Leopold Kronecker was a German mathematician who worked on number theory and logic. He criticized Georg Cantor's work on set theory, was quoted by Weber as having said, "Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk". Kronecker was a student and lifelong friend of Ernst Kummer. Leopold Kronecker was born on 7 December 1823 in Prussia in a wealthy Jewish family, his parents and Johanna, took care of their children's education and provided them with private tutoring at home – Leopold's younger brother Hugo Kronecker would follow a scientific path becoming a notable physiologist. Kronecker went to the Liegnitz Gymnasium where he was interested in a wide range of topics including science and philosophy, while practicing gymnastics and swimming. At the gymnasium he was taught by Ernst Kummer, who noticed and encouraged the boy's interest in mathematics. In 1841 Kronecker became a student at the University of Berlin where his interest did not focus on mathematics, but rather spread over several subjects including astronomy and philosophy.
He spent the summer of 1843 at the University of Bonn studying astronomy and 1843–44 at the University of Breslau following his former teacher Kummer. Back in Berlin, Kronecker studied mathematics with Peter Gustav Lejeune Dirichlet and in 1845 defended his dissertation in algebraic number theory written under Dirichlet's supervision. After obtaining his degree, Kronecker did not follow his interest in research on an academic career path, he went back to his hometown to manage a large farming estate built up by his mother's uncle, a former banker. In 1848 he married his cousin Fanny Prausnitzer, the couple had six children. For several years Kronecker focused on business, although he continued to study mathematics as a hobby and corresponded with Kummer, he published no mathematical results. In 1853 he wrote a memoir on the algebraic solvability of equations extending the work of Évariste Galois on the theory of equations. Due to his business activity, Kronecker was financially comfortable, thus he could return to Berlin in 1855 to pursue mathematics as a private scholar.
Dirichlet, whose wife Rebecka came from the wealthy Mendelssohn family, had introduced Kronecker to the Berlin elite. He became a close friend of Karl Weierstrass, who had joined the university, his former teacher Kummer who had just taken over Dirichlet's mathematics chair. Over the following years Kronecker published numerous papers resulting from his previous years' independent research; as a result of this published research, he was elected a member of the Berlin Academy in 1861. Although he held no official university position, Kronecker had the right as a member of the Academy to hold classes at the University of Berlin and he decided to do so, starting in 1862. In 1866, when Riemann died, Kronecker was offered the mathematics chair at the University of Göttingen, but he refused, preferring to keep his position at the Academy. Only in 1883, when Kummer retired from the University, was Kronecker invited to succeed him and became an ordinary professor. Kronecker was the supervisor of Kurt Hensel, Adolf Kneser, Mathias Lerch, Franz Mertens, amongst others.
His philosophical view of mathematics put him in conflict with several mathematicians over the years, notably straining his relationship with Weierstrass, who decided to leave the University in 1888. Kronecker died on 29 December 1891 in several months after the death of his wife. In the last year of his life, he converted to Christianity, he is buried in the Alter St Matthäus Kirchhof cemetery in Berlin-Schöneberg, close to Gustav Kirchhoff. An important part of Kronecker's research focused on number algebra. In an 1853 paper on the theory of equations and Galois theory he formulated the Kronecker–Weber theorem, without however offering a definitive proof, he introduced the structure theorem for finitely-generated abelian groups. Kronecker studied elliptic functions and conjectured his "liebster Jugendtraum", a generalization, put forward by Hilbert in a modified form as his twelfth problem. In an 1850 paper, On the Solution of the General Equation of the Fifth Degree, Kronecker solved the quintic equation by applying group theory.
