Brief description of the departments of the Faculty of CMC. Faculty of Computational Mathematics and Cybernetics, Moscow State University Department of Mathematical Forecasting Methods

Head of the department: Zhuravlev Yury, Academician of RAS, Professor, Dr.Sc.

Contact information Other contact information

119991, Moscow, GSP-1, Leninskiye Gory, MSU, 2nd Educational Building, CMC Faculty, rooms 530, 532, 573, 680 (Head of the department)

The Department trains specialists in machine learning, data-mining, image processing algorithms and their applications in natural sciences, economics, finance, etc. The Department's specialization includes mathematical methods for diagnosing complex systems (including technical and economic ones), analyzing these systems, constructing optimal or near optimal solutions that are based on an indirect, incomplete, or contradictory information.

During training, students receive a fundamental education in different areas of mathematics such as modern algebra and mathematical logic, theory of algorithms, discrete and combinatorial mathematics, mathematical models of artificial intelligence, including the mathematical methods of pattern recognition, machine learning, image processing, probability theory, applied statistics, graphical models.

Attending practical sessions, students acquire a skill of working with modern databases and software, learn modern programming languages and techniques, gain experience in solving applied problems. Students also have practice in research institutions of the Russian Academy of Sciences, innovative companies, financial organizations, etc. To the time of their masters many of them already have papers in scientific journals and top conferences ’proceedings.

The Department prepares professionals in the development and application of mathematical methods to solve various data processing problems such as scoring systems, fraud detection, retails prediction, bioinformatics, natural language processing, computer vision, expert systems, etc.

Staff members:

Rudakov Konstantin, Corresponding Member of RAS, Professor, Dr.Sc.
Mestetsky Leonid, Corresponding Member of RAS, Professor, Dr.Sc.
Dyakonov Alexander, Professor, Dr.Sc.
Leontyev Vladimir, Professor, Dr.Sc.
Vorontsov Konstantin, Associate Professor, Dr.Sc.
Gurevich Igor, Associate Professor, PhD
Gurov Sergey, Associate Professor, PhD
Dyukova Elena, Associate Professor, Dr.Sc.
Maisuradze Archil, Associate Professor, PhD
Ryazanov Vladimir, Associate Professor, Dr.Sc.
Senko Oleg, Associate Professor, Dr.Sc.
Vetrov Dmitry, Associate Professor, PhD
Kropotov Dmitry, Researcher, Scientific Secretary of the Department

Regular courses:

Algebraic methods in machine learning by Prof. Zhuravlev, 16 lecture hours and 16 seminar hours.
Applied algebra by Prof. Dyakonov, Prof. Leontyev, Assoc. Prof. Gurov, 48 lecture hours and 48 seminar hours.
Machine learning by Assoc. Prof. Voronstov, 32 lecture hours.
Bayesian methods in machine learning by Assoc. Prof. Vetrov, 16 lecture hours and 16 seminar hours.
Graphical models by Assoc. Prof. Vetrov, 16 lecture hours and 16 seminar hours.
Mathematical methods of classification by Prof. Rudakov, 32 lecture hours.
Computer workshop by Assoc. Prof. Maisuradze, 48 lecture hours.
Image processing and analysis by Prof. Mestetsky, 16 lecture hours.
Algorithms, models, algebras by Prof. Dyakonov, 16 lecture hours.
Applied statistics by Assoc. Prof. Voronstov, 16 lecture hours and 16 seminar hours.
Signal Processing by Ass. Prof. Krasotkina, 16 lecture hours.

Special courses:

Bayesian methods of machine learning by Dr. Vetrov, 16 lecture hours.
Computational problems of bioinformatics by Assoc. Prof. Makhortyh and Assoc. Prof. Pankratov, 16 lecture hours.
Image Mining by Assoc. Prof. Gurevich, 16 lecture hours.
Propositional calculus of classical logic by Assoc. Prof. Gurov, 32 lecture hours.
Combinatorial foundations of information theory by Assoc. Prof. Voronstov, 16 lecture hours.
Logical methods in pattern recognition by Assoc. Prof. Dyukova, 16 lecture hours.
Mathematical methods of biometrics by Prof. Rudakov, 16 lecture hours.
Metric Methods of Data Mining by Assoc. Prof. Maisuradze, 16 lecture hours.
Continuous morphological models and algorithms by Prof. Mestetsky, 16 lecture hours.
Non-statistical methods of data mining and classification by Assoc. Prof. Ryazanov, 32 lecture hours.
Generalized spectral-analytical method, 16 lecture hours.

