Within its many activities "Archimedes" special attention to work with the best . To this end, in the "Archimedes" constant mathematical school organized a special working with mid-schoolers who were most successful in math competitions, and are potential candidates for JU-teams in international math competitions. Why and how to "Archimedes" works? International Mathematical Olympiad (IMO) began to organize the 1959th year. Yugoslav team first participated in the Fifth IMO held 1963rd year. Since then we have participated at all IMO, except the 1993rd when we canceled the participation due to the difficult international position in which the then Yugoslavia was and 1994. when we are denied the right to participate because of UN sanctions. Balkan Mathematical Olympiad (BMO) began to organize the 1984th year. Our team has participated in all BMO starting from 1987. year.
Yugoslav Olympic team
Yugoslav Olympic team
after returning from Mar del Plata 1997
Preparation and organization of the participation of our team at IMO Union of Societies of Mathematicians Yugoslavia was confided to a republican society of mathematicians (usually it was Mathematical Society of Serbia). To 1995 the team preparing for the IMO took place during one week before the start of competition. Since 1995. year (when our country back to the movement IMO) preparations are extended to two hours per week. Next, 1996. year introduced a novelty: a potential candidate for the composition of the team for IMO (and BMO) are invited to a week of preparations, which were held earlier this year (in winter), and then came together for another week to prepare for national competitions. Before starting the IMO, as the previous year, were held two weeks of preparation. No, but then felt that this type of work is insufficient to adequately prepare the team for the intense competition in the international competition and the need to work with organized candidates for the Olympic team during the entire school year, and then, when the team determined - with its intensive members.
Many members of our current Olympic team during his eight years of schooling attended the "Archimedes' mathematical school and made the first" mathematical "steps, and winning awards in math competitions. Some of them have lost interest in "Arhimedesovu" school or later in high school have also been successful mathematicians. Most are without difficulty enrolling in high school Mathematics, a math competitions have increased great results. But the competition at the international level was becoming bigger.
- To fill the void in our lives and mathematics to meet the wishes of the students, "Archimedes" from the beginning 1997/98 school year organized a special "Olympic group" to work with talented and most successful mathematicians - srenjoškolcima. To participate in the work of this group were invited to all those who are in high school math competitions in previous years have proven to possess exceptional mathematical talent and ability, so that they can be counted as a candidate for the future of our representative teams. The aim was to them the conditions for mathematical development at the highest level. All costs were covered by the Olympic Group "Archimedes". Symbolic resources for the work requested by the competent institutions, "Archimedes" has not received.
The main activity of "Olympic Group" was the teaching that took place once a week for two hours, usually on Saturdays from 11 am. In cases where the term has been busy (for example, when they held a mathematical competitions), classes were held in some other period (usually Sundays).
At the 22 meetings (60 hours), held during the 1997/98 (October - June), the following subjects: Ireducibilnost polynomials, Liouville's theorem, Dirichlet's theorem, Farejevi arrays, Pell's equation , Severability of integers, Linear Diophantine equations, congruences and residue systems, linear congruences and systems of linear congruences, Congruences of higher order, quadratic congruences, Recurrent relations, Tournament of Towns - Tasks, Math games, Convex functions, exponential congruences, Morlejeva theorem, inequality systems , tasks proposed to the IMO-95.
The work group has been involved a total of 20 students (14 students from the Mathematics High School in Belgrade, two other students from Belgrade High School, three students from high school "JJZmaj" in Novi Sad, and one student from Valjevo high school).
- Most students attend classes year round, and when elected in March Olympic team, are invited to join the group and those team members who attended the "Archimedes".
- "Olympic Group" continued to work and school in 1998/99. year . Principle of operation remained the same. The work of the group were included 12 students, 10 of which were from the Mathematics High School in Belgrade. Most of them were in the Olympic group and the last school year.
- At the 40 meetings (110 hours), held during school's 1998/99. year (October-July) with following subjects: Packing squares, Environment geometric figures, Izoperimetrijski problem, inverse, system geometry, with the tasks of the Tournament of Towns, Combinatorics (generation), Combinatorial geometry (grades angles), graphs, circles that touch, Tasks on the corners, The "whole part", Kronecker's theorem, Theorem Cebis, Cenc hypothesis, binomial coefficients, finite differences, Numeric triangles, Mirhad inequality, Some properties of convex figures, evaluation areas, proposals for tasks IMO in 1998, and Baricentar baricentrical coordinates, The moment of inertia, complex numbers in the pyramid.
