PROBLEMS ON DISCRETE MATHEMATICS Basic educational program

Let us try to summarize the subject of this tutorial. How discrete mathematics curriculum evolved relatively recently - no more than 30 years ago, replacing the course in mathematical logic.
The introduction of such a course is primarily associated with the development of computational techniques, since discrete mathematics contains mathematical disciplines that are the theoretical basis of programming and computer architecture. Discrete mathematics is a collection of mathematical disciplines that do not use the concept of limit or continuity.
In other words, discrete mathematics studies the properties inherent in both infinite and finite sets. Of course, not all sections mathematicians who do not use the concept of a limit are included in the discrete mathematics as a scientific discipline (not to mention a curriculum).
The most important of them - algebra and number theory, are traditionally presented in separate courses. We note one more feature of discrete mathematics - its absence from high school curriculum. If other mathematical disciplines studied in the first year (mathematical analysis, algebra, analytical geometry), rely heavily on school knowledge, discrete mathematics is studied practically from scratch. The exception is the elements of the algebra of logic, studied in the course school computer science and partly the beginning of combinatorics. But several sections of discrete mathematics (for example, graph theory) are widely are used in the extracurricular work of schoolchildren, in particular in school Olympiad mathematics, in the form of problems "for quick wits". Related to this presence in the list of literature of books on extracurricular work with schoolchildren.
Currently discrete mathematics as a scientific discipline includes the following main sections: set theory and relations on sets, algebra of logic, logical calculus, combinatorics, theory
coding and graph theory. All these sections, except for logical calculus and coding theory, are part of the semester course of discrete mathematics and are reflected in this tutorial. For each section brief theoretical information and a set of tasks are given. Examples are given solving typical tasks. When presenting theoretical material, the authors opportunities aimed at an elementary style of presentation accessible to freshmen. The main source of theoretical material was textbook [4], but other literature was also used.
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PROBLEMS ON DISCRETE MATHEMATICS Basic educational program Fast Download
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