Special scientific seminars and directions of research:

Algebraic approach to data mining, machine learning and pattern recognition

(Academician of RAS Yu. I. Zhuravlyov, Corresponding Member of RAS K.V. Rudakov, Dr. S. V. V. Ryazanov, Dr. S. A. G. Dyakonov).

In the framework of an algebraic approach new algorithms are constructed as formulas over initial algorithms (weak learners) or as Boolean functions (logic correctors). The main result is that every algorithm can be presented as a superposition of a recognition operator and a decision rule. It allows one to describe the algorithm results as special matrices - the estimate matrices (outputs of recognition operators) and the result matrices (outputs of decision rules). Operations over algorithms are induced by operations over the corresponding estimate matrices. The algebraic approach allows one to construct formulas over algorithms, the formulas that are correct on the test set (or have better performance than initial algorithms).

Computational learning theory and machine learning applications

(Dr. K. Vorontsov)

One of the most challenging problems in machine learning research is analyzing the general performance of a learning machine. A combinatorial theory of overfitting which gives tight and in some cases exact generalization bounds is developed. These bounds are applied to designing learning algorithms in such machine learning subareas as the ensemble learning, rule induction, the distance learning, features selection, prototype selection. Another research direction is information retrieval, collaborative filtering, and probabilistic topic modeling with applications to the analysis of big collections of scientific documents.

Continuous models in image shape analysis and classification

(Prof. L. Mestetsky)

Approaches and methods of objects shape representation in digital images by continuous models are investigated. Human eye does not see the discrete nature of digital images. Images look like continuous pictures, and it is more customary and simpler to operate “solid” continuous geometric models of the shape. Therefore the use of continuous models significantly simplifies the creation of algorithms for analyzing, classifying, and transforming image shapes. The concept of a figure as a universal continuous model of shape is used. A figure is defined as a closed domain whose boundary consists of the finite number of nonintersecting Jordan curves. Three interconnected methods of figure representation are investigated; these are boundary, medial and circular descriptions. The task of constructing the continuous model for the digital image is reduced to the approximation of this image by continuous figures. Then efficient computational geometry algorithms are applied for the shape analysis and related classification of discrete objects in digital images.

Bayesian Methods in Machine Learning

(Dr. D. Vetrov and D. Kropotov)

The research work is focused on investigating the Bayesian approach in the probability theory and its application for solving different machine learning and computer vision problems. Bayesian methods have become a wide-spread technique in the last 15 years. Their main advantages include an automatic tuning of structural parameters in machine learning models, a correct way for reasoning in case of uncertainty, a possibility of considering structural and probabilistic interactions in data arrays (based on actively developing graphical models concept), and an approach for data and model parameter representation that allows an easy fusion of indirect observations and prior ideas.

The developed techniques are intensively used for solving different applied problems including gene expression analysis in animal brains during cognitive processes.

Data Mining: New Challenges and Methods

The related seminar is designed for 2nd-5th year students, graduate students and anyone interested. It takes place in the spring semester in the form of reports of the participants and invited experts. Topics are diverse. They include (but not limited to) the hypothesis of compactness in pattern recognition; the solution of Boolean equations and synthesis of control circuits; mathematical methods for the analysis of brain activity; characteristics of partially ordered sets; detection of the latent image-based processing of radiographs and photographs of paintings; analysis of formal concepts in applied problems.

Clustering problems

(Academician of RAS Yu. Zhuravlev and Dr. V. Ryazanov)

There are many clustering algorithms based on different principles and leading to different partitions of a given sample. In the absence of statistical models of data, evaluation and comparison problems of clustering arise. Does the resulting clustering correspond to the objective reality, or just get a partition? Criteria for evaluating the quality of clustering and methods of their calculation are designed. These criteria allow us to construct ensembles of clustering algorithms.