In algebraic number theory Kronecker introduced the theory of divisors as an alternative to Dedekind's theory of ideals, which he did not find acceptable for philosophical reasons. Although the general adoption of Dedekind's approach led Kronecker's theory to be ignored for a long time, his divisors were found useful and were revived by several mathematicians in the 20th century. Kronecker contributed to the concept of continuity, reconstructing the form of irrational numbers in real numbers. In analysis, Kronecker rejected the formulation of a continuous, nowhere differentiable function by his colleague, Karl Weierstrass. Named for Kronecker are the Kronecker limit formula, Kronecker's congruence, Kronecker delta, Kronecker comb, Kronecker symbol, Kronecker product, Kronecker's method for factorizing polynomials, Kronecker substitution, Kronecker's theorem in number theory, Kronecker's lemma, Eisenstein–Kronecker numbers. Kronecker's finitism made him a forerunner of intuitionism in foundations of mathematics.
Kronecker was elected as a member of several academies: Prussian Academy of Sciences French Academy of Sciences Roy
Humboldt University of Berlin
Humboldt University of Berlin is a university in the central borough of Mitte in Berlin, Germany. It was established by Frederick William III on the initiative of Wilhelm von Humboldt, Johann Gottlieb Fichte and Friedrich Ernst Daniel Schleiermacher as the University of Berlin in 1809, opened in 1810, making it the oldest of Berlin's four universities. From 1810 until its closure in 1945, it was named Friedrich Wilhelm University. During the Cold War the university found itself in East Berlin and was de facto split in two when the Free University of Berlin opened in West Berlin; the university received its current name in honour of Alexander and Wilhelm von Humboldt in 1949. The university is divided into nine faculties, including its medical school shared with the Free University of Berlin, has a student enrollment of around 32,000 students, offers degree programmes in some 189 disciplines from undergraduate to postdoctorate level, its main campus is located on the Unter den Linden boulevard in central Berlin.
The university is known worldwide for pioneering the Humboldtian model of higher education, which has influenced other European and Western universities, the university has been called "the mother of all modern universities."As of 2017, the university has been associated with 55 Nobel Prize winners, is considered one of the best universities in Europe as well as one of the most prestigious universities in the world for arts and humanities. It was regarded as the world's preeminent university for the natural sciences during the 19th and early 20th century, is linked to major breakthroughs in physics and other sciences by its professors such as Albert Einstein. Former faculty and notable alumni include eminent philosophers, artists, politicians, mathematicians and Heads of State; the University of Berlin was established on 16 August 1809, on the initiative of the liberal Prussian educational politician Wilhelm von Humboldt by King Friedrich Wilhelm III, during the period of the Prussian Reform Movement.
The university was located in a palace constructed from 1748-1766 for the late Prince Henry, the younger brother of Frederick the Great. After his widow and her ninety-member staff moved out, the first unofficial lectures were given in the building in the winter of 1809. Humboldt faced great resistance to his ideas, he submitted his resignation to the King in April 1810, was not present when the school opened that fall. The first students were admitted on 6 October 1810, the first semester started on 10 October 1810, with 256 students and 52 lecturers in faculties of law, medicine and philosophy under rector Theodor Schmalz; the university celebrates 15 October 1810 as the date of its opening. From 1828 to 1945, the school was named the Friedrich Wilhelm University, in honor of its founder. Ludwig Feuerbach one of the students, made a comment on the university in 1826: "There is no question here of drinking and plesant communal outings. Compared to this temple of work, the other universities appear like public houses."The university has been home to many of Germany's greatest thinkers of the past two centuries, among them the subjective idealist philosopher Johann Gottlieb Fichte, the theologian Friedrich Schleiermacher, the absolute idealist philosopher G.
W. F. Hegel, the Romantic legal theorist Friedrich Carl von Savigny, the pessimist philosopher Arthur Schopenhauer, the objective idealist philosopher Friedrich Schelling, cultural critic Walter Benjamin, famous physicists Albert Einstein and Max Planck; the founders of Marxist theory Karl Marx and Friedrich Engels attended the university, as did poet Heinrich Heine, novelist Alfred Döblin, founder of structuralism Ferdinand de Saussure, German unifier Otto von Bismarck, Communist Party of Germany founder Karl Liebknecht, African American Pan Africanist W. E. B. Du Bois and European unifier Robert Schuman, as well as the influential surgeon Johann Friedrich Dieffenbach in the early half of the 1800s; the structure of German research-intensive universities served as a model for institutions like Johns Hopkins University. Further, it has been claimed that "the'Humboldtian' university became a model for the rest of Europe with its central principle being the union of teaching and research in the work of the individual scholar or scientist."
