# Mathematics

Since the founding of the Mathematical Grammar School, professional groups of mathematics professors have had a special place and role, due to the nature of the school. The greatest successes are the big contributions to the development of the school system in our country.

We also achieved the biggest number of foreign and domestic awards for both professors and students and all of them are related to the work of our professional groups of mathematics professors.

Throughout the years, the main activities of these groups were:

- Implementation of regular classes with the constant improvement of curricula and introduction of new methods of teaching.
- Scientific, professional and pedagogical training of professors of mathematics and constant rejuvenation of assets by engaging young professors, mostly former students of the Mathematical Grammar School.
- Additional classes, especially through the preparation of students for competitions, both national and international. Also our professors actively participate in the work of the committee and jury for the competitions, and groups of mathematics professors have repeatedly hosted the Republican contest in mathematics, and once, in 2001 the International Mathematical “Balkanijada”
- Preparation of textbooks and other literature, primarily for regular, but also for additional classes, for both our grammar school, and for other schools.
- Participation at seminars, summer and winter schools
- Cooperation with other mathematical groups with similar programs in the country and the world.

As for the founding and the early years of our professional mathematical group we cannot omit Professors: Vojin Dajovic, his wife Milica Ilic-Dajovic and Vladimir Micic. Not only were they aware of how a school like this is needed, but they were the ones who established the mathematical group. They also gave their vast experience in working with young, talented mathematicians and created a special academic atmosphere in school. We can say that they were the ones who made the Mathematical Grammar School so specific. Professor Dajovic insisted from the beginning on involving a lot of young assistants from the University of Belgrade because he was aware of their immense contributions to raising students' knowledge and also the reverse process, that by working in this environment they would acquire the necessary experience for their educational work at the University. Here are some of the names: Ljubomir Protic, Jovan Malisic, Branislav Mirkovic, Mioljub Nikic, Arif Zolic, Bosko Jovanovic, Enes Udovicic, Mila Mrsevic, Miroslav Asic, Djordje Dugosija, Jovan Vukomirovic and many others.

From all our full-time teachers in the school, Branka Djerasimovic and Zivota Joksimovic especially stand out. Coming from a "mathematical family" Branka Djerasimovic, as a young professor with a lot of enthusiasm, passed on her passion for geometry to many generations of students of the Mathematical Grammar School. She always had time and patience for students, their ups and downs, endless energy for the extra work, participation in competitions, seminars, and magazines. Unfortunately a relentless disease stopped her before she gave all she could to the Mathematical Grammar School. Almost at the same time a young but already well-known professor of mathematics, Zivota Joksimovic, came to the Mathematical Grammar School.

After some time he became a symbol for teaching of algebra and analysis, an idol of our students and colleagues. His brightest students were the ones who achieved the greatest success in international Olympiads in mathematics in 1974 and 1999. Unfortunately the end of his radiant professorial career and the end of his life arrived at the same time. As soon as the first generations of students graduated from Faculty of Mathematics, our Grammar School has started the process; perhaps the most important for future work of our professional mathematical group - continuous hiring of our former students to work with new generations. Armed with knowledge and enthusiasm, by the nature of things, the best math students were becoming a mainstay in the teaching of mathematics in the seventies. Either as full-time employees, or working part-time: Zoran Kadelburg, Ljubomir Cukic, Vladimir Jankovic, Milan Bozic, Lazar Milin, Mirko Janc, Srdjan Ognjanovic, Dragoslav Ljubic, Vesna Jevremovic and Pavle Mladenovic.

Since the founding of the school our students were dominant in mathematical competitions. The first winners of the International Mathematical Olympiad in 1968 were: Kadelburg Zoran and Slavko Simic. The winnings were multiplied already the next year. On the domestic scene, republic competitions become almost school competitions for the students of the Mathematical Grammar School. Thus, for example, in 1978, in Cacak on the state competition in mathematics, all the prizes for all four grades were won by students from the Mathematical Grammar School, and in 1974 that seven of eight participants in the Yugoslav Olympic team in mathematics were students of the Mathematical Grammar School. All awards, except one, were won by students of the Mathematical Grammar School at the federal competition in Becej in 1998, and in 1998 and 1999, complete Yugoslav Olympic team consisted of students of the Mathematical Grammar School. The vast majority of these outstanding young mathematicians later took part in the school, either as teachers, or in preparation for the competitions of their young peers.