Intellectual data-mining: new problems and methods

(Dr. S. Gurov and Dr. A. Maisuradze)

Data-mining in metric spaces

(Dr. A. Maisuradze)

Analysis and estimation of information contained in images

(Dr. I. Gurevich)

Logical methods of pattern recognition

(Dr. E. Dyukova)

Combinatorial methods of information theory

(Dr. V. Leontyev)

Problem-oriented methods of pattern recognition

(Corresponding Member of RAS Prof. K. Rudakov and Dr. Yu. Chekhovich)

Recent papers

V.V. Ryazanov and Y.I. Tkachev, Estimation of Dependences Based on Bayesian Correction of a Committee of Classification Algorithms // Computat. Mathem. and Math. Physics, vol. 50. no. 9, pp. 1605-1614, 2010.
V.V. Ryazanov, Some Imputation Algorithms for Restoration of Missing Data // Lecture Notes in Computer Science (LNCS), vol. 7042, pp. 372-379, 2011.
K. Vorontsov, Exact Combinatorial Bounds on the Probability of Overfitting for Empirical Risk Minimization // Pattern Recognition and Image Analysis, vol. 20, no. 3, pp. 269-285, PDF, 427Kb, 2010.
K. Vorontsov and A. Ivakhnenko, Tight Combinatorial Generalization Bounds for Threshold Conjunction Rules // Lecture Notes on Computer Science. 4th International Conference on Pattern Recognition and Machine Intelligence (PReMI'11), Russia, Moscow, June 27 – July 1, pp. 66–73, PDF, 153Kb, 2011.
N. Spirin and K. Vorontsov, Learning to Rank with Nonlinear Monotonic Ensemble // Lecture Notes on Computer Science. 10th International Workshop on Multiple Classidier Systems (MCS-10). Naples, Italy, June 15–17, pp. 16–25, PDF, 490Kb, 2011.
D. Vetrov and A. Osokin, Graph Preserving Label Decomposition in Discrete MRFs with Selfish Potentials // Proceedings of International Workshop on Discrete Optiization in Machine learning (DISSML NIPS 2011), 2011.
Osokin, D. Vetrov and V. Kolmogorov, Submodular Decomposition Framework for Inference in Associative Markov Networks with Global Constraints // Proceedings of International Conference on Computer Vision and Pattern Recognition (CVPR2011), N.Y., USA, Springer, pp. 135-142, 2011.
Yangel and D. Vetrov, Image Segmentation with a Shape Prior Based on Simplified Skeleton // Proceedings of International Workhop on Energy Minimization Methods (EMMCVPR2011), 2011.
Dyakonov, Two Recommendation Algorithms Based on Deformed Linear Combinations // Proc. of ECML-PKDD, 2011, Discovery Challenge Workshop, pp. 21-28, 2011.
Dyakonov, Theory of Equivalence Systems for Describing Algebraic Closures of a Generalized Estimation Model. II // Computational Mathematics and Mathematical Physics, vol. 51, no. 3, pp. 490-504, 2011.
N. Dyshkant, L. Mestetskiy, B.H. Shekar and Sharmila Kumari, Face recognition using kernel component analysis // Neurocomputing, vol. 74, no. 6, pp. 1053-1057, 2011.
B.H. Shekar, Sharmila Kumari, N. Dyshkant and L. Mestetskiy, FLD-SIFT: Class Based Scale Invariant Feature Transform for Accurate Classification of Faces // Comm. in Computer and Information Science, 1, Computer Networks and Information Technologies, vol. 142, part 1, pp. 15-21, 2011.
Kurakin and L. Mestetskiy, Hand gesture recognition through on-line skeletonization - application of continuous skeleton to real-time shape analysis // Proceedings of the International conference on computer vision theory and applications (VISAPP 2011), Vilamoura, Portugal, 2011, March 5-7, pp. 555-560, 2011.
Bakina, A. Kurakin and L. Mestetskiy, Hand geometry analysis by continuous skeletons // Lecture Notes in computer science, Image analysis and recognition, Springer, vol. 6753/2011, part 2, pp. 130-139, 2011.
I.G. Bakina and L.M. Mestetskiy, Hand Shape Recognition from Natural Hand Position // Proceedings of the IEEE International Conference on Hand-Based Biometrics, Hong Kong Polytechnic University, Hong Kong, pp. 170-175, 2011.
Bilateral Russian-Indian Scientific Workshop on Emerging Applications of Computer Vision: Workshop Proc. / Ed. by A. Maysuradze - Moscow, MAKS Press, 2011 .-- 224 p. ISBN 978-5-317-03937-0
D.P. Vetrov, D.A. Kropotov, A.A. Osokin and D.A. Laptev, Variational segmentation algorithms with label frequency constraints // Pattern Recogn. and Image Anal., vol. 20, no. 3, pp. 324-334, 2010.
D.P. Vetrov, D.A. Kropotov, A.A. Osokin, A. Lebedev, V. Galatenko and K. Anokhin, An interactive method of anatomical segmentation and gene expression estimation for an experimental mouse brain slice // Proc. of 7th Intern. Conf. on Computational Intelligence Methods for Biostatistics and Bioinformatics, Palermo, Italy: Springer, no. 1, pp. 23-34, 2010.
D.P. Vetrov and V. Vishnevsky, The algorithm for detection of fuzzy behavioral patterns // Proc. of Measuring Behavior 2010, 7th Intern. Conf. on Methods and Techniques in Behavioral Research, Eindoven, Holland: Springer, no. 1, pp. 41-45, 2010.
S.I. Gurov, New principle for specifying a priori distribution and consistency interval estimate // Scientific Computing. Proc. of the Intern. Eugene Lawler Ph.D. School. Waterford, Ireland: WIT press, pp. 8-20, 2010.
S.I. Gurov, Probability estimation of 0-event // Scientific Computing. Proc. of the Intern. Eugene Lawler Ph.D. School. Waterford, Ireland: WIT press, pp. 198-209, 2010.
A.I. Maysuradze, Domain-oriented bases in spaces of finite metrics of a given rank // Scientific Computing. Proc. of the Intern. Eugene Lawler Ph.D. School. Waterford, Ireland: WIT press, pp. 210-221, 2010.
D.P. Vetrov, D.A. Kropotov and A.A. Osokin, 3-D mouse brain model reconstruction from a sequence of 2-d slices in application to allen brain atlas // Computational Intelligence Methods for Bioinformaticcs and Biostatistics. Lecture Notes in Computer Science, Berlin, Germany: Springer, no. 6160, pp. 291-303, 2010.
E.V. Djukova, Yu.I.Zhuravlev and R.M. Sotnezov, Construction of an ensemble of logical correctors on the basis of elementary classifiers // Pattern Recogn. and Image Anal., vol. 21, no. 4, pp. 599-605, 2011.
D.P. Vetrov and B.K. Yangel, Image segmentation with a shape prior based on simplifies skeleton // Proc. of Intern. Workshop on Energy Minimization Methods. Berlin, Germany: Springer, pp. 148-161, 2011.