In addition to the strong anchoring of traditional subjects, such as science, philosophy, history and medicine, the university developed to encompass numerous new scientific disciplines. Alexander von Humboldt, brother of the founder William, promoted the new learning. With the construction of modern research facilities in the second half of the 19th Century teaching of the natural sciences began. Famous researchers, such as the chemist August Wilhelm Hofmann, the physicist Hermann von Helmholtz, the mathematicians Ernst Eduard Kummer, Leopold Kronecker, Karl Weierstrass, the physicians Johannes Peter Müller, Albrecht von Graefe, Rudolf Virchow and Robert Koch, contributed to Berlin University's scientific fame. During this period of enlargement, the university expanded to incorporate other separate colleges in Berlin. An example would be the Pépinière and the Collegium Medico-chirurgicum. In 1717, King Friedrich I had built a quarantine house for Plague at the city gates, which in 1727 was rechristened by the "soldier king" Friedrich
Vienna is the federal capital and largest city of Austria, one of the nine states of Austria. Vienna is Austria's primate city, with a population of about 1.9 million, its cultural and political centre. It is the 7th-largest city by population within city limits in the European Union; until the beginning of the 20th century, it was the largest German-speaking city in the world, before the splitting of the Austro-Hungarian Empire in World War I, the city had 2 million inhabitants. Today, it has the second largest number of German speakers after Berlin. Vienna is host to many major international organizations, including the United Nations and OPEC; the city is located in the eastern part of Austria and is close to the borders of the Czech Republic and Hungary. These regions work together in a European Centrope border region. Along with nearby Bratislava, Vienna forms a metropolitan region with 3 million inhabitants. In 2001, the city centre was designated a UNESCO World Heritage Site. In July 2017 it was moved to the list of World Heritage in Danger.
Apart from being regarded as the City of Music because of its musical legacy, Vienna is said to be "The City of Dreams" because it was home to the world's first psychoanalyst – Sigmund Freud. The city's roots lie in early Celtic and Roman settlements that transformed into a Medieval and Baroque city, the capital of the Austro-Hungarian Empire, it is well known for having played an essential role as a leading European music centre, from the great age of Viennese Classicism through the early part of the 20th century. The historic centre of Vienna is rich in architectural ensembles, including Baroque castles and gardens, the late-19th-century Ringstraße lined with grand buildings and parks. Vienna is known for its high quality of life. In a 2005 study of 127 world cities, the Economist Intelligence Unit ranked the city first for the world's most liveable cities. Between 2011 and 2015, Vienna was ranked second, behind Melbourne. In 2018, it replaced Melbourne as the number one spot. For ten consecutive years, the human-resource-consulting firm Mercer ranked Vienna first in its annual "Quality of Living" survey of hundreds of cities around the world.
Monocle's 2015 "Quality of Life Survey" ranked Vienna second on a list of the top 25 cities in the world "to make a base within."The UN-Habitat classified Vienna as the most prosperous city in the world in 2012/2013. The city was ranked 1st globally for its culture of innovation in 2007 and 2008, sixth globally in the 2014 Innovation Cities Index, which analyzed 162 indicators in covering three areas: culture and markets. Vienna hosts urban planning conferences and is used as a case study by urban planners. Between 2005 and 2010, Vienna was the world's number-one destination for international congresses and conventions, it attracts over 6.8 million tourists a year. The English name Vienna is borrowed from the homonymous Italian version of the city's name or the French Vienne; the etymology of the city's name is still subject to scholarly dispute. Some claim that the name comes from Vedunia, meaning "forest stream", which subsequently produced the Old High German Uuenia, the New High German Wien and its dialectal variant Wean.
