A program that acquires how to solve problems in mathematics

  • Authors:
  • Machiko Fujiwara;Kenzo Iwama

  • Affiliations:
  • Engicom Corporation, Kita-ku, Tokyo, Japan;Engicom Corporation, Kita-ku, Tokyo, Japan

  • Venue:
  • WSEAS Transactions on Computers
  • Year:
  • 2009

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Abstract

In mathematics, a sequence of sentences describes how to solve a problem; for instance, sentences, "Calculate the least common multiple of 10 and 15. Firstly divide 10 and 15 by 2. Results are '5' and 'cannot divide'. '5' and 'cannot divide' are not 1 and 1. Divide 5 and 15 by 2. Results are 'cannot divide' and 'cannot divide'." and so on, describe how to calculate the least common multiple of 10 and 15. While example sequences of sentences are given to our program, the program transforms the example sequences to generate a procedure, pG, to solve a problem. For instance, a generated procedure, pGp, checks if a given number is a prime number, another procedure, pGc, calculates the least common multiple of any two numbers, and another procedure, pGf, adds given two fractions. This paper explains our program that generates procedures, one after another, each of which solves one mathematical problem. The paper also argues, as a result of generating a procedure, pG, the meaning of a sentence (or sentences) is represented in the generated procedure, pG.