Novikov Alexander, Rodomanov Anton, Osokin Anton, and Vetrov Dmitry. Putting mrfs on a tensor train. Journal of Machine Learning Research, 32 (1): 811–819, 2014.
A. Osokin and D. Vetrov. Submodular relaxation for inference in markov random fields. IEEE Transactions on Pattern Analysis and Machine Intelligence, 99, 2014.
Bartunov Sergey and Vetrov Dmitry. Variational inference for sequential distance dependent chinese restaurant process. Journal of Machine Learning Research, 32 (1): 1404-1412, 2014.
L. Mestetskiy. Representation of linear segment voronoi diagram by bezier curves. In Proceedings of the 24th International Conf. GRAPHICON-2014, pages 83–87. Academy of Architecture and Arts SFedU Rostov-on-Don, 2014.
S.V. Ablameyko, A.S. Biryukov, A.A. Dokukin, A.G. D'yakonov, Yu I. Zhuravlev, V.V. Krasnoproshin, V.A. Obraztsov, M. Yu Romanov, and V.V. Ryazanov. Practical algorithms for algebraic and logical correction in precedent-based recognition problems. Computational Mathematics and Mathematical Physics, 54 (12): 1915-1928, 2014.
Tsoumakas Grigorios, Papadopoulos Apostolos, Qian Weining, Vologiannidis Stavros, D "yakonov Alexander, Puurula Antti, Read Jesse, Svec Jan, and Semenov Stanislav. Wise 2014: Multi-label classification of print media articles to topics. Lecture Notes in Computer Science , 8787: 541-548, 2014.
Vorontsov K. V. Additive Regularization for Topic Models of Text Collections // Doklady Mathematics. 2014, Pleiades Publishing, Ltd. - Vol. 89, No. 3, pp. 301-304.
Vorontsov K. V., Potapenko A. A. Tutorial on Probabilistic Topic Modeling: Additive Regularization for Stochastic Matrix Factorization // AIST'2014, Analysis of Images, Social networks and Texts. Springer International Publishing Switzerland, 2014. Communications in Computer and Information Science (CCIS). Vol. 436. pp. 29–46.
Uspenskiy VM, Vorontsov KV, Tselykh VR, Bunakov VA Information Function of the Heart: Discrete and Fuzzy Encoding of the ECG-Signal for Multidisease Diagnostic System // in Advances in Mathematical and Computational Tools in Metrology and Testing X (vol. 10), Series on Advances in Mathematics for Applied Sciences, vol. 86, World Scientific, Singapore (2015) pp 375-382.
Vorontsov K. V., Potapenko A. A. Additive Regularization of Topic Models // Machine Learning Journal. Special Issue “Data Analysis and Intelligent Optimization with Applications” (to appear).