The most challenging blow for the Mathematical Grammar School was during the seventies and that was the decision to reform the educational sysetem. Everything that took years to create disappeared in an instant due to the careless government decisions of that time. The cooperation with the University was abolished, work in properly selecting talents was unabled and also the number of students in classes was increased. On the other hand, an unexpected recognition arrived from the same educational bureaucracy – the Mathematical Grammr School model of work and curricula was copied for many other schools (for exampel the mathematical – technical school).

A big group of young, ambitious professors from other Belgrade High Schools began working at the Mathematical Grammar School at the same time. Some of them were: Ljubinka Petkovic, Nenad Lazarevic, Mihailo Veljkovic (they stayed in our school until the present day, whereas others, for various reasons, didn't; among them were: Maja Mucalov, young and always smiling, Slobodan Tmusic, a renowned professor, who passed on his vast experience in working with high school students to the generations of students of the Mathematical Grammar School until his heart failure. This period was also special due to the fact that our professional group of mathematics professors,realized that there is not nearly enough literature, and so they begin thier work on the preparations of the work books with math problems. In the first ten years of the Mathematical Grammar School numerous Russian textbooks and workbooks was used: Fihtegoljc, Modenov, Cuberbiler, Lidski and many, many others. Workbooks in our language were extremely rare. Because of this, teachers were preparing work material from certain areas and, from time to time, multiplied and distributed it to students. Technical capabilities at that time were very modest, but great enthusiasm overcame all the problems. However, just in time of so called "vocational education" at the beginning of the eighties our professional group of mathematics professors decided to publish two workbooks, one for third grade (Mathematical Logic, Geometry, Trigonometry, Calculus and Probability - whose authors were Srdjan Ognjanovic, Mihailo Veljkovic, Branka Djerasimovic, Slobodan Tmusic, Zivota Joksimovic and Vesna Jevremovic)and one for the fourth (Linear Algebra, Analytical Geometry and Calculus from authors - Mihaila Veljkovica, Zivote Joksimovica i Srdjana Ognjanovica. Workbooks were published in 1984 and provided great help to our students. Other schools used them as well.

Since 1986 out professional mathematical group began intensive work on restoring Mathematical Grammar School. A commission was formed - Vladimir Micic, Ljubomir Protic, Zoran Kadelburg and Srdjan Ognjanovic. They tried to change the currently unsustainable situation through the institutions of the system, but also outside of it. Modeled after the old, new curricula were written, after obtaining the approval of the Educational Council. The new curricula had to be similar to the old one, but also in an experimental form. And so the energetic work began to return the identity - entrance examinations, teaching staff, cooperation with the University, the Mathematical Institute and Mathematical Society of Serbia. Programming and Computer Science became compulsory subjects and because of the increasing presence and importance of these subjects, it was decided to separate from the Mathematics group new professional group for Computer Science only. They constituted two directions in the beginning - general and programming, but during the experiment, which was completed in 1995, this idea was dropped. The first generation of the new program was enrolled in 1988 and immediately came success, primarily in competitions in Mathematics. During the period from 1993 to 1995, when international sanctions against our country demonstrated its pointlessness of the ban our students from participating at the international competitions, which are usually single, the cooperation with the most famous mathematical grammar school in the world - Moscow gymnasium "Kolmogorov" was quite successful. Grammar School "Kolmogorov” is under the auspices of the University of Lomonosov. Russian and our students have had several meetings, and this was a great opportunity for teachers to share their experiences.

The problem of lack of textbooks for students of Mathematical Grammar School was gradually resolved with tremendous dedication of our associates’ Zivorad Ivanovic and publishing company "Krug" who published the following textbooks: - Geometry I (Mitrovic, Ognjanovic, Veljkovic, Lazarevic, Petkovic) - Analysis I (Dragovic, Zolid, Kadelburg, Ognjanovic) - Analysis II (Kadelburg, Micic, Ognjanovic) - Analysis III (Kadelburg, Micic, Ognjanovic) - Analysis IV (Kadelburg, Micic, Ognjanovic) - Trigonometry II (Dugosija, Ivanovic, Milin) - Probability and Statistics (Malisic) - Probability and Statistics - a collection of problems (Malisic) - Solid geometry(Ivanovic, Ognjanovic) - Math H - Preparatory problems for enrollment in our school (Ognjanovic) In addition to this they released a textbook for linear algebra and analytic geometry (Milicic, Bajkovic, Doric, Veljkovic, Lazarevic, Ciric). Members of Mathematical professional group were also the authors of a large number of books - literature for the work of young mathematicians, mainly published by the Mathematical Society of Serbia. Our professional mathematical group significantly enhanced its personnel by including the old, and some new colleagues: Academic Milosav Marjanovic, Zoran Sami, Zoran Ivkovic, Milutin Obradovic, Dusan Georgijevic, Pavle Milicic, Milos Milicic, Mirjana Doric, Rade Todorovic etc. At that time, two experienced professors Dragoljub Jovanovic and Mihail Sopic begin to work at Mathematical Grammar School as permanent employees, and Vera Jockovic joined them later. During the nineties, the tradition of teaching geometry was lovingly nurtured by Milan Mitrovic.

