and a computer scientist would design the operating systems for both.
It's not quite as simple as "software v. hardware," but that can be a helpful way to remember the core differences between computer science and computer engineering.
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