# Mathematical Grammar School

Mathematical Grammar School (Serbian: Математичка гимназија Београд, romanized: Matematička gimnazija Beograd, abbr. "MG" or "MGB"), is a special school for gifted and talented students of mathematics, physics and informatics located in Belgrade, Serbia.
The School has developed its own Mathematical Grammar School Curriculum in various mathematics, physics, and IT subjects. There are approx. 160 teachers employed, mostly scientists. One half of the professors comes from University of Belgrade staff, Institute of Physics Belgrade, and Mathematical Institute of Serbian Academy of Sciences and Arts. More than half of the teachers are former students of the school. The average professors' work experience is 18 years.
In 2011, the school had 550 students aged 12–19. There were 155 girls and 395 boys.

## History

The school was established in 1966, following the model of Kolmogorov School at Moscow University which had been launched in Moscow a year earlier, in 1965, under Lomonosov Moscow State University, by one of the greatest mathematicians of the 20th century, Andrei Nikolayevich Kolmogorov, and which was later named after him – Kolmogorov School.
In 1977, as part of a statewide education reform in former Yugoslavia, the School was merged into the streamlined secondary education (in Serbian: srednje usmereno obrazovanje), thus cancelling many, but not all, specifics and advantages over other schools. At that time principal, Milan Raspopović was desperately pulling strings in scientific and policy-making community to re-establish special status, special rights, special funding, and special curriculum. As a result, eleven years later, in 1988, the School was officially re-established as a specialized school, this time in the form of an experimental education institution. New curriculum was officially published in 1989, in Official Gazette of Socialist Republic of Serbia, no.2, 15 April 1989.
The "experimental status" finally concluded in 1995, when the School was recognized as a "Specialized school for talented/gifted students in mathematics, informatics, physics, and other natural sciences" by the Serbian Ministry of Education. At the same time, the School was given the status of a "school of special national importance", as the first school of its kind in Yugoslavia.
Although MGB is formally classified as a special secondary school ("srednja škola", grades nine to twelve in the Serbian education system, for funding and other legal reasons), it enrolls experimental classes of the seventh and eighth grade primary school (age 12 and above). It is the only school in Serbia and in all states formed from former Yugoslavia that has merged elementary school (or part of it) and high school.
Students of Mathematical Grammar School have the highest grade point average (GPA) compared to students from other schools and the same rule applies to their university studies, whether in Serbia or abroad.
See also: Academic grading in Serbia and Education in Serbia.

## List of school principals

The School has had 7 principals in its history, all of whom are authors of university, high school, and elementary school textbooks and accompanying collections of solved problems and questions. Five principals were mathematicians, and one – and the longest serving principal – was a physicist.
Five MGB principals with Doctor of Sciences titles, and one with Doctor of Science title, earned their degrees at University of Belgrade and served as university professors and as professors at Mathematical Grammar School.
| Year | Principal |
| 1966–1968 | Ranko Radovanović, Magister of Sciences, director of Educational and Pedagogical Institute |
| 1968–1971 | Dušan Adnađević, Doctor of Sciences in Mathematics, University of Belgrade; Faculty of Natural Sciences and Mathematics, retired |
| 1971–2001 | Milan Raspopović, Doctor of Sciences in Physics and Philosophy, University of Belgrade; Faculty of Electrical Engineering, retired |
| 2001–2004 | Ljubomir Protić, Doctor of Sciences in Mathematics; University of Belgrade |
| 2004–2008 | Vladimir Dragović, Doctor of Sciences in Mathematics, University of Belgrade; Faculty of Mathematics |
| 2008–2019 | Srđan Ognjanović, Magister of Sciences, University of Belgrade; Faculty of Mathematics |
| 2019–present | Mirjana Katić, University of Belgrade; Faculty of Mathematics |

## Competitions

The School prepares students for various national and international competitions science competitions. As of 2012 Mathematical Grammar School students had won several hundred medals from top international competitions around the world. They won 121 medals at International Science Olympiads, about the same number at Junior Olympiads, and about double that number at other top competitions, mostly in USSR, Russia, China, India, and Europe.

