“Recommended mathematical topics for computer science majors”

Abstract

Although there is not universal agreement on a definition of computer science, I believe that it is the inclusion of a quantitative (mathematical) approach to our discipline that distinguishes “computer science” from “computer programming”. Mathematics provides both an established language with which to precisely define terms and established methods for problem solving. For example, the rather vague statement that “algorithm A is better than algorithm B” may be formulated unambiguously and verified or refuted with respect to certain performance measurements using the formalism of algorithm analysis (l). Mathematical methods also point toward the possibility of proving that an algorithm provides acceptable performance for large classes of inputs, a conclusion which often cannot be supported on the basis of case-by-case testing (5). I will now discuss certain mathematical ideas which naturally arise in computer science courses and cite relevant examples which will hopefully convince the reader that these ideas are worthy of formal study. Suggestions are then offered regarding the inclusion of these studies in the four-year computer science curriculum.

Know Your Discipline: Teaching the Philosophy of Computer Science

“…The connection between mathematics and computer science is discussed further, using a number of articles by eminent computer scientists (e.g., Dijkstra, 1974;Knuth, 1974b). The post-software crisis debates of whether there should be more or less mathematics in the computing curricula are discussed (e.g., Atchison et al, 1968;Austing, Barnes, Bonnette, Engel, & Stokes, 1977;Davis, 1977;Glaser, 1974;Hamming, 1969;Kandel, 1972;Khalil & Levy, 1978;Ralston & Shaw, 1980;Wishner, 1968). The students are asked to form a position of their own and write a 200-300 word response to Hoare; they are then required to read each others' responses and to write follow-ups to each others' texts.…”