Gurov S.I. Estimation of the reliability of a classification algorithm as based on a new information model // Comput. Mathematics and Math. Phys. 2013.53.N 5. P. 640-656.
Nekrasov K.V., Laptev D.A., Vetrov D.P. Automatic determination of cell division rate using microscope images // Pattern Recogn. and Image Anal. 2013.23.N. 1.P. 105-110.
Osokin A.A., Amelchenko E.M., Zworikina S.V., Chekhov S.A., Lebedev A.E., Voronin P.A., Galatenko V.V., Vetrov D.P., Anokhin K.V. Statistic parametric mapping of changes in gene activity in animal brain during acoustic stimulation // Bulletin of Experimental Biology and Medicine. 2013.154. N 5.P. 697-699.
Voronin P.A., Vetrov D.P., Ismailov K. An approach to segmentation of mouse brain images via intermodal registration // Pattern Recogn. and Image Anal. 2013.23.N. 2.P. 335-339.
Zhuravlev Y.I., Laptin Y., Vinogradov A., Likhovid A. A comparison of some approaches to the recognition problems in care of two classes // Information Models & Analyses. 2013. 2. N 2.P. 103-111.
Chernyshov V.A., Mestetskiy L.M. Mobile machine vision system for palm-based recognition // Proc. of 11th Intern. Conf. Pattern Recogn. and Image Anal .: New Information Technologies. N 1. Samara: ISOI RAN, 2013. P. 398-401.
Djukova E.V., Lyubimtseva M.M., Prokofjev P.A. Logical correctors in recognition problems // Proc. of 11th Intern. Conf. Pattern Recogn. and Image Anal .: New Information Technologies. N 1. Samara: ISOI RAN, 2013. P. 82-83.
Dyshkant N.F. Comparison of point clouds acquired by 3d scanner // Discrete Geometry for Computer Imagery. 17th Intern. Conf. Lecture Notes in Computer Science. N 7749. Berlin, Germany: Springer, 2013. P. 47-58.
Gurov S.I., Prokasheva O.V., Onishchenko A.A. Classification methods based on formal concept analysis // The 35th European FCAIR 2013-Formal Concept Analysis Meets Information Retrieval. N 1. M .: Publishing House of the National Research University Higher School of Economics, 2013. P. 95-104.
Mestetskiy L.M., Zimovnov A.V. Curve-skeleton extraction using silhouettes "medial axes // GraphiCon" 2013. 23rd International Conference on Computer Graphics and Vision. Conference proceedings. Vladivostok: Dalnauka, 2013. P. 91-94.
Osokin A., Kohli P., Jegelka S. A principled deep random field model for image segmentation // 2013 IEEE Conf. on Computer Vision and Pattern Recogn. N.Y., USA: IEEE Computer Society Press, 2013. P. 1971-1978.
Zhuravlev Y.I., Gurevich I., Trusova Yu., Vashina V. The challenge the problems and the tasks of the descriptive approaches to imaage analysis // Proc. of 11th Intern. Conf. Pattern Recogn. and Image Anal .: New Information Technologies. N 1. Samara: ISOI RAN, 2013. P. 30-35.
Dyakonov A.G. Deformation of responses of data analysis algorithms // Spectral and Evolution Problems. No. 23. Simferopol, Ukraine: Taurida National V. Vernadsky University, 2013. P. 74-78.