Others believe that the name comes from the Roman settlement name of Celtic extraction Vindobona meaning "fair village, white settlement" from Celtic roots, vindo-, meaning "bright" or "fair" – as in the Irish fionn and the Welsh gwyn –, -bona "village, settlement". The Celtic word Vindos may reflect a widespread prehistorical cult of a Celtic God. A variant of this Celtic name could be preserved in the Czech and Polish names of the city and in that of the city's district Wieden; the name of the city in Hungarian, Serbo-Croatian and Ottoman Turkish has a different Slavonic origin, referred to an Avar fort in the area. Slovene-speakers call the city Dunaj, which in other Central European Slavic languages means the Danube River, on which the city stands. Evidence has been found of continuous habitation in the Vienna area since 500 BC, when Celts settled the site on the Danube River. In 15 BC the Romans fortified the frontier city they called Vindobona to guard the empire against Germanic tribes to the north.
Close ties with other Celtic peoples continued through the ages. The Irish monk Saint Colman is buried in Melk Abbey and Saint Fergil served as Bishop of Salzburg for forty years. Irish Benedictines founded twelfth-century monastic settlements. Evidence of these ties persists in the form of Vienna's great Schottenstift monastery, once home to many Irish monks. In 976 Leopold I of Babenberg became count of the Eastern March, a 60-mile district centering on the Danube on the eastern frontier of Bavaria; this initial district grew into the duchy of Austria. Each succeeding Babenberg ruler expanded the march east along the Danube encompassing Vienna and the lands east. In 1145 Duke Henry II Jasomirgott moved the Babenberg family residence from Klosterneuburg in Lower Austria to Vienna. From that time, Vienna remained the center of the Babenberg dynasty. In 1440 Vienna became the resident city of the Habsburg dynasty, it grew to become the de facto capital of the Holy Roman Empire in 1437 and a cultural centre for arts and science and fine cuisine.
Hungary occupied the city between 1485 and 1490. In the 16th and 1
International Olympiad in Informatics
The International Olympiad in Informatics is an annual competitive programming competition for secondary school students. It is the second largest olympiad, after International Mathematical Olympiad, in terms of number of participating countries; the first IOI was held in 1989 in Bulgaria. The contest consists of problem-solving of algorithmic nature. To deal with problems involving large amounts of data, it is necessary to have not only programmers, "but creative coders, who can dream up what it is that the programmers need to tell the computer to do; the hard part isn't the programming, but the mathematics underneath it." Students at the IOI compete on an individual basis, with up to four students competing from each participating country. Students in the national teams are selected through national computing contests, such as the Australian Informatics Olympiad, British Informatics Olympiad, Indian Computing Olympiad or Bundeswettbewerb Informatik; the International Olympiad in Informatics is one of the most prestigious computer science competitions in the world.
UNESCO and IFIP are patrons. On each of the two competition days, the students are given three problems which they have to solve in five hours; each student works on his/her own, with only a computer and no other help allowed no communication with other contestants, books etc. To solve a task the contestant has to write a computer program and submit it before the five-hour competition time ends; the program is graded by being run with secret test data. From IOI 2010, tasks are divided into subtasks with graduated difficulty, points are awarded only when all tests for a particular subtask yield correct results, within specific time and memory limits. In some cases, the contestant's program has to interact with a secret computer library, which allows problems where the input is not fixed, but depends on the program's actions – for example in game problems. Another type of problem has known inputs which are publicly available during the five hours of the contest. For these, the contestants have to submit an output file instead of a program, it is up to them whether they obtain the output files by writing a program, or by hand, or by a combination of these means.
