Moscow State University
Moscow State University is a coeducational and public research university located in Moscow, Russia. It was founded on 23 January 1755 by Mikhail Lomonosov. MSU was renamed after Lomonosov in 1940 and was known as Lomonosov University, it houses the tallest educational building in the world. Its current rector is Viktor Sadovnichiy. According to the 2018 QS World University Rankings, it is the highest-ranking Russian educational institution and is considered the most prestigious university in the former Soviet Union. Ivan Shuvalov and Mikhail Lomonosov promoted the idea of a university in Moscow, Russian Empress Elizabeth decreed its establishment on 23 January 1755; the first lectures were given on 7 May. Russians still celebrate 25 January as Students' Day. Saint Petersburg State University and Moscow State University engage in friendly rivalry over the title of Russia's oldest university. Though Moscow State University was founded in 1755, its competitor in St. Petersburg has had a continuous existence as a "university" since 1819 and sees itself as the successor of an academy established on 24 January 1724, by a decree of Peter the Great.
The present Moscow State University occupied the Principal Medicine Store on Red Square from 1755 to 1787. Catherine the Great transferred the University to a Neoclassical building on the other side of Mokhovaya Street. In the 18th century, the University had three departments: philosophy and law. A preparatory college was affiliated with the University until its abolition in 1812. In 1779, Mikhail Kheraskov founded a boarding school for noblemen which in 1830 became a gymnasium for the Russian nobility; the university press, run by Nikolay Novikov in the 1780s, published the most popular newspaper in Imperial Russia: Moskovskie Vedomosti. In 1804, medical education split into clinical and obstetrics faculties. During 1884–1897, the Department of Medicine—supported by private donations, the municipal and imperial governments—built an extensive, 1.6-kilometer-long, state-of-the-art medical campus in Devichye Pole, between the Garden Ring and Novodevichy Convent. The campus, medical education in general, were separated from the Moscow University in 1930.
Devichye Pole was operated by the independent I. M. Sechenov First Moscow State Medical University and by various other state and private institutions; the roots of student unrest in the University reach deep into the nineteenth century. In 1905, a social-democratic organization emerged at the University and called for the overthrow of the Czarist government and the establishment of a republic in Russia; the imperial government threatened to close the University. In 1911, in a protest over the introduction of troops onto the campus and mistreatment of certain professors, 130 scientists and professors resigned en masse, including such prominent men as Nikolay Dimitrievich Zelinskiy, Pyotr Nikolaevich Lebedev, Sergei Alekseevich Chaplygin. After the October Revolution of 1917, the institution began to admit the children of the proletariat and peasantry. In 1919, the University abolished fees for tuition and established a preparatory facility to help working-class children prepare for entrance examinations.
During the implementation of Joseph Stalin's first five-year plan, prisoners from the Gulag were forced to construct parts of the newly expanded University. After 1991, nine new faculties were established; the following year, the University gained a unique status: it is funded directly from the state budget, thus providing the University a significant level of independence. On 6 September 1997, the French electronic musician Jean Michel Jarre, whom the mayor of Moscow had specially invited to perform, used the entire front facade of the University as the backdrop for a concert: the frontage served as a giant projection screen, with fireworks and searchlights all launched from various points around the building; the stage stood directly in front of the building, the concert, entitled "The Road To The 21st Century" in Russia but renamed "Oxygen In Moscow" for worldwide release in video/DVD, attracted a world-record crowd of 3.5 million people. On 19 March 2008, Russia's most powerful supercomputer to date, the SKIF MSU was launched at the University.