### International Olympiads

MGB students have won many national and international awards.
| Number of medals | Competition |
| 121 | International Mathematics Olympiad |
| 52 | International Physics Olympiad |
| 23 | International Olympiad in Informatics |
| 28 | International Astronomy Olympiad |
| 8 | International Olympiad on Astronomy and Astrophysics |
| 16 | Olympiads in General Science |
| more than 400 | various other international competitions |

### Year 2009

In 2009, during July and August, students of Mathematical Grammar School won 12 medals in International Olympiads: 5 medals in Olympiads in Mathematics, 4 medals in International Physics Olympiad, 3 medals in International Olympiad in Informatics, 3 medals in International Olympiad on Astronomy and Astrophysics, 1 medal, and 3 honorable mentions in International Astronomy Olympiad.
The total number of gold, silver, and bronze medals, and honorable mentions, won in various international competitions in 2009 is 70.

### Year 2010

At the 2010 International Mathematics Olympiad (5–15 July 2010, Kazakhstan), Serbia was represented by a team of 6 competitors, all 6 students from Mathematical Grammar School, 15–19 years old. The result is Serbia ranks 10th in the world, with 1 gold, 3 silver, and 1 bronze medal won, and the Mathematical Gymnasium school ranks as the best (rank: 1) school among all special and/or regular schools in the world.
| Medals | Competition |
| 1 gold, 3 silver, 2 bronze | 51st International Mathematics Olympiad, Kazakhstan |
| 4 bronze | 41st International Physics Olympiad, Zagreb, Croatia |
| 1 bronze | 22nd International Olympiad in Informatics, Canada |
| 1 gold, 1 silver, 2 bronze, 1 honorable mention. | International Astronomy Olympiad, Crimea, Ukraine |
| 1 gold, 2 silver, 1 bronze, 1 h.m. | International Olympiad on Astronomy and Astrophysics, China |
| 5 gold, 4 silver, 3 bronze | Mathematics, Kolmogorov Special School, International Competition, Moscow, Russia |
| 3 gold, 3 silver | "Archimedes" International Competition in Mathematics, Romania MGB awarded "Absolute Winner" title. MGB student Vukašin Stojisavljević was overall ranked as first. |
| 1 bronze | Balkans Olympiad in Informatics, Montenegro |
| 1 silver, 1 bronze | 14th Junior Balkan Mathematical Olympiad, Romania |
| 2 gold, 2 bronze, 2 silver | XXVII Balkan Mathematical Olympiad, Moldavia |
| 2 silver, 2 bronze | Euler's Russian Olympiad in Mathematics, Russia |
| 2 silver, 1 bronze, 1 h.m. | Romanian Master in Mathematics, Romania Romanian Master in Mathematics is an Olympiad for the selections of the 20 top countries in the last International Mathematical Olympiad, i.e. for the best 100 high-school mathematicians in the world |
| 1 silver, 3 bronze | 7th Junior Scientific Olympiad, Nigeria |
| In total: 57 medals, 3 honorable mentions | at some of the major international competitions in 2010. |
In 2010, students of Mathematical Gymnasium have won 28 medals and honorable mentions namely: at 2010 Olympiad in Mathematics (5–15 July 2010, Kazakhstan) 6 medals: 1 gold, 3 silver, 2 bronze; at Euler's Russian Olympiad in Mathematics (24–27 March 2010, Russia), Mathematical Gymnasium was the only non-Russian competitor and its 4-members team won 4 medals: 2 silver and 2 bronze; in highly selective Romanian Master in Mathematics (24 February – 2 March 2010, Romania): 2 silver and 1 bronze medal, and 1 honorable mention (Romanian Master in Mathematics is an olympiad for the selections of the 20 top countries in the last IMO. The level of the competition is IMO-like. The format had been 4 problems in 5 hours in 2009, in 2010 it was changed to 3 problems in 4 hours, two days format.); at XXVII Balkan Mathematical Olympiad (3–8 May, Moldavia) 6 medals: 2 gold, 2 bronze, 2 silver; at International competition "Archimedes" (7–18 June 2010, Bucharest), Mathematical Grammar School won the first place, and its 6 students took 6 medals: 3 gold and 3 silver medals; at XIV Junior Balkan Mathematical Olympiad (18–22 June 2010): 1 silver medal and 1 honorable mention.

