In recent years, in view of the transformation in education in the Russian Federation, it has been necessary to introduce different technical facilities and new educational methods into the educational process. An introduction of training systems into the educational process concerns every educational method. New methods use various results from such fields as pedagogy, psychology, cybernetics, mathematics, and linguistics. Automated training systems consist of 3 components: informational, didactic, and ergonomic. This paper considers 2 components: didactic and ergonomic. They provide maximum learning with minimum energy consumption on the part of the trainee, in acceptable working conditions. As an example, this paper considers educational systems of calculus mathematics and mathematical geophysics realized in the Novosibirsk State University and Institute, Russian Federation.