The comparative analysis of the most common systems of computer mathematics is made and their structure is described. The main functions of the systems of computer mathematics are determined and benefits and disadvantages of using the systems Derive, Mathematika, Matlab, Mathcad, Maple, MuPad, Gran, GeoGebra are directed. The Ukrainian software tool Gran is described which is used for graphical analysis of functions (Gran1), the systems of geometrical objects on the plane (Gran-2D) and objects in space (Gran-3D). The systems which are used for solving the algebra tasks (Mathematika, Matlab, Mathcad, Maple) are considered and the mathematical packages which can be used in the process of teaching the dynamic geometry (DG, Сabri II Plus, Geometers’SketchPad) are pointed. The system of dynamic geometry GeoGebra is considered in details which is the universal means for teaching algebra, geometry, mathematical analysis, theory of probability, mathematical statistics and other sections of mathematics. The system GeoGebra in the process of teaching mathematical subjects is used as means for visualization of investigated objects, expressions, illustration of the methods of construction; as environment for modeling and empirical study of the properties of the investigated objects; as a tool- measuring complex that provides the user with a set of specialized tools for creating and transforming an object, as well as measuring its predetermined parameters. The examples of solving the tasks in the system of dynamic mathematics GeoGebra with the main instructions of this process are considered. The processes of solving tasks in the system of dynamic mathematics GeoGebra and the other systems are analyzed.

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