Its peak performance of 60 TFLOPS makes it the fastest supercomputer in the Commonwealth of Independent States. Since 1953, most of the faculties have been situated on Sparrow Hills, in the southwest of Moscow, 5 km from the city centre; the main building was designed by architect Lev Vladimirovich Rudnev. In the post-war era, Joseph Stalin ordered seven huge tiered neoclassic towers to be built around the city, it was built using Gulag labour. Located on Moscow's outskirts at the time of its construction, the location of the main building is now about half-way between the center of Moscow a
Russia the Russian Federation, is a transcontinental country in Eastern Europe and North Asia. At 17,125,200 square kilometres, Russia is by far or by a considerable margin the largest country in the world by area, covering more than one-eighth of the Earth's inhabited land area, the ninth most populous, with about 146.77 million people as of 2019, including Crimea. About 77 % of the population live in the European part of the country. Russia's capital, Moscow, is one of the largest cities in the world and the second largest city in Europe. Extending across the entirety of Northern Asia and much of Eastern Europe, Russia spans eleven time zones and incorporates a wide range of environments and landforms. From northwest to southeast, Russia shares land borders with Norway, Estonia, Latvia and Poland, Ukraine, Azerbaijan, China and North Korea, it shares maritime borders with Japan by the Sea of Okhotsk and the U. S. state of Alaska across the Bering Strait. However, Russia recognises two more countries that border it, Abkhazia and South Ossetia, both of which are internationally recognized as parts of Georgia.
The East Slavs emerged as a recognizable group in Europe between the 3rd and 8th centuries AD. Founded and ruled by a Varangian warrior elite and their descendants, the medieval state of Rus arose in the 9th century. In 988 it adopted Orthodox Christianity from the Byzantine Empire, beginning the synthesis of Byzantine and Slavic cultures that defined Russian culture for the next millennium. Rus' disintegrated into a number of smaller states; the Grand Duchy of Moscow reunified the surrounding Russian principalities and achieved independence from the Golden Horde. By the 18th century, the nation had expanded through conquest and exploration to become the Russian Empire, the third largest empire in history, stretching from Poland on the west to Alaska on the east. Following the Russian Revolution, the Russian Soviet Federative Socialist Republic became the largest and leading constituent of the Union of Soviet Socialist Republics, the world's first constitutionally socialist state; the Soviet Union played a decisive role in the Allied victory in World War II, emerged as a recognized superpower and rival to the United States during the Cold War.
The Soviet era saw some of the most significant technological achievements of the 20th century, including the world's first human-made satellite and the launching of the first humans in space. By the end of 1990, the Soviet Union had the world's second largest economy, largest standing military in the world and the largest stockpile of weapons of mass destruction. Following the dissolution of the Soviet Union in 1991, twelve independent republics emerged from the USSR: Russia, Belarus, Uzbekistan, Azerbaijan, Kyrgyzstan, Tajikistan and the Baltic states regained independence: Estonia, Lithuania, it is governed as a federal semi-presidential republic. Russia's economy ranks as the twelfth largest by nominal GDP and sixth largest by purchasing power parity in 2018. Russia's extensive mineral and energy resources are the largest such reserves in the world, making it one of the leading producers of oil and natural gas globally; the country is one of the five recognized nuclear weapons states and possesses the largest stockpile of weapons of mass destruction.
Russia is a great power as well as a regional power and has been characterised as a potential superpower. It is a permanent member of the United Nations Security Council and an active global partner of ASEAN, as well as a member of the Shanghai Cooperation Organisation, the G20, the Council of Europe, the Asia-Pacific Economic Cooperation, the Organization for Security and Co-operation in Europe, the World Trade Organization, as well as being the leading member of the Commonwealth of Independent States, the Collective Security Treaty Organization and one of the five members of the Eurasian Economic Union, along with Armenia, Belarus and Kyrgyzstan; the name Russia is derived from Rus', a medieval state populated by the East Slavs. However, this proper name became more prominent in the history, the country was called by its inhabitants "Русская Земля", which can be translated as "Russian Land" or "Land of Rus'". In order to distinguish this state from other states derived from it, it is denoted as Kievan Rus' by modern historiography.
