THE SIGNIFICANCE OF THE THEORY OF ALGORITHMS FOR MODERN PROFESSIONAL EDUCATION AND METODOLOGY OF ITS TEACHING
V. I. Igoshin
Saratov State University, Saratov, Russian Federation
Keywords: интуитивное понимание алгоритма, формальные теории алгоритмов, машины Тьюринга, рекурсивные функции, нормальные алгоритмы Маркова, компьютерные науки, информационные технологии, методика обучения теории алгоритмов, Intuitive understanding of the algorithm, formal theories of algorithms, Turing machine, recursive functions, Markov normal algorithms, computer science, information technology, methods of teaching the theory of algorithms
Abstract
The article explores the role and relevance of the theory of algorithms in the fundamen- talization of mathematical education of specialists in the field of computer science and information technology, trained at vocational schools and higher institutions. In this case, the theory of algorithms appears in two fields; the first field assumes theory of specific algorithms (or intuitively-containing theory of algorithms) whereas the second one implies a formal-logical (abstract) theory of algorithms. In the first case, the theory of algorithms explores algorithms as means for solving specific problems, and the problem of developing this kind of algorithm is seen as the basic one. This algorithm should be implemented by a modern computer in real time. The second problem assumes comparing different specific algorithms for solving the same problem in terms of their complexity, mainly in terms of the time required to solve the problem. Due to this fact, the classes of complexity of algorithms P and NP appear followed by the problem of relationships between these classes. These problems are not solved until now. In the second case, the theory of algorithms creates mathematical (abstract) concepts of the algorithm and explores the properties of these concepts. In the 30s and the first postwar years of the XX century, several abstract concepts of the algorithm, or formalizations of the intuitive understanding of the algorithm, were developed. This is a Turing machine, recursive functions as functions computable by some algorithm, normal algorithms of A. A. Markov. The abstract theory of algorithms establishes the equivalence of these abstract concepts. The problem of these algorithms existing is seen as the most important one. In particular, the abstract theory of algorithms establishes the absence of algorithms for solving a number of mass problems. This paper describes a methodological system of teaching algorithm theory, taking into account its two intuitive and abstract fields.
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