Sergei Kurgalin [Сергей Кургалин] - The Discrete Math Workbook: A Companion Manual Using Python, 2nd Edition

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The second edition of the book comes out after a short period of time compared to the first one, which we believe is connected with the increased interest in discrete mathematics among specialists in the field of computer science. Now we use Python as a programming language. The choice of this language is determined by its universality and rapid growth in popularity in the world. In our opinion, Python is good enough for teaching methods of design and analysis of algorithms.

We have kept the structure of the material the same in the second edition: each chapter consists of a theoretical part containing basic definitions, theorems, and typical schemes of problem-solving, then we give problems for solving in a classroom led by a teacher or for self-study.

More than 50 new problems with solutions and answers have been added to the book, as well as control questions for each chapter to check the knowledge of basic definitions and theoretical facts. In a number of cases clarifying comments were made or observed for inaccuracies corrected in solutions and proofs.

The authors would like to express their grateful acknowledgment to all who expressed their wishes or suggested ways to improve the book after the publication of the first edition.

We are grateful to our colleagues Alexey Bukhovets, Valeria Kaverina, Alexander Loboda, Peter Meleshenko, and Mikhail Semenov for their useful discussions, advices, and critical comments. Also, at Springer, we would like to thank Senior Editor, Wayne Wheeler, and Associate Editor, Simon Rees.

Nikolai Paukov helped us a lot in debugging and checking the program code of the algorithms presented in the book.

All remaining errors and inaccuracies, of course, remain on the authors' conscience.

Rapid development of information and communication technologies is a characteristic feature of the current time period. Training specialists who meet the requirements of the time in the field of such technologies leads to the necessity of paying special attention to their mathematical education. Herewith it is desirable to shape knowledge presented in the form of a practical part of mathematical courses in such a way that after performing these tasks students get the required competencies. One of the mathematical courses which is taught, as a rule, in early semesters is the course of discrete mathematics. A number of general courses and specialist disciplines included in the cycle of specialist training in the field of information technologies are based on the present course. Thus, mathematical logic and theory of algorithms form the theoretical foundation of informatics, Boolean algebra serves as a basis for methods of electronic circuit development, theory of graphs is used when constructing multiprocessor computing systems and computer networks, and in programming. To teach students the competent practical application of their theoretical knowledge is one of the methodological objectives the given study guide can help with.

The study guide was created over a number of years and is backed up by the teaching experience of the course at the Department of Computer Science of Voronezh State University. Its contents correspond to Federal State Educational Standards on the following training programmes: Information Systems and Technologies, Program Engineering, and Radiophysics. The existing problem books on discrete mathematics and mathematical logic do not fully cover the necessary volume and information scope upon the abovementioned programmes to graduate fully skilled subject matter experts; therefore this study guide provides a large number of problems of a wide range of difficulty for these training programmes.