The name Rus itself comes from the early medieval Rus' people, Swedish merchants and warriors who relocated from across the Baltic Sea and founded a state centered on Novgorod that became Kievan Rus. An old Latin version of the name Rus' was Ruthenia applied to the western and southern regions of Rus' that were adjacent to Catholic Europe; the current name of the country, Россия, comes from the Byzantine Greek designation of the Rus', Ρωσσία Rossía—spelled Ρωσία in Modern Greek. The standard way to refer to citizens of Russia is rossiyane in Russian. There are two Russian words which are commonly
Sabir Medgidovich Gusein-Zade is a Russian mathematician and a specialist in singularity theory and its applications. He studied at Moscow State University, where he earned his Ph. D. in 1975 under the joint supervision of Sergei Novikov and Vladimir Arnold. Before entering the university, he had earned a gold medal at the International Mathematical Olympiad. Gusein-Zade co-authored with V. I. Arnold and A. N. Varchenko the textbook Singularities of Differentiable Maps. A professor in both the Moscow State University and the Independent University of Moscow, Gusein-Zade serves as co-editor-in-chief for the Moscow Mathematical Journal, he shares credit with Norbert A’Campo for results on the singularities of plane curves. S. M. Gusein-Zade. "Dynkin diagrams for singularities of functions of two variables". Functional Analysis and Its Applications, 1974, Volume 8, Issue 4, pp. 295–300. S. M. Gusein-Zade. "Intersection matrices for certain singularities of functions of two variables". Functional Analysis and Its Applications, 1974, Volume 8, Issue 1, pp. 10–13.
A. Campillo, F. Delgado, S. M. Gusein-Zade. "The Alexander polynomial of a plane curve singularity via the ring of functions on it". Duke Mathematical Journal, 2003, Volume 117, Number 1, pp. 125–156. S. M. Gusein-Zade. "The problem of choice and the optimal stopping rule for a sequence of independent trials". Theory of Probability & Its Applications, 1965, Volume 11, Number 3, pp. 472–476. S. M. Gusein-Zade. "A new technique for constructing continuous cartograms". Cartography and Geographic Information Systems, 1993, Volume 20, Issue 3, pp. 167–173
The Lenin Prize was one of the most prestigious awards of the Soviet Union for accomplishments relating to science, arts and technology. It was created on June 23, 1925 and awarded until 1934. During the period from 1935 to 1956, the Lenin Prize was not awarded, being replaced by the Stalin Prize. On August 15, 1956, it was reestablished, continued to be awarded on every even-numbered year until 1990; the award ceremony was Vladimir Lenin's birthday. The Lenin Prize is different from the Lenin Peace Prize, awarded to foreign citizens rather than to citizens of the Soviet Union, for their contributions to the peace cause; the Lenin Prize should not be confused with the Stalin Prize or the USSR State Prize. Some persons were awarded both the USSR State Prize. On April 23, 2018, the head of the Ulyanovsk Oblast, Sergey Ivanovich Morozov reintroduced the Lenin Prize for achievements in the humanities and art to coincide with the 150th birthday of Lenin in 2020. Note: This list is incomplete and differs in detail from the complete and much longer Russian list, is in chronological order.