Pascal will have been removed as an available programming language by 2019.:11IOI 2010 for the first time had a live web scoreboard with real-time provisional results. Submissions will be scored as soon as possible during the contest, the results posted. Contestants will be aware of their scores, but not others', may resubmit to improve their scores. Starting from 2012, IOI has been using the Contest Management System for developing and monitoring the contest; the scores from the two competition days and all problems are summed up separately for each contestant. At the awarding ceremony, contestants are awarded medals depending on their relative total score; the top 50% of the contestants are awarded medals, such that the relative number of gold: silver: bronze: no medal is 1:2:3:6. Prior to IOI 2010, students who did not receive medals did not have their scores published, making it impossible for a country to be ranked by adding together scores of its competitors unless each wins a medal. From IOI 2010, although the scores of students who did not receive medals are still not available in the official results, they are known from the live web scoreboard.
In IOI 2012 the top 3 nations ranked by aggregate score were subsequently awarded during the closing ceremony. Analysis of female performance shows 77.9 % of women obtain no medal, while 49.2 % of men obtain no medal. "The average female participation was 4.4% in 1989–1994 and 2.2% in 1996–2014." It suggests women participate much more on the national level, claiming sometimes a double-digit percentage of women participate on the first stage. President of the IOI, Richard Forster, says the competition has difficulty attracting women and that in spite of trying to solve it, "none of us have hit on quite what the problem is, let alone the solution."In IOI 2017 held in Iran, due to not being able to participate in Iran, the Israeli students participated in an offsite competition organized by IOI in Russia.:11 Due to visa issues, the full USA team was unable to attend, although one contestant Zhezheng Luo was able to attend by traveling with the Chinese team and winning gold medal and 3rd place in standings.
The following is a list of the top performers in the history of the IOI. The P sign indicates a rare achievement in IOI history; the U sign indicates an unofficial participation, where a contestant participated in a host's second team. First and third places among gold medalists are indicated where appropriate; this list includes only those countries where the national selection contest allows the same participant to go multiple times to the IOI. Most participating countries use feeder competitions to select their team. A number of these are listed below: International Science Olympiad ACM International Collegiate Programming Contest Central European Olympiad in Informatics Online judge International Mathematical Olympiad International Olympiad in Informatics community Facebook Group for the International Olympiad in Informatics IOI International Committee Website IOI Statistics IOI Secretariat Website
Erwin Rudolf Josef Alexander Schrödinger, sometimes written as Erwin Schrodinger or Erwin Schroedinger, was a Nobel Prize-winning Austrian physicist who developed a number of fundamental results in the field of quantum theory: the Schrödinger equation provides a way to calculate the wave function of a system and how it changes dynamically in time. In addition, he was the author of many works in various fields of physics: statistical mechanics and thermodynamics, physics of dielectrics, colour theory, general relativity, cosmology, he made several attempts to construct a unified field theory. In his book What Is Life? Schrödinger addressed the problems of genetics, looking at the phenomenon of life from the point of view of physics, he paid great attention to the philosophical aspects of science and oriental philosophical concepts and religion. He wrote on philosophy and theoretical biology, he is known for his "Schrödinger's cat" thought-experiment. On 12 August 1887, Schrödinger was born in Erdberg, Austria, to Rudolf Schrödinger and Georgine Emilia Brenda Schrödinger.
He was their only child. His mother was of half half English descent. Although he was raised in a religious household as a Lutheran, he called himself an atheist. However, he had strong interests in Eastern religions and pantheism, he used religious symbolism in his works, he believed his scientific work was an approach to the godhead, albeit in a metaphorical sense. He was able to learn English outside school, as his maternal grandmother was British. Between 1906 and 1910 Schrödinger studied in Vienna under Franz S. Friedrich Hasenöhrl, he conducted experimental work with Karl Wilhelm Friedrich "Fritz" Kohlrausch. In 1911, Schrödinger became an assistant to Exner. At an early age, Schrödinger was influenced by Arthur Schopenhauer; as a result of his extensive reading of Schopenhauer's works, he became interested throughout his life in colour theory and philosophy. In his lecture "Mind and Matter", he said that "The world extended in space and time is but our representation." This is a repetition of the first words of Schopenhauer's main work.