A group of former students of the Mathematical Grammar School must be specially mentioned, because after the success of the International Mathematical Olympiad and more than successful studying at the university, with scientific work, they found time to work with students of the new generation in our school. These are some of them who are active since the beginning of the nineties: Ninoslav Ciric, Miodrag Zivkovic, Sava Krstic, Predrag Tanovic, Milos Arsenovic, Vladimir Dragovic, Aleksandar Vucic, Novica Blazic, Djurica Jovanov, Milena Radnovic, Dragoljub Keckic, Darko Milinkovic and many others. Seminars were held within the school, preparation for the entrance exam in mathematics for students enrolling in the first grade of high schools and colleges, but also additional classes for students of all grades of elementary school, even for preschool children. Professors, members of the Mathematical group, regularly participated in expert and scientific seminars and conferences in the country and abroad, cooperated with mathematical journals, working in committees of the Ministry of Education of Serbia, to improve education in the country, published scientific papers, were the authors of a huge number of textbooks and exercise books for all levels - from elementary school to post-graduate studies. They also came to the idea to establish the Department of Mathematical Grammar School at some schools outside Belgrade in order to popularize and develop mathematical education.

Thus, very well-functioning Mathematical departments developed in Novi Sad, Nis, Kragujevac, Valjevo, Kraljevo, Krusevac, Senta, and for some time in Podgorica and Leskovac. At the initiative of our professional mathematical group the school year of 1994-95 was the first time when mentor teaching was being carried out, using mentoring work that until then in our country did not exist anywhere. Classes were held in groups of 4 to 6 students. Such work allows much faster progress for the most talented students, deepening and broadening their knowledge, and differentiation in complexity, content, method and speed of learning. Additional teaching was also held as preparation for competitions. This preparation was usually run by our former students, Olympians, now students who through this also prepare themselves so that when they graduate, they can engage in regular work of the Mathematical Grammar School.

We should also mention an outstanding collection of math problems proposed for the International Mathematical Olympiad compiled by Vladimir Jankovic, Dusan Djukic, Ivan Matic and Nikola Petrovic and published by Springer, the world's leading publisher of scientific literature, which is available on the website of the Mathematical Grammar School. With a goal to harmonize the evaluation criteria of 1992, we introduced common written assignments, primarily from the analysis with algebra, then from other mathematical subjects. These problems provide objective evaluation in the form of multiple-choice tests since 1994, and since 2005 our professional mathematical group has been working intensively on further standardization and approximation of criteria and demands. They also organize traditional Mathematical Grammar School contest; provide support to our students for participation in the Tournament of the Towns and to conferences for young scientists.

Mathematical Grammar School team also participated in various competitions and tournaments in the World. Our professional mathematical group had an idea to extend the work of the Mathematical Grammar School to the best and most talented young mathematicians and students in primary schools. Favorable conditions for the realization of this idea came to pass in 2004. Many plans and programs were prepared, numerous consultations with experts were held, mathematicians and psychologists talked with students and their parents and so they began an experimental work with two classes of the seventh and eighth graders. On this occasion successful cooperation with a number of primary schools in Belgrade was established.

This work was crowned with excellent results which have surpassed all expectations. Our professional mathematical group is constantly taking care of its rejuvenation. When hiring new professors, the preference is given to young mathematicians who were the best students, and that means the former students of the Mathematical Grammar School. Our work with children of younger ages is constantly evolving. As a part of this project, what particularly attracted the public eye was the "Mathematical kindergarten" which gathers every Sunday and even children who still don’t go to school are more than welcome to attend. All of these years of work of our professional mathematical group were marked by enthusiasm, love and sacrifice. The results achieved have certainly far exceeded the idea of the founders of the Mathematical Grammar School. Just as we expect the future results will exceed our current expectations.