Nikolai Kravkov Alexander Chernyshov Nikolai Demyanov Sergei Sergeyev-Tsensky Giorgi Melikishvili Dimitri Nalivkin Okhotsimsky Dmitrii Evgenievich Pyotr Novikov Sergei Prokofiev Dmitri Shostakovich Nikolay Bogolyubov Grigori Chukhrai Vladimir Veksler Mikhail Sholokhov Alexander Bereznyak Sviatoslav Richter Juhan Smuul Aleksei Pogorelov Korney Chukovsky Nikolai Aleksandrovich Nevsky Vladimir Marchenko Chinghiz Aitmatov Hanon Izakson Mikhail Kalashnikov Vladimir Kotelnikov, 1964, Innokenty Smoktunovsky Vladimir Igorevich Arnol'd, Andrey Nikolaevich Kolmogorov Alexander Sergeevich Davydov Alexei Alexeyevich Abrikosov Antonina Prikhot'ko Emmanuel Rashba Vladimir Broude Igor Grekhov Igor Moiseyev Ilya Lifshitz Mikhail Svetlov Valery Panov Yevgeny Vuchetich Yuri Nikolaevich Denisyuk Agniya Barto Yuri Ozerov for his work Liberation, 1972 Yuri Bondarev writer, for his work Liberation, 1972 Igor Slabnevich Cinematographer for his work Liberation, 1972 Alexander Myagkhov Art Director for his work Liberation, 1972 Konstantin Simonov Vladimir Lobashev Mikhail Simonov Gavriil Ilizarov Anatol Zhabotinsky Boris Pavlovich Belousov Otar Taktakishvili Boris Babaian Vladimir Teplyakov Eugene D. Shchukin Kaisyn Kuliev Alykul Osmonov Irena Sedlecká 1988 year Rudolf M. MuradyanFor a series of innovative works “New quantum number – color and establishment of dynamical regularities in the quark structure of elementary particles and atomic nuclei” published during 1965 – 1977.
1958 year Alexander M. Andrianov Lev Andreevich Artsimovich Olga A. Bazilevskaya Stanislav I. Braginskiy Igor' N. Golovin Mikhail A. Leontovich Stepan Yu. Lukyanov Samuil M. Osovets Vasiliy I. Sinitsin Nikolay V. Filippov Natan A. YavlinskiyFor research of powerful pulse discharges in gas for production of the high-temperature plasma, published in years.1964 year Aleksandr Emmanuilovich Nudel'man For a series of innovative automatic cannons.1966 year Yuri Raizer1972 year Vsevolod A. Belyaev Oleg Borisovich Firsov For a series of work "Elementary processes and non-elastic scattering at nuclear collisions”. Vadim I. Utkin1978 year Vladilen S. Letokhov and Veniamin P. Chebotayev 1982 year Viktor V. OrlovFor the work on fast neutron reactors.1984 year Valentin F. DemichevFor production of special chemical compounds and development of conditions of their application.1984 year Boris B. Kadomtsev Oleg P. Pogutse Vitaliy D. ShafranovFor a series of work "The theory of thermonuclear toroidal plasma".
1976 year Nikolai Krasovski Alexander B. Kurzhanski Yury Osipov A. Subbotin 1965 year Sergei S. Bryukhonenko For his work on Advanced R
In mathematics and physics, a soliton is a self-reinforcing solitary wave packet that maintains its shape while it propagates at a constant velocity. Solitons are caused by a cancellation of dispersive effects in the medium. Solitons are the solutions of a widespread class of weakly nonlinear dispersive partial differential equations describing physical systems; the soliton phenomenon was first described in 1834 by John Scott Russell who observed a solitary wave in the Union Canal in Scotland. He reproduced the phenomenon in a wave tank and named it the "Wave of Translation". A single, consensus definition of a soliton is difficult to find. Drazin & Johnson ascribe three properties to solitons: They are of permanent form. More formal definitions exist. Moreover, some scientists use the term soliton for phenomena that do not quite have these three properties. Dispersion and nonlinearity can interact to produce localized wave forms. Consider a pulse of light traveling in glass; this pulse can be thought of as consisting of light of several different frequencies.
Since glass shows dispersion, these different frequencies travel at different speeds and the shape of the pulse therefore changes over time. However the nonlinear Kerr effect occurs. If the pulse has just the right shape, the Kerr effect cancels the dispersion effect, the pulse's shape does not change over time, thus is a soliton. See soliton for a more detailed description. Many solvable models have soliton solutions, including the Korteweg–de Vries equation, the nonlinear Schrödinger equation, the coupled nonlinear Schrödinger equation, the sine-Gordon equation; the soliton solutions are obtained by means of the inverse scattering transform, owe their stability to the integrability of the field equations. The mathematical theory of these equations is a broad and active field of mathematical research; some types of tidal bore, a wave phenomenon of a few rivers including the River Severn, are'undular': a wavefront followed by a train of solitons. Other solitons occur as the undersea internal waves, initiated by seabed topography, that propagate on the oceanic pycnocline.
