The tutorial is designed to help you choose an effective solution for your task and talk about standard approaches to solving computer science problems. Some of the problems considered in the manual have already met you in the course of mathematics. Sometimes solutions different from those already known are proposed for these problems. These methods are primarily focused on the use of a computer that allows you to perform large amounts of calculations in a short time. The book consists of 5 chapters, which provide information from such areas of mathematics as geometry, arithmetic, combinatorics and theory of algorithms. The chapters contain theoretical material, problems for repetition, problems of increased complexity and problems for self-solution.