COMPUTER TOOLS FOR SOLVING MATHEMATICAL PROBLEMS: A REVIEW

The rapid development of digital computer hardware and software has had a dramatic influence on mathematics, and vice versa. The advanced hardware and modern sophisticated software such as computer visualization, symbolic computation, computer-assisted proofs, multi-precision arithmetic and powerful libraries, have provided resolution to many open problems, very difficult mathematical problems, and discovering new patterns and relationships, far beyond a human capability. In the first part of the paper, we give a short review of some typical mathematical problems solved by computer tools. In the second part we present some new original contributions, such as an intriguing consequence of the presence of roundoff errors, distribution of zeros of random polynomials, dynamic study of zero-finding methods, a new three-point family of methods for solving nonlinear equations and two algorithms for the inclusion of a simple complex zero of a polynomial.