Atmospheric solitons exist, such as the morning glory cloud of the Gulf of Carpentaria, where pressure solitons traveling in a temperature inversion layer produce vast linear roll clouds. The recent and not accepted soliton model in neuroscience proposes to explain the signal conduction within neurons as pressure solitons. A topological soliton called a topological defect, is any solution of a set of partial differential equations, stable against decay to the "trivial solution". Soliton stability is due to topological constraints, rather than integrability of the field equations; the constraints arise always because the differential equations must obey a set of boundary conditions, the boundary has a nontrivial homotopy group, preserved by the differential equations. Thus, the differential equation solutions can be classified into homotopy classes. No continuous transformation maps a solution in one homotopy class to another; the solutions are distinct, maintain their integrity in the face of powerful forces.
Examples of topological solitons include the screw dislocation in a crystalline lattice, the Dirac string and the magnetic monopole in electromagnetism, the Skyrmion and the Wess–Zumino–Witten model in quantum field theory, the magnetic skyrmion in condensed matter physics, cosmic strings and domain walls in cosmology. In 1834, John Scott Russell describes his wave of translation; the discovery is described here in Scott Russell's own words: I was observing the motion of a boat, drawn along a narrow channel by a pair of horses, when the boat stopped – not so the mass of water in the channel which it had put in motion. I followed it on horseback, overtook it still rolling on at a rate of some eight or nine miles an hour, preserving its original figure some thirty feet long and a foot to a foot and a half in height, its height diminished, after a chase of one or two miles I lost it in the windings of the channel. Such, in the month of August 1834, was my first chance interview with that singular and beautiful phenomenon which I have called the Wave of Translation.
Scott Russell spent some time making theoretical investigations of these waves. He built wave tanks at his home and noticed some key properties: The waves are stable, can travel over large distances The speed depends on the size of the wave, its width on the depth of water. Unlike normal waves they will never merge – so a small wave is overtaken by a large one, rather than the two combining. If a wave is too big for the depth of water, it splits into two, one big and one small. Scott Russell's experimental work
The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union, a meeting that takes place every four years. The Fields Medal is regarded as one of the highest honors a mathematician can receive, has been described as the mathematician's Nobel Prize, although there are several key differences, including frequency of award, number of awards, age limits. According to the annual Academic Excellence Survey by ARWU, the Fields Medal is regarded as the top award in the field of mathematics worldwide, in another reputation survey conducted by IREG in 2013-14, the Fields Medal came after the Abel Prize as the second most prestigious international award in mathematics; the prize comes with a monetary award which, since 2006, has been CA$15,000. The name of the award is in honour of Canadian mathematician John Charles Fields. Fields was instrumental in establishing the award, designing the medal itself, funding the monetary component.
The medal was first awarded in 1936 to Finnish mathematician Lars Ahlfors and American mathematician Jesse Douglas, it has been awarded every four years since 1950. Its purpose is to give recognition and support to younger mathematical researchers who have made major contributions. In 2014, the Iranian mathematician Maryam Mirzakhani became the first female Fields Medalist. In all, sixty people have been awarded the Fields Medal; the most recent group of Fields Medalists received their awards on 1 August 2018 at the opening ceremony of the IMU International Congress, held in Rio de Janeiro, Brazil. The medal belonging to one of the four joint winners, Caucher Birkar, was stolen shortly after the event; the ICM presented Birkar with a replacement medal a few days later. The Fields Medal has for a long time been regarded as the most prestigious award in the field of mathematics and is described as the Nobel Prize of Mathematics. Unlike the Nobel Prize, the Fields Medal is only awarded every four years.