Bondarenko N.N., Zhuravlev Yu.I. Algorithm for choosing conjunctions for logical recognition methods // Comput. Math. and Math. Phys. 2012. 52. No. 4. P. 746-749.
D "yakonov A.G. Criteria for the singularity of a pairwise L1-distance matrix and their generalizations // Izvestiya. Mathematics. 2012.76. N 3.P. 517-534.
Onishchenko A.A., Gurov S.I. Classification based on formal concept analysis and biclustering: possibilities of the approach // Computational Mathematics and Modeling. 2012.23.N 3. P. 329-336.
Voronin P.A., Adinetz A.V., Vetrov D.P. A new measure for distance-field based shape matching // GraphiCon "2012. 22nd International Conference on Computer Graphics and Vision. Conference Proceedings. M .: MAKS Press, 2012. P. 101-106.
D "yakonov A.G. A blending of simple algorithms for topical classification // Rough Sets and Current Trends in Computing. Lecture Notes in Computer Science. N 7413. Berlin, Germany: Springer, 2012. P. 432-438.
Osokin A.A., Vetrov D.P. Submodular relaxation for MRFs with high-order potentials // Computer Vision - ECCV 2012. Workshops and Demonstrations. Lecture Notes in Computer Science. N 7585. Berlin, Germany: Springer, 2012. P. 305-314.
Voronin P.A., Vetrov D.P. Robust distance fields for shape-based registration // Intellectualization of information processing: 9th international conference. M .: Torus Press, 2012. P. 382-385.
Yangel B.K., Vetrov D.P. Globally optimal segmentation with a graph-based shape prior // Intellectualization of information processing: 9th international conference. M .: Torus Press, 2012. P. 456-459.

President - Academician of the Russian Academy of Sciences Evgeny Ivanovich Moiseev
Acting Dean - Academician of the Russian Academy of Sciences Igor Anatolyevich Sokolov

Faculty of Computational Mathematics and Cybernetics (CMC) Moscow state university named after MV Lomonosov is the leading educational center in Russia for training personnel in the field of fundamental research in applied mathematics, computational mathematics, computer science and programming.

The faculty was founded in 1970. The very fact of its creation, the development of a structure and main directions scientific activities The CMC faculty is entirely indebted to one of the largest scientists in Russia - Academician Andrei Nikolaevich Tikhonov. The efforts of A.N. Tikhonov on the creation of the CMC faculty received the support of Academician M.V. Keldysh - at that time the president of the USSR Academy of Sciences. Besides A.N. Tikhonov, who was the dean of the CMC faculty in the first 20 years of its existence, the first members of the faculty played an important role: Academician L.S. Pontryagin, Corresponding Members of the USSR Academy of Sciences L.N. Bolshev and S.V. Yablonsky and professors I.S. Berezin and Yu.B. Germeier.

Over the past years, the faculty has formed the leading scientific schools in Russia in various fundamental areas of applied mathematics and computer science: in the theory of ill-posed problems, in mathematical physics and the spectral theory of differential equations, in nonlinear dynamic systems and control processes, in computational methods and mathematical modeling, in game theory and operations research, in optimal control and systems analysis, in mathematical cybernetics and mathematical logic, in probability theory and mathematical statistics, in applied and theoretical programming, in the architecture of computing systems and networks.

The CMC faculty includes 19 departments: Mathematical Physics, Computational Methods, General Mathematics, Functional Analysis and Its Applications, Scientific Research Automation, Computational Technologies and Modeling, Supercomputers and Quantum Informatics, Nonlinear Dynamic Systems and Control Processes, Optimal Control, System Analysis, mathematical statistics, operations research, mathematical forecasting methods, mathematical cybernetics, system programming, algorithmic languages, computer systems automation, information security, English.

Among the heads of the departments are academicians Yu.I. Zhuravlev, A.B. Kurzhansky, E.I. Moiseev, Yu.S. Osipov, I.A. Sokolov, E.E. Tyrtyshnikov, B.N. Chetvertushkin, Corresponding Member V.V. Voevodin, A.I. Avetisyan, R.L. Smelyansky.

Training at the faculty is carried out according to the following basic educational programs for training bachelors and masters: 010300 "Fundamental Informatics and Information Technologies", 010400 "Applied Mathematics and Informatics".

