The work aims to offer those interested – students and teachers – a logical, efficient and challenging algorithm for exploring the labyrinth of mathematics, being a useful tool in both teaching-learning and recapitulation.Going through it means for teachers a landmark of current activity and assessment hours, and for students a way to systematize knowledge, at a pace that can ensure their success. One of the novelty elements of the paper is the design and organization of exercises and problems on two levels: one aimed at the usual level (average) – the student interested in clarifying and fixing his notions and results presented in class – and one addressed to the level performing, represented by the student eager to participate in competitions and school Olympics.
In this way, we want to develop everyone’s confidence in their own strengths, so that the ever-increasing interest in mathematics is a guarantee of everyone’s success. To this end, all 10 chapters contain, at the beginning, a theoretical summary and end with three tests, which may be the subject of extemporals or theses.
The selected problems are ordered gradually, according to their difficulty, those addressed to students passionate about mathematics being grouped in the recap paragraph at the end of each chapter. On the other hand, we aimed to ensure that the number of problems necessary for understanding the theory, the formation of computational skills and logical thinking is large enough, but we also considered ensuring the variety of types of exercises and solving ideas, so as to avoid monotony.
Most exercises / problems are accompanied by solutions with complete demonstrations, but due to lack of space, density and volume of material (over 1500 problems) we had to limit ourselves to some indications or only to indicate the result.
The concentric and gradual organization of the notions involved in the proposed exercises and problems, the resizing stages of the theoretical and informative material, the integrative vision on the seventh grade program and the development of a differentiated system of assimilation and verification of students’ knowledge, an efficient and useful work guide for students and teachers, in completing the training route in which they are involved.