### Year 2011

In the All Russian Mathematical Competition, organized by the Kolmogorov Special School, the Mathematical Grammar School won, "The Absolute First Prize in all categories", and one MGB student, Teodor von Burg, won the gold medal, first prize, and maximum number of points. This is the 2nd time MGB won the Kolmogorov competition.
| Medals | Competition |
| 1 gold, 1 silver, 1 honorable mention | Romanian Master in Mathematics, Romania Romanian Master in Mathematics is an Olympiad for the selections of the 20 top countries in the last International Mathematical Olympiad, i.e. for the best 100 high-school mathematicians in the world |
| so far: 2 medals, 1 honorable mentions | at some of the major international competitions in 2011. |

### Other prizes and awards

Students of Mathematical Grammar School have won many other prizes in addition to the International Science Olympiads.
As part of the "27 Club", which Erste Bank implemented for the third consecutive year in 2010, with the aim to promote talented young people and help them to get well-deserved public recognition for their work and the results, 2010 year's award winners were declared. In the category of science, the winner of a Grand Prize was Luka Milićević, and the winner of Erste Bank Prize in the field of natural and technical sciences and technology was Dušan Milijančević. Both students are final year students of D-division of Mathematical Grammar School.
At Microsoft's Imagine Cup, students of Mathematical Grammar School were in finals, among top 6 teams in the world.
Other numerous medals from the Balkans Olympiads in Mathematics, Physics and Informatics are being won every year.

## Curriculum and core subjects

Main areas of study are divided into sub-branches or sub-disciplines. Courses are delivered on a per-semester basis.

### Mathematics

Mathematics is divided into fields of Algebra, Geometry, Linear Algebra, Analytical Geometry, Mathematical Analysis, Probability, Statistics, Numerical Analysis, and Selected Chapters in Mathematics.

### Physics

Physics is taught from Newtonian mechanics, Fluid Dynamics, Waves, Optics, Electricity, Magnetism, to modern physics, usually ending with STR, Relativistic Dynamics, Quantum Theory, Quantum Mechanics, Molecular Physics, Physical Chemistry, Atomic Physics, Solid State Physics, Quantum Optics, Nuclear Physics, Nuclear Engineering, Elementary Particle Physics, introduction to Astrophysics and Cosmology, General Relativity, and some basic introductions to String Theory, Cosmology, and M-Theory.

### Informatics and computer science

There are 5 computer labs in Mathematical Gymnasium, with ca. 110 dual core and quad core computers, and one super-computer. The School operates its own wireless network. Students gain knowledge in programming languages (Pascal, Delphi, C, C++, C#, Java; Fortran; Prolog), operating systems (Windows, Linux, Unix), databases and DBMS (Oracle Database, Microsoft SQL Server, PostgreSQL, MySQL), and in various IT and ICT fields.
There are 10 two-semester (2×19 weeks) IT courses students must pass during schooling. There is one special (additional) week in each semester, reserved for IT subjects only (so called "block classes"), for students to have lessons only in ICT subjects.

### Business and finance

School offers modules in financial mathematics, as well as in business related studies.

### History of school's IT Department

The first professor of programming in MGB was Ljubomir Protić, professor at University of Belgrade, Faculty of Mathematics, who started teaching programming subjects from school year 1968/69.; 33 years later, professor Protić served as Principal of Mathematical Grammar School (2001–2004).
Later on, many University of Belgrade professors, primarily from Faculty of Mathematics, Faculty of Electrical Engineering, and Faculty of Physics, as well as from Belgrade Institute of Physics and from Vinča Institute of Nuclear Sciences, joined informatics teaching staff at Mathematical Grammar School.