The curriculum for students enrolled in the Faculty of Computational Mathematics and Cybernetics of Moscow State University under bachelor's degree programs provides for fundamental mathematical training. Students study mathematical analysis, theory of functions of a complex variable, functional analysis, linear algebra, analytical geometry, ordinary differential equations, equations of mathematical physics, probability theory, mathematical statistics, mathematical logic, discrete mathematics, numerical methods, operations research, game theory, optimal control , extreme problems.

Faculty students are taught a wide range of courses related to computing technology and programming: algorithms and algorithmic languages, computer architecture and assembly language, operating systems, application software, computer graphics, parallel computing, databases, operating systems, artificial intelligence, object-oriented programming, computer networks, network technologies, programming systems, verification of programs on models, object-oriented analysis and design, formal methods of program specification.

Practical work on computers, including work on high-performance computing systems, takes a significant place in training. During their studies, students learn to work in several operating systems and learn at least three programming languages. All students study English and the humanities cycle.

In the first two courses, training is conducted in general curricula and programs. The main focus is on general mathematical training and theoretical and applied programming. Recently, much attention has been paid to the use of supercomputers, supercomputer technologies in modeling, parallel computing. Starting from the third year, students undergo specialization in their chosen departments. Each student works in a special seminar and has his own supervisor.

Graduates of the bachelor's department can continue their studies in the magistracy of the faculty. The term of study for a master's degree is 2 years. Admission to the magistracy is carried out on a competitive basis. Graduates of the Faculty's master's degree, who have shown a penchant for research work, can continue their studies in the graduate school of the faculty. The term of study in full-time postgraduate study is 4 years.

Preparation of masters in the direction "Applied Mathematics and Informatics" is carried out according to the programs: "Computational Technologies and Modeling", "Spectral Theory of Differential Operators and Control of Distributed Systems", " Numerical Methods and mathematical modeling "," Computer methods in mathematical physics, inverse problems and image processing "," Modern methods mathematical modeling ”,“ Operations research and actuarial mathematics ”,“ Discrete structures and algorithms ”,“ Discrete control systems and their applications ”,“ Statistical analysis and risk forecasting ”,“ Information security of computer systems ”,“ Theory of nonlinear dynamic systems: analysis , synthesis and control "," Mathematical modeling methods and optimization methods controlled processes"," Logical and combinatorial methods of data analysis "," Mathematical methods of system analysis, dynamics and control "," Intelligent systems "," Intelligent analysis of big data "," Compiler technologies "," Programming technologies "," Supercomputer systems and applications " , "Distributed systems and computer networks", "Quantum informatics", "Software for computer networks", "Mathematical and software for information security", "Mathematical and computer methods of image processing", "Technologies of parallel programming and high-performance computing", "Large data: infrastructure and methods for solving problems ”. Preparation of masters in the direction "Fundamental Informatics and Information Technologies" is carried out according to the programs: "Open Information Systems", "Information Systems for Enterprise Management".

Education at the faculty is unthinkable without close connection with science. Students are necessarily involved in scientific research carried out in the departments of the faculty, in academic institutes or in scientific laboratories. Research laboratories have been created at the faculty: mathematical physics, computational electrodynamics, modeling heat and mass transfer processes, inverse problems, mathematical methods of image processing, mathematical modeling in physics, difference methods, open information technologies, statistical analysis, mathematical problems of computer security, computational workshop and information systems, computing systems, information systems in education and scientific research, computer graphics and multimedia, programming technologies, electronic computers, tools in mathematical modeling, industrial mathematics, as well as student research laboratory Intel and Microsoft Technology Lab.

The faculty is well equipped with computers. There are several computer classes equipped with the most modern multimedia technology and software based on Intel processors, several classes of workstations running UNIX operating systems. All classes are united into a local area network based on fiber-optic communication with Internet access. The faculty has several graphics stations, including the HP Apollo-9000, a high-performance cluster, and the IBM eServer pSeries 690 Regatta multiprocessor supercomputers. In 2008, the faculty installed a supercomputer IBM Blue Gene / P with a capacity of about 30 teraflops (trillions of floating point operations per second). Since 2009, the Lomonosov supercomputer has been in operation.