- The speakers were: Dr Vladimir Jankovic , Djordje Milicevic Miroslav Treml, Dr. Ratko Tosic, etc. Miodrag Zivkovic. Were selected according to the strictest criteria. Four of them have participated in past International Mathematical Olympiad (IMO), where they won seven medals (one gold, five silver and one bronze). Most of the lectures during the two years he held a long-time associate of "Archimedes" and renowned expert in working with gifted young lovers of mathematics - Dr Vladimir Jankovic Faculty of Sciences in Belgrade.
For all lectures listeners were given mimeographed consisting of choice of task and often theoretical introduction. They also organized making photocopies of books that are here can be found, are a classic high school math literature.
- 1999/2000 school year (October-June), Olympic Group has continued to work. It was early October. with 22 students (20 students from MG in Belgrade, according to one student from Novi Sad and Valjevo). Besides the above mentioned, are also included new teachers in their work, for example: Dr. Milos Arsenovic (the old "silver" Olympian), Dusan Djukic and Ivan Matic (Young Olympians). Principle of operation remained the same. At the 28 meetings (76 hours) dealt with topics: Quadratic Diophantine equations, theorems Pique, Recurrent equations, rational values of trigonometric functions, exponential congruences, functional equations, Blihveldova theorem, Combinatorics (generating), Combinatorial geometry, harmonic division, Tasks for the 21st Tournament of Towns, Selected problems of competition, selected tasks from the IMO.
They were with us first and only continuous systematic preparation (all year) candidate for the Olympic team and the team, which took place the previous three years.
- The results were there. Here are just a success in international competitions.
- At the international mathematical competitions 1998th and 1999. Our six-member team has achieved much better results than previous years. On Balkan Mathematical Olympiad (BMO) 1998. she was the second (1997. fourth year, 1999. was not involved - because of the war) and all team members have won medals. To 39 IMO 1998. in Taiwan, our team was on 10 among the 76 teams with 5 silver medals (the 38th IMO 1997. year 20-21. among 82 teams). It is little known that in this year (1998) to the IMO the only Yugoslav team had more points (much higher) than the previous IMO. On the 40th International mathematical Olympiad (IMO ) in mid-July 1999. The Yugoslav team in Romania is ranked 14 place among 80 countries and all team members have won medals (six medals): one gold ( Dusan Djukic ), two silver and three bronze.
On 41.Internacionalnoj Mathematical Olympiad (IMO) in mid-July 2000. in South Korea, won four medals got "Arhimedesovcima" - JU-team members (see section SUCCESS ).
- The Olympic group worked during the school 2000/2001 year (fourth years) with 15-20 students (who regularly attend the Mathematical High School in Belgrade). Held of 30 meetings (80 hours).
Topics were covered: Positional numbering systems, the measurement tasks, Parity permutations, graphs, Continued fractions, exponential congruences, basic analytic inequalities and their applications, Karamata inequality Karnoova theorem, circles that touch , Casey's theorem and applications, Apollonius configuration, Combinatorial geometry, Dekartoovo rule and related methods for locating the real roots of polynomials, Quadratic forms, Cauchy's theorem on convex polyhedra, with the tasks of the Tournament of Towns (more meetings, all variants), problems with the cities of the Summer Conference Tournament , tasks with earlier IMO, the IMO proposed tasks, tasks of the 38th IMO, Various issues.
The speakers were: Dr Vladimir Jankovic , Miodrag Zivkovic, Dr. Danko Jocic, Djordje Milicevic, Dusan Djukic .
At the Balkanic mathematics (3-9. May in Belgrade) all "Arhimedesovci" JU-team members have won medals (5 medals). Similarly, the International Mathematical Olympiad (1-July 14 2,001th in Washington) all four medals were given to "Arhimedesovci".
- Olympic Group has worked in the academic 2001/2002. year with 18-20 students (all from MG). There have been 25 meetings (75 hours). Topics covered: Formula on / off, a fantastic task (Conway), Blihfeld's theorem, Operator differences, Finite and divided differences, with the 42nd Tasks IMO, the 23rd Tasks Tournament of Towns (more meetings), Polynomials, Inequalities, Quadratic Diophantine equations, similarity (tasks), tasks on the corners, circles enrolled in a triangle (tasks), tasks of circles that touch, Complex numbers and their applications in geometry.
Speakers: Dr Vladimir Jankovic , Dr. Milos Arsenovic, Dr Ivan Anic, Dusan Dukic, Milivoje Lukic .
On the 19th Balkanic in mathematics for high school students (Turkey, 25-30. April 2002.) In the hexagonal team there were three "Arhimedesovca" and they all won medals. To 43 IMO (held in July in England) in PI-team there were three "Arhimedesovca" and they all won medals. The participants at the International Mathematics Tournament of Towns (from the period 1999-2002) are discussed in a separate section (International Tournament of Towns). And in this competition all "Arimedesdovci" received awards.