### School's IT club

Programmers club at Faculty of Electrical Engineering was opened by the MG alumni in 1983, by MG alumnus Dejan Ristanović (graduated in 1981). At the same time was opened Programmers club of Mathematical Grammar School. Dejan Ristanović and MGB alumni founded and run "PC Press" publishing house.
All of part-time ICT teachers and special ICT teachers are former MGB students.

## Sports

The school teams regularly play in tournaments in volleyball, handball, basketball, and football. There is an active swimming section each generation has several divers among students. Students can train in karate, taekwondo, judo, and aikido. There are active badminton and table tennis sections. Mountaineering, biking, and hiking are the most popular outdoor activities.
Yachting was very popular during the eighties and nineties, and the School had national team members who competed around the world.

## Notable alumni

Notable alumni include athletes Slobodan Soro and Rajko Jokanović, chess player Alisa Marić, former Minister of Telecommunications and Information Society in the Government of Serbia Aleksandra Smiljanić, and former Mayor of Belgrade Nenad Bogdanović.

## Sponsorships

Mathematical Gymnasium has been sponsored by JAT Airways (national air-traffic company), Telekom Srbija (Telecom Serbia, the largest telecom operator in former Yugoslavia and in modern Serbia), and the Serbian Academy of Sciences and Arts,

## Distinguished guests

Mathematical Grammar School has been visited by many distinguished guests. Among notable guests outside the world of mathematics, physics and informatics, were, during last 5 years only (i.e. after 2005), among many others:
* former Serbian Prime Minister Zoran Đinđić,
* Serbian President Boris Tadić,
* former Belgrade Mayor Nenad Bogdanović, himself an alumnus of MGB,
* then Serbian Prime Minister Vojislav Koštunica,
* Serbian Patriarch Pavle,
* Serbian Patriarch Irinej,
* Alexander, Crown Prince of Yugoslavia,
* Katherine, Crown Princess of Yugoslavia,
* Kim Young-Hee, Ambassador of the Republic of Korea.
On Monday, 21 June 2010, Michael O'Sullivan, Director of the Cambridge Commonwealth Trust paid visit to Mathematical Grammar School.

## Legal status

The School operates as a public school and acts as a member of Serbian education system, which is governed by the Ministry of Education.
Formally a part of former Yugoslav and now Serbian state educational system (i.e. financed by the state), Mathematical Grammar School had a status of "experimental school", which allowed it to operate autonomously since its foundation.
It has funding independent from general high school funding and is helped both by the state and by the University of Belgrade. University pay scale applies to all employees.
Mathematical Grammar School has the following legal statuses:
* "Experimental school whose aim is to reinforce mathematical education for students which show a special gift for mathematics and natural sciences", according to the decision of the Educational Council of SR Serbia (Decision no. 110-32/89 from 18 January 1989);
* "School for talented students in the areas of mathematics and natural sciences", according to the decision of the Ministry of Education of Serbia;
* "School of special national interest", according to the decision of the Government of the Republic of Serbia. (please see picture on the right)

## Building and facilities

The school's main building has an area of 2,144.98 m$^2$, not including basement labs.
It has 11 specialized classrooms (5 for informatics related subjects, 2 for physics, 1 for mathematics, 1 for chemistry, 1 for biology, 1 for foreign languages), 1 server room with equipment for administration of over 100 LAN and WLAN stations in the School, 13 large classrooms and 3 smaller classrooms for mentor teaching and preparation for competitions. Other rooms include the assembly hall, the ceremonial hall, a library with over 10,000 books and textbooks and a mediatheque, basement laboratories, the MG TV studio(a student run YouTube program), administrative staff rooms, cleaning staff rooms, secretary's office, accounting department, copy center, psychologist's office, and the offices of the principal and vice principal.