Possible approaches to building the information and mathematical models to evaluate of the effectiveness and quality of the University are discussed in this paper. We characterize cycle of university management, determine the factors affecting the performance activity of universities, identify indicators of assessment of effectiveness and quality, formulate the problem of university management through the organization of control by this indicators. Proposes and explains the concept of integrated distributed information space and state the main problems that must be overcome in its implementation. Discusses the choice of the mathematical model of the organization of control of the effectiveness and quality of the University as a basis for making management decisions. Examines the complexity of the task of assessment of quality at the University, posit that the decision this problems by standard methods is very difficult. For the particular case of the solution of this task provides an example of using the randomized algorithm of stochastic optimization.