Presented program meets modern requirements, Applied to students of mechanical and mathematical faculties of universities in the field of classical mathematical logic and algorithm theory , students in the specialty "Computer Security", and state standard in this specialty and takes into account experience, accumulated by the Department of Mathematical Methods of Information Protection of Samara State University in the process of training students of this specialty , as well as the practice of leading scientific and educational centers of Russia . The program is designed for a three-semester period of study and consists of six sections: introductory concepts of mathematical logic Counting of statements ; Predicate calculation ; Theory of Recursive Functions ; Theory of Algorithms ; Arithmeticization of the logical inference process, recursive irresolvability, and deductive incompleteness of formal arithmetic. The program is aimed primarily at studying a wide range of purely mathematical results. Definition of "formal systems" , which is intended to accurately describe and investigate the formal-deductive method in mathematics and the closely related concept of algorithm and computable function. This complex also includes all classical results on first-order formal systems. existence of a non-contradictory deductively complete expansion of a non-contradictory formal system, existence of a model of a non-contradictory formal system with a counting individual domain, semantic completeness of classical predicate calculus, recursive insolubility of classical predicate calculus; recursive irresolvability, deductive incompleteness and consistency of formal arithmetic