The book is based on lectures given to teachers at the University of Illinois. Its main goal is to show the connection between mathematics and computational science, to acquaint the reader with a machine-oriented approach to solving mathematical problems. Using numerous examples (from graph theory, combinatorics, theory of random processes, number theory), the authors strive to demonstrate the solution of problems using computers: mathematical formulation, algorithm construction, interpretation of the results obtained. The individual chapters of the book are written almost independently, making the material easier to read and perceive. The book will be useful and interesting to a wide range of potential computer users; it is available to junior and high school students.