نبذة مختصرة : Cilj ovog rada je obraditi i proučiti dodatne teme iz matematike koje se pojavljuju na matematičkim natjecanjima, ali se ne obrađuju na redovnoj nastavi. Rad je zamišljen kao radni priručnik za dodatnu nastavu. Svaka tema se prvo opisuje, potom se rješava nekoliko zadataka s primjenom teme te se potom obrađuju zadaci s natjecanja. Na početku ćemo reći ponešto o samoj pripremi i edukaciji učitelja za dodatnu nastavu. Predložit ćemo i mogućnosti poboljšanja pripreme učitelja. Potom ćemo se upoznati s metodom uzastopnih približavanja te Gaussovom dosjetkom. Naučit ćemo što je to Dirichletov princip, te kako ga primjenjujemo. Pojasnit ćemo i što su diofantske jednadžbe te gdje ih koristimo, a na kraju ćemo se upoznati s logičkim i kombinatornim zadacima te zadacima s prebrojavanjima. ; The goal of this master thesis is to interpret and study additional topics in mathematics that appear in mathematics competitions but are not covered in regular classes. A thesis is intended to serve as a teacher’s handbook for advanced mathematics classes. Each topic is described, and the description is followed by several solved tasks with the application of the topic and eventually the tasks from the competitions are presented and solved. At the beginning, we will say something about the preparation and education of teachers for teaching in advanced classes. We will also give suggestions on how to improve teacher training. Then we will learn about the method of successive approximations and Gauss's Trick. We will learn what the Dirichlet principle is, and how we apply it. We will also explain what Diophantine equations are and where we use them, and at the end we will get acquainted with logical and combinatorial tasks and tasks with counting.
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