Preface These proceedings contain the papers of Local organization committee the 48th International Youth School- conference “Modern Problems in Alexey Borbunov, Pavel Chistyakov, Mathematics and its Applications” Konstantin Efimov, Sergey Goryainov, SoProMat-2017 («Современные проблемы Vladislav Kabanov, Dmitry Khlopin, Natalia математики и ее приложений», Maslova, Ekaterina Neznakhina, Natalia СоПроМат-2017) held at the Krasovskii Novoselova, Alexandr Osipov, Maksim Institute of Mathematics and Mechanics Pasynkov, Sergei Pravdin, Aleksei Rodin, (IMM UrB RAS) in Yekaterinburg (Russia) and Leonid Shalaginov (Krasovskii Institute on the 5th – 11th February, 2017. SoProMat of Mathematics and Mechanics). aims to bring together researchers from pure Programme committee and applied mathematics as well as computer science. The topics in mathematics We appreciate the efforts of the include algebra, approximation of functions, programme committee, namely Yurii functional analysis, differential equations, Averboukh, Alexey Danilin, Mikhail optimal control problems and differential Gomoyunov, Mikhail Khachay, Dmitry games, topology and geometry, Khlopin, Victor Kostousov, Alexander mathematical modelling and numerical Kovalevsky, Alexandr Makhnev, Natalia methods, mathematical biology. The topics Maslova, Alexandr Osipov, Denis in computer science embrace theoretical Perevalov, Sergei Pravdin, Andrey Sozykin informatics, technical vision, robotics, (Krasovskii Institute of Mathematics and parallel and distributed calculations. Mechanics), Ivan Simonov (Ural Federal University). We received 110 abstracts and chose 103 of them to be presented as oral talks. Acknowledgments Moreover, 14 plenary invited talks were given. After the conference, we selected 40 We acknowledge financial support from long papers, including 2 invited, from a total Krasovskii Institute of Mathematics and of 46 submissions. Each submitted paper Mechanics and Russian Foundation for was reviewed by members of the Basic Research (RFBR). programme committee. We would like to 11 August 2017 thank the keynote speakers, the programme committee, the authors of the papers, and the Alexandr Makhnev, Sergei Pravdin participants, for without these people there would be no conference. Scientific chairs Yurii Averboukh, Alexey Danilin, Mikhail Gomoyunov, Mikhail Khachay, Dmitry Khlopin, Victor Kostousov, Alexander Kovalevsky, Alexandr Makhnev, Denis Perevalov, Sergei Pravdin (Krasovskii Institute of Mathematics and Mechanics), Ivan Simonov (Ural Federal University).