In 1914 Erwin Schrödinger achieved Habilitation. Between 1914 and 1918 he participated in war work as a commissioned officer in the Austrian fortress artillery. In 1920 he became the assistant to Max Wien, in Jena, in September 1920 he attained the position of ao. Prof. equivalent to Reader or associate professor, in Stuttgart. In 1921, he became o. Prof. in Breslau. In 1921, he moved to the University of Zürich. In 1927, he succeeded Max Planck at the Friedrich Wilhelm University in Berlin. In 1934 Schrödinger decided to leave Germany, he became a Fellow of Magdalen College at the University of Oxford. Soon after he arrived, he received the Nobel Prize together with Paul Dirac, his position at Oxford did not work out well. In 1934, Schrödinger lectured at Princeton University. Again, his wish to set up house with his wife and his mistress may have created a problem, he had the prospect of a position at the University of Edinburgh but visa delays occurred, in the end he took up a position at the University of Graz in Austria in 1936.
He had accepted the offer of chair position at Department of Physics, Allahabad University in India. In the midst of these tenure issues in 1935, after extensive correspondence with Albert Einstein, he proposed what is now called the Schrödinger's cat thought experiment. In 1938, after the Anschluss, Schrödinger had problems because of his flight from Germany in 1933 and his known opposition to Nazism, he issued a statement recanting this opposition. However, this did not appease the new dispensation and the University of Graz dismissed him from his job for political unreliability, he suffered harassment and received instructions not to leave the country, but he and his wife fled to Italy. From there, he went to visiting positions in Ghent University. In the same year he received a personal invitation from Ireland's Taoiseach, Éamon de Valera – a mathematician himself – to reside in Ireland and agree to help establish an Institute for Advanced Studies in Dublin, he moved to Clontarf, became the Director of the School for Theoretical Physics in 1940 and remained there for 17 years.
He retained his Austrian citizenship. He wrote around 50 further publications on various topics, including his explorations of unified field theory. In 1944, he wrote What Is Life?, which contains a discussion of negentropy and the concept of a complex molecule with the genetic code for living organisms. According to James D. Watson's memoir, DNA, the Secret of Life, Schrödinger's book gave Watson the inspiration to research the gene, which led to the discovery of the DNA double helix structure in 1953. Francis Crick, in his autobiographical book What Mad Pursuit, described how he was influenced by Schrödinger's speculations about how genetic information might be stored in molecules. Schrödinger stayed in Dublin until retiring in 1955, he had a lifelong inter
International Mathematical Olympiad
The International Mathematical Olympiad is an annual six-problem mathematical olympiad for pre-college students, is the oldest of the International Science Olympiads. The first IMO was held in Romania in 1959, it has since been held annually, except in 1980. More than 100 countries, representing over 90% of the world's population, send teams of up to six students, plus one team leader, one deputy leader, observers; the content ranges from difficult algebra and pre-calculus problems to problems on branches of mathematics not conventionally covered at school and not at university level either, such as projective and complex geometry, functional equations and well-grounded number theory, of which extensive knowledge of theorems is required. Calculus, though allowed in solutions, is never required, as there is a principle that anyone with a basic understanding of mathematics should understand the problems if the solutions require a great deal more knowledge. Supporters of this principle claim that this allows more universality and creates an incentive to find elegant, deceptively simple-looking problems which require a certain level of ingenuity.
