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“Recommended mathematical topics for computer science majors”

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Published:02 February 1977Publication History
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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.

References

  1. 1 Aho, Alfred and Hopcroft, John and Ullman, Jeffrey, The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, Massachusetts, 1974. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. 2 Augenstein, Moshe and Tenebaum, Aaron, "A Lesson In Recursion and Structured Programming", SIGCSE Bulletin, February, 1976, pp. 17-23. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. 3 Berztiss, A.T., "The Why and How of Discrete Structures", SIGCSE Bulletin, September, 1976, pp. 30-32. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. 4 Dahl, O.-J. and Dijkstra, E.W. and Hoare, C.A.R., Structured Programming, Academic Press, London and New York, 1972, pp. 72-82. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. 5 Hantler, S.L. and King, J.C., "An Introduction to Proving the Correctness of Programs", Computing Surveys, September, 1976, pp. 331-353. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. 6 Jackson, Glenn A., "A Graphical Technique for Describing Recursion", SIGCSE Bulletin, September, 1976, pp. 30-32. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. 7 Polya, George, Mathematical Discovery Vol I, John Wiley and Sons, 1962, pp. 60-98.Google ScholarGoogle Scholar
  8. 8 Prather, Ronald, Discrete Mathematical Structures for Computer Science, Houghton Mifflin Company, Boston, 1976, pp. 220-229. Google ScholarGoogle ScholarDigital LibraryDigital Library

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          cover image ACM SIGCSE Bulletin
          ACM SIGCSE Bulletin  Volume 9, Issue 3
          Special issue eighth technical symposium on computer science education
          Aug 1977
          82 pages
          ISSN:0097-8418
          DOI:10.1145/382175
          Issue’s Table of Contents
          • cover image ACM Conferences
            SIGCSE '77: Proceedings of the eighth SIGCSE technical symposium on Computer science education
            February 1977
            82 pages
            ISBN:9781450374101
            DOI:10.1145/800106

          Copyright © 1977 ACM

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          Association for Computing Machinery

          New York, NY, United States

          Publication History

          • Published: 2 February 1977

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