You're describing software engineering, not computer science.
CS is big-O, Chomsky hierarchy, finite automata, type theory, and computability classes. It's the study of algorithms & data structures, not their implementations. In other words, CS is a branch of math.
Theoretical computer science is a division or subset of general computer science and mathematics that focuses on more abstract or mathematical aspects of computing and includes the theory of computation.
CS is big-O, Chomsky hierarchy, finite automata, type theory, and computability classes. It's the study of algorithms & data structures, not their implementations. In other words, CS is a branch of math.