The selection process differs by country, but it consists of a series of tests which admit fewer students at each progressing test. Awards are given to the top-scoring 50% of the individual contestants. Teams are not recognized—all scores are given only to individual contestants, but team scoring is unofficially compared more than individual scores. Contestants must not be registered at any tertiary institution. Subject to these conditions, an individual may participate any number of times in the IMO; the International Mathematical Olympiad is one of the most prestigious mathematical competitions in the world. In January 2011, Google sponsored €1 million to the International Mathematical Olympiad organization; the first IMO was held in Romania in 1959. Since it has been held every year except in 1980; that year, it was cancelled due to internal strife in Mongolia. It was founded for eastern European member countries of the Warsaw Pact, under the USSR bloc of influence, but other countries participated as well.
Because of this eastern origin, the IMOs were first hosted only in eastern European countries, spread to other nations. Sources differ about the cities hosting some of the early IMOs; this may be because leaders are housed well away from the students, because after the competition the students did not always stay based in one city for the rest of the IMO. The exact dates cited may differ, because of leaders arriving before the students, at more recent IMOs the IMO Advisory Board arriving before the leaders. Several students, such as Zhuo Qun Song, Teodor von Burg, Lisa Sauermann, John Lian, Josh Li and Christian Reiher, have performed exceptionally well in the IMO, winning multiple gold medals. Others, such as Grigory Margulis, Jean-Christophe Yoccoz, Laurent Lafforgue, Stanislav Smirnov, Terence Tao, Sucharit Sarkar, Grigori Perelman, Ngô Bảo Châu and Maryam Mirzakhani have gone on to become notable mathematicians. Several former participants have won awards such as the Fields Medal; the examination consists of six problems.
Each problem is worth seven points, so the maximum total score is 42 points. No calculators are allowed; the examination is held over two consecutive days. The problems chosen are from various areas of secondary school mathematics, broadly classifiable as geometry, number theory and combinatorics, they require no knowledge of higher mathematics such as calculus and analysis, solutions are short and elementary. However, they are disguised so as to make the solutions difficult. Prominently featured are algebraic inequalities, complex numbers, construction-oriented geometrical problems, though in recent years the latter has not been as popular as before; each participating country, other than the host country, may submit suggested problems to a Problem Selection Committee provided by the host country, which reduces the submitted problems to a shortlist. The team leaders arrive at the IMO a few days in advance of the contestants and form the IMO Jury, responsible for all the formal decisions relating to the contest, starting with selecting the six problems from the shortlist.
The Jury aims to order the problems so that the order in increasing difficulty is Q1, Q4, Q2, Q5, Q3 and Q6. As the leaders know the problems in advance of the contestants, they are kept separated and observed; each country's marks are agreed between that country's leader and deputy leader and coordinators provided by the host country, subject to the decisions of the chief coordinator and a jury if any disputes cannot be resolved. The selection process for the IMO varies by country. In some countries those in East Asia, the selection process involves several tests of a difficulty comparable to the IMO itself; the Chinese contestants go through a camp. In others, such as the United States, possible participants go through a series of easier standalone competitions that increase in difficulty. In the United States, the tests include the American Mathematics Competitions, the American Invitational Mathematics Examination, the United States of America Mathematical Olympiad, each of, a competition in its own right.
For high scorers in the final competition for the team selection, there is a summer camp, like that of China. In countries of the former Soviet Union and other eastern Europ
First Austrian Republic
The First Austrian Republic was created after the signing of the Treaty of Saint-Germain-en-Laye on 10 September 1919—the settlement after the end of World War I which ended the Habsburg rump state of Republic of German-Austria—and ended with the establishment of the Austrofascist Federal State of Austria based upon a dictatorship of Engelbert Dollfuss and the Fatherland's Front in 1934. The Republic's constitution was enacted in 1 October 1920 and amended on 7 December 1929; the republican period was marked by violent strife between those with left-wing and right-wing views, leading to the July Revolt of 1927 and the Austrian Civil War of 1934. In September 1919, the Habsburg rump state of German-Austria was given reduced borders by the Treaty of Saint Germain, which ceded German-populated regions in Sudetenland to Czechoslovakia, German-populated South Tyrol to Italy and a portion of Alpine provinces to the Kingdom of Serbs and Slovenes. Despite Austrian protests this treaty forbade Anschluss, or union of Austria with Germany, without League of Nations consent.