The faculty has close working contacts with large IT companies such as Intel, Microsoft, Microsoft Research, IBM, Hewlett-Packard, Sun, Cisco, SAP, Samsung; many Russian companies: Luxoft, Redlab, IT, Garant, Consultant-Plus, DVM, Kaspersky Lab, Mail.Ru Group and others. The faculty has a regional academy CISCO. Together with the institutes of the Russian Academy of Sciences, the faculty has created an educational and scientific center for supercomputer modeling.

There are no problems with the employment of graduates of the faculty. Faculty graduates work in all areas where computer technology is used: academic and research institutes, higher educational institutions, state and government agencies, banks, insurance, financial, consulting firms, Russian and foreign firms, etc. About a third of graduates continue postgraduate studies.

The faculty has agreements with a number of foreign universities on cooperation and student exchange. The combination of deep theoretical training with active practical and research work under the guidance of teachers and researchers makes the graduates of the faculty competitive in the labor market.

Strange descriptions of chairs ... which means "One of the few places where there is competition in mathematical results." - did not understand

Let's try about SA ...
website of the department http://sa.cs.msu.su/

This department stands out from the rest ... in that it provides the most complete and high-quality mathematical education at the faculty.

The core of the curriculum is courses on optimal management. The essence of OA is to optimally move and control object A into set B. For all its abstractness, this problem has wide application in completely different areas. So object A can be a rocket, a machine gun in a plant, the plant itself as part of the economy, or even a portfolio of securities.

It is clear that in order to solve this problem, in the general case, you need to know a sickly carriage of mathematics - all this is given within the framework of department courses ... in functional and convex analysis (CA is the only department that helps OM to take credit for funkan), identification theory, i.e. stability , i.e. dynamical systems + some classes of ODE and PDE + Kalman filter and basic things about time series. The theory is accompanied by voluminous hands-on assignments that students complete in Matlab, the leading mathematical package for quantum engineers and financiers. Also, students are told how this whole theory is applied in mathematical biology, economics and financial mathematics ...

Despite the breadth of coverage - the depth of the material corresponds to the best traditions of the Soviet period ... the department also takes a responsible attitude to checking the knowledge of students - which favorably distinguishes its typical rasping attitude in other departments ... a student can take the exam-test ad infinitum until he learns the material ... my personal best was - 6 attempts (after I learned all the definitions - theorem proving - problem solving - the test was obtained in 20 minutes). As a result, CA students do not experience the slightest problem in passing on-line courses, which are read at a disgusting level due to the sheer number of lecturers.

The department employs wonderful specialists:
Kurzhansky is a founding father, a megamind, rarely visits Russia, but is always in touch, very demanding, stern but fair.
Bratus is one of the leading specialists in mathematical biology in the country, a very pleasant person with a very difficult fate.
Shananin is one of the country's leading specialists in mathematical economics
Arutyunov - pure mathematics, convex analysis, devotes a lot of time to his students
Lotov - multicriteria optimization, sits at the Institute of the Russian Academy of Sciences - I had little contact with him
Smirnov is a financial mathematics, SN does a lot of applied projects, his research interests are random processes, a wonderful person, but he has very little time for students.
And also several young guys Darin, Tochilin, Rublev
Unfortunately, many of them have to work part-time in other places, because the salary of professors is simply inadequate ... as a result, their time is limited, but if a student really wants to discuss something in scientific work, then they will always find time

Every year the department manages to collect talented children. Learning difficulties unite the team - I still keep in touch with many classmates - although I live on the other end the globe... Surprisingly, in terms of the percentage of honors graduates, the department is stable among the leaders at the faculty. The quality of theses also compares favorably with other departments, where most people work from the 4th year and their diplomas resemble a formal reply and not a serious one. scientific work... The department assumes full employment, rarely does anyone manage to combine it with work on the 3-4 course ... I had to combine it - because of this, unfortunately, I received much less knowledge at the department than I could.

Who do graduates work and is it worth it? Like the guys from other departments of the Academy of Sciences, they mainly work in IT and finance ... in our country, the demand for strong applied mathematicians is small - there is an opportunity to go to continue studying abroad (PhD)

Sometimes I ask myself which department I would choose if I were transported into the past - and I answer that I would choose SA again.

PS: Sori for my mistakes in the language, I don't often write in Russian.