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Higher mathematics


Department of Higher Mathematics




Currently, the department employs 34 people, including:

1 member correspondent of the Russian Academy of Sciences;

8 professors;

16 associate professors;

7 senior teachers;

2 assistants,

including 16 candidates and 9 doctors of science.


  1. Faculty of Motor Transport
  2. Faculty of Road and Technological machines
  3. Energy and Environmental Faculty
  4. Faculty of Road building



  • Mathematical analysis;
  • Linear Algebra and Analytical Geometry
  • Equations of mathematical physics
  • Theory of functions of a complex variable
  • Graph Theory and Mathematical Logic
  • Optimization methods
  • Operations research
  • Differential equations
  • Probability Theory, Mathematical Statistics, and Theory of Random Processes
  • Mathematical modeling
  • Numerical methods
  • Management theory
  • Software and hardware informatics
  • Computer programming
  • Computer graphics
  • Computer operating systems and networks
  • Databases
  • Discrete Math
  • Application Programming and Software Packages
  • Sustainability theory
  • Approximation Methods
  • Partial Differential Equations
  • Functional analysis
  • Special Heads of Applied Mathematics
  • Theory of ordinary differential equations
  • Differential equations and their application
  • Theory of Extreme Problems
  • Computing and Networks in the Industry
  • Intelligent systems
  • Interactive graphic systems
  • Computational methods and mathematical packages
  • Mathematical Data Processing Methods
  • Intelligent car systems
  • Intelligent systems in the modeling of traffic flows
  • Fundamentals of Engineering and Scientific Experiment
  • Computer Technology Learning
  • Computer Learning Basics



  • Functional analysis
  • Asymptotic Analysis
  • Principles of building mathematical models
  • Intelligent systems
  • Logic and architecture of computing environments
  • Parallel and Distributed Programming
  • Statistical analysis
  • Theory of Fuzzy Sets and Fuzzy Logic
  • Schedule theory and generalized transport problem
  • Information and Complexity
  • Distributed computing
  • Cryptographic methods of information security
  • Modeling complex socio-technical systems
  • Dynamic systems
  • Random walks on networks
  • Queuing theory
  • Graph Theory and Their Applications
  • Processing visual information and pattern recognition
  • Traffic flow theory
  • Mathematical methods in biology and psychology
  • Discrete Mathematics Problems
  • Numerical problems of mathematical physics

Science Achievements

Since the mid-90s of the last century, a research direction on the mathematical modeling of traffic flows and the design of intelligent systems in the automotive industry, formed by Professor A.P. Buslaev, has been developing at MADI. These studies are directly correlated with the following Basic Research Programs of the Russian Academy of Sciences, namely, “Fundamentals of creating algorithms and software for high-performance computing” and “Fundamental mathematics and its applications”.
Professor A.P. Buslaev developed a deterministic-stochastic approach for modeling traffic flows. The data on the basis of which the specific implementation of the model is refined is collected using detectors on highways, as well as using mobile laboratories equipped with video capture tools, mobile sensors, and smartphones. Mobile laboratory created by A.P. Buslaev on the basis of the Department of Higher Mathematics MADI, allowed to obtain, process and analyze video data, using the developed hardware software and computer vision methods, to calculate the characteristics and make further amendments to the mathematical models under consideration.

One of the applications of the developed algorithms was the detection of road surface defects to further increase the roadway capacity.

The use of mathematical models of traffic contributes to solving the problems of optimal control organization on road networks. The adequacy of mathematical models is based on checking of data obtained from measurements on highways. This determines the relevance of developing data processing algorithms obtained as a result of such measurements, in particular, video analysis algorithms for the characteristics of the traffic flow, algorithms for image recognition in an uncontrolled dynamic environment, and data transfer processes optimization during the operation of vehicles.

The employees of the department of Higher Mathematics, graduate students and undergraduates carry out research work commissioned by the Ministry of Education and the Russian Foundation for Basic Research:

  • «Models, mathematical problems and saturated flow theorems on complex chainmail networks»
  • «Client - SSSR server system for monitoring, modeling and managing distributed socio-technical objects»
  •  «Investigation of the properties of cluster and stochastic simulation models of flows on regular networks»
  • «Computer methods for traffic modeling on networks and info-communication technologies for verification and testing»
  •  «On qualitative theorems in the problem of modeling the motion of many-particle systems along discrete lattices»
  • «Algorithms and technology for on-line recognition of moving objects and flow characteristics on mobile devices»
  • «Study of the qualitative properties of information flows on linear-ring networks»


Students Activity

  • Systems of Signals Generating and Processing in the Field of on Board Communications, Moscow, Russia;
  • Systems of Signal Synchronization, Generating and Processing in Telecommunications (SYNCHROINFO), Yaroslavl, Russia;
  • International Conference Computational and Mathematical Methods in Science and Engineering, Rota, Cadis, Spain;
  • International scientific-methodical and research conference MADI;
  • International Conference "Information Technologies and Innovations in Transport", Oryol, Russia;
  • Multiconference on management issues, Divnomorskoye, Gelendzhik, Russia;
  • International Conference on Machine Vision (ICMV), Amsterdam, The Netherlands;
  • International Conference on Digital Solutions for Automotive Industry, Roadway Maintenance and Traffic Control (DS ART)


The department’s teachers are well-known scientists in the field of mathematical modeling, robotics, elastic body physics, as well as leading industry experts, with the help of which students receive relevant knowledge and skills that are in demand in the modern labor market in the context of digitalization of the economy.

Throughout the entire period of study, in addition to obtaining theoretical knowledge in the walls of MADI, students have the opportunity to attend Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, as well as gaining practical skills in such companies as:

  • LLC «Center for Design Technologies of State Public Institution Center for Organization of Traffic of the Government of Moscow»
  • LLC « Rostelecom Data Storage Center»
  • State Company «Russian Highways»
  • LLC «Tanais»
  • PJSC  «SDM-Bank»
  • LLC "ErPi Band

and others in the process of the implemented practices.

Students interested in a scientific career are given the opportunity to participate with reports in Russian and international conferences, grants and publish their results in leading scientific journals indexed by the Web of Science, Scopus, RSCI databases.

Implemented study methods allow graduates to remain sought-after specialists, despite the constantly changing trends in the development of society.

Where you can work

Graduates of the Department of Higher Mathematics are in demand in the market in various fields of economics and economy:

  • administration and development of databases
  • computer modeling
  • computer industry
  • banking
  • telecommunications
  • education
  • big data analysis.

The main employers for graduates are international and Russian companies:

  • «Rostelecom»
  • «Rosatom»
  • LLC «NetCracker»
  • «Vimpelcom»
  • BSS «Russian Space Systems»

and others.

The most promising professions are:

  • business analyst
  • mathematician-analyst
  • database programmer
  • system programmer
  • SMM
  • scientific worker.


Head of the Department: Ph.D., Doctor of Technical Sciences, prof. Yashina Marina Viktorovna

Phone: +7 (499) 155-04-36


Email: mathematics@madi.ru