Advanced Training for Tver’s Math Professors by HSE ICRT
Fifty persons from four institutions participated in the course. The majority (forty-three attendees) were the professors of Tver State University’s three departments: Applied Mathematics and Cybernetics, Physical-Technical, and Mathematical. Among the listeners were five doctors of sciences and more than twenty candidates of sciences. Four participants work in the field of professional programming.
In the first part of the course, the trainees were taught classical logic of statement and that of predicates, their syntax, semantics, major laws, and use in mathematics. Intuitionistic logic that describes constructive reasonings was also discussed, as well as the constructivity and non-constructivity of some often-used mathematical proofs. Classical and intuitionistic logics were mentioned throughout the course.
The second part of the course was devoted to algebraic problems of mathematical theories. Participants learned about some formalisations of the concept of the algorithm, and with results on algorithmic decidability or undecidability of various mathematical problems including those of logic, arithmetics, group theory, etc.
The third part described various approaches to the estimation of the efficiency of algorithms and computational complexity of the problems. The trainees studied different classes of complexity and unsolved problems of the computational complexity theory including one of the seven-millennium problems - P vs NP problem. The course demonstrated the links between this problem and those of logic, graph, language, and game theories, etc.
The course ended with the stories of Tver logicians who work or worked at Tver State University, their contribution to mathematical logic, the theory of algorithms, and theory of computational complexity. The theorems named after these logicians were also mentioned.
Classes were lively, with attendees asking many questions and actively discussing the problems. Some discussions continued after the classes - the course has touched upon the important aspects of knowledge in mathematics.
In the end, many participants expressed their gratitude for new and interesting knowledge. Yulia Chemarina, dean of the Department of Mathematics of Tver State University also expressed her gratitude and hope for further cooperation with HSE ICRT.