1 General information about electronic textbooks.

What is "The electronic textbook" and in what its differences from the normal textbook? Usually electronic textbook represents a set of the training, controlling, simulating and other programs placed on magnetic carriers (solid or flexible disks) PEVM in which the main scientific maintenance of a subject matter is reflected. EU often adds normal, and is especially effective when it: provides practically the instantaneous back communication; helps to find quickly necessary information (including context-sensitive search) which search in the normal textbook is complicated; significantly saves time in case of repeated references to hypertext explanations; along with the short text - shows, tells, simulates, etc. (exactly opportunities here are shown and advantages of multimedia technologies) allows quickly, but at speed the most suitable for a specific individual to check knowledge of a certain section.

It is possible to refer to shortcomings of EU not absolutely good physiology of the display as means of perception of information (perception from the screen of text information is much less convenient and it is effective, than reading the book) and higher cost in comparison with the book.

1.1 Requirements to system "electronic textbook"

Basis the principles for the environment of electronic textbooks include.

For effective functioning of the person in electronic system of training regardless of the task solved by the researcher, methods of visualization of basic data, the intermediate results of processing providing the uniform form of submission of the current and finite information in the form of displays, adequate to visual sensation of the person and the received results convenient for single-digit interpretation are of particular importance. The important requirement of the interface is its intuitivism. It should be noted that controlling elements of the interface shall be convenient and noticeable, at the same time they shan't distract from the main contents, except for cases when controlling elements are the main contents.

1.2 Requirements to design system "electronic textbook"

Requirements to design system "electronic textbook" the Technique of teaching of the discrete mathematics is a private component of system of pedagogical sciences. Much attention in pedagogics is paid to the didactics justifying and opening the contents, methods and organizational forms of education. Training activity is built according to the didactic principles on the basis of visualization, consciousness, systematic character, accessibility and durability of assimilation of knowledge, skills. Important condition of strong assimilation of knowledge is art of the teacher to cause interest to a subject. It is necessary to remember that computer textbooks are only the means strengthening possibilities of the teacher, but not his substitute. From this point of view we consider the problems connected to development of computer school textbooks.

First, users we break into categories. In perception of information and the form of messages of users the essential role is played by personal factors. In automated learning systems of the characteristic of trainees shall be represented in the form of models of trainees. It is necessary to set number of indexes by which the trainee is characterized, thus indexes can change on time.

Secondly, we develop model of knowledge which defines set of knowledge, skills which needs to be created at the trainee. Based on information on, whether the object of training is transferred to a required status or not, the decision on training continuation is made.

The study of features of the identity of the trainee is necessary in order that it was possible to define, what external conditions, what forms of interaction with a computer are for it the most suitable. Important point is the accounting of models of system of memory of the person. By development of a dialog it is necessary to create functions of submission of information for storage of sensor information, short-term memory, long-time memory.За последние годы число школ и классов с углубленным изучением математики резко увеличилось. Система предназначена для углубленного изучения дискретной математики и рассчитана на поступающих в академии, университеты, а также на начинающих учителей школ с углубленным изучением математики.

AOS consists of a triptych of electronic textbooks: "Trainer", "Program", "Labour training".

"Trainer" contains a specific didactic material. The set of the tasks is given in it, first of all the increased difficulty. To tasks solutions are proposed. In the textbook materials of entrance examinations, the mathematical Olympic Games of different years, materials of summer schools and collections, the materials published in different issues for persons, interested in mathematics are given. For example, logs of "American Mathematical Monthly", "Alpha" etc.

In the textbook "Program" main objectives and tasks of profound study of mathematics at high school are listed. We don't concern standard programs and we read justified study it is aware of algebra of the section "Introduction in Boolean algebra". In this section are considered: commutability, associativity, reversibility, contractility, existence of a neutral element, the reverse element, independence of properties, uniqueness of a neutral element, uniqueness of the reverse element, with associativity of action, communication between a reducibility and reversibility; equivalence of different determination of group; cyclic subgroups; classification of movements; main groups of conversions.

It is aware of geometry we offer the section "Introduction in Lobachevsky's plane geometry" since the Lobachevski geometry has huge developing and methodological value therefore pupils shall be though to some extent with it are acquainted. We give a material according to the following program: property of exterior angle of a triangle, sign of parallelism of straight lines; defect of a triangle, its property; equivalence of the 5th postulate and the statement about equality of the amount of angles of a triangle; independence of parallelism of a choice of a point through which the straight line is drawn; Lobachevsky's function, sign of dispersing straight lines; sign of equality of triangles on three angles; proportionality of the area of a triangle and its defect; description of models of Cayley-Klein and Poincare.

The electronic textbook "Labor training" contains introduction in "Calculus mathematics". Here the pupil learns to transfer mathematical theorems to a practical harmony, to make computing algorithms. The textbook contains the following material: absolute and relative errors, actions with approximate values; the linear interpolation, direct and reverse; Lagrange's interpolation polynomial; decision of linear equation systems Gauss method; numerical solution of the equations (bisection method, method of chords, method of tangents; combined method of chords and tangents, method of iterations); the linear programming (the transport task, concept about a simplex-method); approximative integration (rectangular formula, trapezoid rule, Simpson's formula); numerical solution of differential equations; Euler's method.

Ease in mastering and use of this environment for generation of electronic textbooks is reached due to application of visual technologies and possibility of use by the specialist subject teacher of any text and graphics editors for writing of contents of the electronic textbook. For convenience of operation the environment on generation of electronic textbooks assumes project development by separate parts that allows to organize operation over the textbook of several specialists subject teachers.