So I've delved into programming, and gotten experienced with the fundamentals. However, the more I learn, the more I question the central object of comp. science, computation, and its foundation. According to Wikipedia, "Computation is any type of calculation that follows a well-defined model understood and expressed as, for example, an algorithm." This is well enough, but I am interested in the concept of the mathematical function and its relation to computation. During the incipient phase of computer science, Turing and many others seemed to characterize computability in terms of functions. For example, the Church-Turing thesis is stated as saying that there is no effective model of computing that can compute more mathematical functions than a Turing machine. This seems to imply that all computations involve the mathematical idea of functions (perhaps this is due to that computing involves algorithms, and functions can effectively model algorithms). Essentially, my question is, is the notion of computation wholly related to functions? Are the two terms somehow synonymously related?