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The accuracy of compound Poisson approximation to the sum S = w 1 S 1 +w 2 S 2 +· · ·+w N S N is estimated. Here S i are sums of independent or weakly dependent random variables, and w i denote weights. The overall smoothing effect of S on w i S i is estimated by Lévy concentration function.

The article investigates possibilities to use Mensa puzzles in education of gifted children. Mensa – largest and probably the most famous international organisation of people with high IQ, that includes people of various races, beliefs, age and social background, who pass a special test. In the article, we explore how the puzzles developed by the organization could be applied both working with the students that are gifted in mathematics, and making the usual math lessons at school more interesting.

The article explores symmetry as tactics in solving various mathematical problems. Although in Mathematics curriculum while learning about Geometry, symmetry is taught and simple straightforward exercises are solved, it is argued that the application of symmetry could be much wider. It is especially useful as a strategy in solving non-standard math problems. The article presents examples of the use of such tactics as well as results from the experiment on the use of symmetry at school.