Since 1970, the Austrian Mathematical Olympiad (ÖMO) has been held each year. The International Mathematical Olympiad (IMO), which took place for the first time in Romania in 1959, and has since been held every year by another country, was taken as an example.

### Topics

At the Mathematical Olympiad, most problems cover one of the following topics:

- number theory
- equations, inequality and systems of equations
- sequences and series
- combinatorics
- polynomials, functions and functional equations
- geometry

As the theory needed for solving these problems is hardly covered in the regular lessons, there are some preparation courses at some high schools were certain useful "tricks" are taught (at least in Austria).

I personaly took part in the course "Preparation to the Mathematical Olympiad" at my school (GRG XXI, Franklinstraße 21) from 1995 to 1999 (from the ninth to the twelth grade). In the school year 1995/96, the course was held by Prof. Heinrich, whereas the following three years, Prof. Czakler gave the lectures.

### Competitions

At the end of each school year, several competitions took place – namely at two different levels: On one hand, there are two competitions for the beginners (that is to say, pupils from the ninth and sometimes from tenth grade), and on the other hand, there are several competitions for the more advanced pupils. Since my participation in the Mathematical Olympiad back "in the old days" (that is to say, in the 1990s), there were some minor changes in the organization of the competitions described below. The current setup is explained in detail on the unofficial ÖMO Website (in German, however).

For the beginners, one competition takes place at the school where the preparation course is held. The best pupils are then allowed to participate in a competition for pupils from the same federal state. In ninth grade (school year 1995/96), I achieved the first place in the competition at my school and therefore qualified for the Vienna Beginner's Competition, where I finally achieved the fourth place.

Due to my success and the fact that I enjoyed the preparation course quite much, I took part in the Mathematical Olympiad in the following year, too – even though the course was unfortunately no longer led by Prof. Heinrich. This time, I took part in the Advanced Competition, which is held in several stages:

After the competition at school, there is a Regional Competition (three of them take place in Austria – one for Vienna, Lower Austria and Burgenland, one for Styria and one for the other federal states of Austria). At each of these three competitions, the leading eight to ten students are allowed to take part in the Austrian competition, for which they are prepared during a two-week preparation course held yearly in Raach am Hochgebirge (near Gloggnitz, Lower Austria) in May/June. The best six students from all over Austria represent their country at the International Mathematical Olympiad, where over 450 students from over 80 countries from all over the world take part. The students who achieved the seventh to the twelvth place are allowed to participate in the Austrian-Polish Mathematical Competition, which takes place alternating in Austria and in Poland since 1978.

During my first year at the Advanced Competitions, I was already able to qualify for a participation at the Austrian Competition. Especially the time I spent in Raach during the two-week course I enjoyed very much – despite the exhausting six hours of courses of mathematics each day – as we still had enough time for other more relaxing activities such as playing table tennis, and I was able to make a lot of new friends. So, I participated again in the following year, and was able to achieve the seventh place in the Austrian competition. In other words, I missed the qualification for the International Mathematical Olympiad by just one place, and was able to participate in the Austrian-Polish Mathematical Competition, which was then held in the polish town of Toruń. In my final year at high school, I achieved the third place at the Austrian Mathematical Olympiad, and was thus allowed to participate in the 40th International Mathematical Olympiad, which took part in Bucharest, Romania (on the occasion of 40th anniversary of the IMO as the first IMO was held in Bucharest in 1959).

In addition to the competitions mentioned above there are several other competions which are independent thereof (such as the "Turnier der Städte"). However, I did not participate in any such competition.

#### Austrian-Polish Mathematical Competition 1998

Between June 24 and July 3, 1998, the Austrian-Polish Mathematical Competition took place in Toruń. The first days were spent with a sightseeing tour through Toruń as well as several trips to cities nearby, for instance Chełmno and Malbork.

On June 29 and June 30, the individual competition took place, and on July 1, we challenged in the team competition, where the six members of each of the two teams are "locked up" together in one room, and should solve tree problems together within four hours. On the following day, the prize giving ceremony was held where each contestant recieved a diploma. I managed to achieve the fifth place (among twelve contestants). At the team competition, the polish students were ahead by a nose (well, at little more than that) and could take home their cup.

More detailed information about my stay in Poland may be found in my ÖPMW Diary – most of which is only in German, however.

#### International Mathematical Olympiad 1999

Between July 13 and July 22, 1999, the 40th International Mathematical Olympiad took place in Bucharest (Romania). Also this time, a broad sightseeing program was offered the 450 contestents coming from more than 80 differnt countries: a tour through Bucharest (as well as several other visits in mueseums and other places of interests) and a one-day trip to Castle Peleş as well as Castle Bran, where Count Vlad Tepes alias Dracula once lived.

Before that (after the opening ceremony on July 15), however, we had to solve the six problems of the competition on July 16 and July 17, which were indeed very challenging.

On July 21, a pompous prize giving cermony and a farewell banquet was held, where all Austrian team members together recieved one silver as well as two bronze medals, and therefore achieved the 29th place in the (inofficial) country ranking. Unfortunately, I was not among the lucky medallists.

If you are interested in my experiences at the IMO in Romania, you may have a look at my IMO Diary, which is again mainly in German.