- Olympic group worked in the school 2002/2003 year with 20 students (17 from the MG, one of the grammar school Obrenovac and two from other schools).
- Held 25 meetings (75 hours). Topics covered: Tasks with BMO and IMO, the tasks of the Tournament of Towns, Chebyshev's theorem, ekstremalne problems in geometry, remains China's theorem, Kronecker's theorem, inequalities, helium theorem, Numeric triangles, inequalities systems, linear recurrent equations, combinatorial tasks (with counting ), Combinatorial geometry, essay on the table POLIMIN, Forests potency of natural numbers, symmetric polynomials, ekstremalne problems Izoperimetrijski problem, Various tasks.
Speakers: Dr Vladimir Jankovic , Dr. Djordje Dugosija, Dr. Milos Arsenovic, Dr Ivan Anic, Dusan Dukic, Milivoje Lukic .
The hexagonal cast our country's 20th Balkanic in mathematics for high school students (Tirana, 1-9. May 2003) and 44 IMO (Tokyo, 9-19. July 2003) there were four "Arhimedesovca" and won a total of 7 medals (3 silver and 4 bronze) and a compliment. The participation and success in International Mathematics Tournament of Towns in school's 2002/2003. year are discussed in a separate section (International Tournament of Towns). And in this competition all "Arimedesians" received awards.
- The Olympic group has the academic year 2003/2004. year with 20-23 students (20 from 2 MGI from other schools). In the framework of "Archimedes" was held 13 meetings (40 hours) and several meetings of the Faculty of Mathematics (organized jointly with the Mathematical Society of Serbia).
Speakers from the "Archimedes": Dr Vladimir Jankovic, Dr. Milos Arsenovic, Dusan Djukic . Topics covered: The tasks of the IMO, Diophantine equations, inequalities, Baricentar, exponential congruences, Chains and antilanci, Tasks with the Tournament of Towns, Complex numbers and planimetry, Various tasks.
The speakers were: Dr. Milos Arsenovic, Vladimir Jankovic and Dusan Djukic (with the Olympic gold medal).
On the 21st Balkanic in mathematics for high school students , which was held in early May in Turkey hexagonal SCG team was 5 "Arhimedesovca" and they all won medals (prizes). On the 45th International Mathematical Olympiad (IMO) for high school students, held in Athens on 4-18. July 2004. , in the hexagonal M-team also consisted of 5 "Arhimedesovca"-prepared students in the group and Olympic medals than 5 all went back "Arhimedesovcima": two silver ( Marko Radovanovic and Milan Novakovic ) and three bronze ( George Baralic, Uros Rajkovic, Aleksandar Pejčev ). The colors of Belgrade on the 16th Summer Tournament konfrenciji cities, held in Belarus in early August 2004, defended the four "Archimedes" Olympian and they all get prizes (to be discussed in detail in sections International Tournament of Towns and Success )
- The Olympic group worked in the school 2004/2005 . years (eight years) and in two sections: the first Olympic group (I r. secondary schools with 23 students) and the second group (II, III, IV r. SS with 5-6 students). See detailed in a separate notice (little competition).
- The Olympic group worked in the school 2005/2006 . (nine years) with 16 students (14 from II development. Mathematics High School, one of I r. MG 1 and VIII of the r. PS), the same principles as before.
- The Olympic group worked in the school 2006/2007 . years (ten years) and with two classes: first Olympic group (students and rye. secondary schools, mostly from MG) and other Olympic groups (II-IV r. SS), a total of 26 students.
- The Olympic group worked in the school 2007/2008 . years (eleven years) with about 20 students (mostly from MG). This is discussed further discussed in a separate notice.
- The Olympic group worked in the school 2008/2009 . year (twelve years).
- The Olympic group worked in the school 2009/2010 . years (thirteen years) with about 20 participants.
- The Olympic group worked in the school 2010/2011 . year (year XIV).
- The Olympic group worked in the school 2011/2012 . year (year XV).
- The Olympic group worked in the school 2012/2013 . year (year XVI).
- The Olympic group worked in the school 2013/2014 . year (XVII).
- The Olympic group worked in the school 2014/2015 . year (XVIII).
- The Olympic group will work in the school 2015/2016 . year (XIX). For information (Small contest) click here !
- "Archimedes" project was completed and procurement of books from abroad for members of the Olympic Groups , and continue copying the few books that are not available.
- The self and "Archimedes" Libraries , which contains over 25,000 books and a large number of sets of periodicals. In content and number of titles to the Library Of Unified in Belgrade. At the high school service (especially in the preparation of graduation papers), students and teachers. It is still not complete anktivirana library. Until a proper solution, which would allow the activation of the complete library, particularly one of its active segment that is of interest primarily for members of the Olympic group.

© 1998 - 2015, MS "Archimedes"