The new Republic was created by the will of Allies who did not want the defeated Germany to expand its borders. The new state managed to prevent two land claims from being taken by their neighbours; the first was the south-eastern part of Carinthia, inhabited by Slovenians. It was prevented from being taken over by the new SHS-state through a Carinthian plebiscite on October 10, 1920, in which the majority of population chose to remain with Austria; the second prevented land-claim was Hungary's claim to Burgenland, under the name "Western Hungary", had been part of the Hungarian kingdom since 907. It was inhabited by a German-speaking population, but had Croat- and Hungarian-speaking minorities. Through the Treaty of St. Germain it became part of the Austrian Republic in 1921. However, after a plebiscite, disputed by Austria, the provincial capital city of Sopron remained in Hungary; the treaty of Saint Germain angered the German population in Austria who claimed that it violated the Fourteen Points laid out by United States President Woodrow Wilson during peace talks the right to "self-determination" of all nations.
Many of them felt that with the loss of 60% of the territory of the prewar empire, Austria was no longer economically and politically viable as a separate state without union with Germany. In a now small country of 6.5 million people, with its population of 2 million, was left as an imperial capital without an empire to feed it, as only 17.8% of Austrian land was arable. For much of the early 1920s, Austria's survival was much in doubt; this was because Austria had never been a German/Austrian nation state in the true sense of the term. Although the Austrian state had existed in one form or another for 700 years, it had no real unifying force other than the Habsburg dynasty and the provincial identities of Tyroleans and others were much stronger; the new constitution created bi-cameral legislature with upper house Bundesrat formed by representatives from federal Lands and lower house Nationalrat, where deputies were elected in universal elections. The Federal President was elected for a four-year term in a full session of both houses, while the Chancellor was elected by the Nationalrat.
As no political party gained parliamentary majority, Austria was governed by coalitions of conservative Christian Social Party and right-wing Greater German People's Party or Landbund which were more conservative than the first government of Social Democrat Karl Renner of 1919–20, that had established a number of progressive socioeconomic and labour legislations. After 1920, Austria's government was dominated by the anti-Anschluss Christian Social Party which retained close ties to the Roman Catholic Church; the party's first Chancellor Ignaz Seipel came to power in May 1922 and attempted to forge a political alliance between wealthy industrialists and the Roman Catholic Church. After the legislative elections of October 17, 1920 Social Democrats lost parliamentary majority and remained in the opposition until 1934, when they were banned by Dollfuss. Christian Socials won Social Democrats 69, Greater Germany Party 20 and Peasants Union 8 seats. Michael Hainisch was elected Federal President.
After October 1923 elections Ignaz Seipel stayed in power and resigned in November 1924 when he was succeeded by Rudolf Ramek. In December 1928 Cristian Social Wilhelm Miklas was elected to the post of Federal President and on 7 December 1929 Constitution was amended, reducing the rights of parliament, making the Federal President electable by a popular vote and giving him the right to appoint the federal government and to issue emergency laws. After the 1930 legislative elections Social Democrats emerged as the largest party with 72 seats, but Christian Social Chancellor Otto Ender created a coalition government without them. Despite the nation having a steady political party in power, the politics of the nation were fractious and violent, with both Social Democrat and right-wing political paramilitary forces clashing with each other; the country was divided between the conservative countryside population and Social Democrat controlled Red Vienna. In 1927, during a political clash in Schattendorf, an old man and a child were shot and killed by Heimwehr.
On 14 July 1927 the shooters were acquitted and left-wing supporters began a massive protest during which the Ministry of Justice building was burned. To restore order police and army shot and killed 89 people and injured 600; the huge protest is known as the July Revolt of 1927. Social Democrats called for a general strike which la