This textbook contains a set of tasks and exercises necessary to consolidate and expand the lecture material of the disciplines "Mathematical Logic and Theory of Algorithms" and "Discrete Functions," studied as part of the training of students of higher educational institutions studying in the field of information security. The manual includes problems related to algebra and calculus of propositions, algebra and calculus of predicates, theory of discrete functions, including questions of their group classification, theory of algorithms and questions of complexity of algorithms. The textbook will also be useful for university students who study discrete mathematics and mathematical logic.