The Fields Medal has an age limit: a recipient must be under age 40 on 1 January of the year in which the medal is awarded. This is similar to restrictions applicable to the Clark Medal in economics; the under-40 rule is based on Fields's desire that "while it was in recognition of work done, it was at the same time intended to be an encouragement for further achievement on the part of the recipients and a stimulus to renewed effort on the part of others." Moreover, an individual can only be awarded one Fields Medal. This is in contrast with the Nobel Prize, awarded to an individual or an entity more than once, whether in the same category, or in different categories; the monetary award is much lower than the 8,000,000 Swedish kronor given with each Nobel prize as of 2014. Other major awards in mathematics, such as the Abel Prize and the Chern Medal, have larger monetary prizes compared to the Fields Medal; the medal was first awarded in 1936 to the Finnish mathematician Lars Ahlfors and the American mathematician Jesse Douglas, it has been awarded every four years since 1950.
Its purpose is to give recognition and support to younger mathematical researchers who have made major contributions. In 1954, Jean-Pierre Serre became the youngest winner of the Fields Medal, at 27, he retains this distinction. In 1966, Alexander Grothendieck boycotted the ICM, held in Moscow, to protest Soviet military actions taking place in Eastern Europe. Léon Motchane and director of the Institut des Hautes Études Scientifiques and accepted Grothendieck's Fields Medal on his behalf. In 1970, Sergei Novikov, because of restrictions placed on him by the Soviet government, was unable to travel to the congress in Nice to receive his medal. In 1978, Grigory Margulis, because of restrictions placed on him by the Soviet government, was unable to travel to the congress in Helsinki to receive his medal; the award was accepted on his behalf by Jacques Tits, who said in his address: "I cannot but express my deep disappointment—no doubt shared by many people here—in the absence of Margulis from this ceremony.
In view of the symbolic meaning of this city of Helsinki, I had indeed grounds to hope that I would have a chance at last to meet a mathematician whom I know only through his work and for whom I have the greatest respect and admiration."In 1982, the congress was due to be held in Warsaw but had to be rescheduled to the next year, because of martial law introduced in Poland on 13 December 1981. The awards were announced at the ninth General Assembly of the IMU earlier in the year and awarded at the 1983 Warsaw congress. In 1990, Edward Witten became the first physicist to win the award. In 1998, at the ICM, Andrew Wiles was presented by the chair of the Fields Medal Committee, Yuri I. Manin, with the first-ever IMU silver plaque in recognition of his proof of Fermat's Last Theorem. Don Zagier referred to the plaque as a "quantized Fields Medal". Accounts of this award make reference that at the time of the award Wiles was over the age limit for the Fields medal. Although Wiles was over the age limit in 1994, he was thought to be a favorite to win the medal.
In 2006, Grigori Perelman, who proved the Poincaré conjecture, refused his Fields Medal and did not attend the congress. In 2014, Maryam Mirzakhani became the first woman as well as the first Iranian to win the Fields Medal, Artur Avila became the first South American and Manjul Bhargava became the first person of Indian origin to do so. President Rouhani congratulated her for this
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work to solve mathematical problems. Mathematics is concerned with numbers, quantity, space and change. One of the earliest known mathematicians was Thales of Miletus, he is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number", it was the Pythagoreans who coined the term "mathematics", with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypatia of Alexandria, she succeeded her father as Librarian at the Great Library and wrote many works on applied mathematics. Because of a political dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked and scraping off her skin with clamshells.
Science and mathematics in the Islamic world during the Middle Ages followed various models and modes of funding varied based on scholars. It was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. Funding for translation of scientific texts in other languages was ongoing throughout the reign of certain caliphs, it turned out that certain scholars became experts in the works they translated and in turn received further support for continuing to develop certain sciences; as these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences. An example of a translator and mathematician who benefited from this type of support was al-Khawarizmi. A notable feature of many scholars working under Muslim rule in medieval times is that they were polymaths. Examples include the work on optics and astronomy of Ibn al-Haytham; the Renaissance brought an increased emphasis on science to Europe.
During this period of transition from a feudal and ecclesiastical culture to a predominantly secular one, many notable mathematicians had other occupations: Luca Pacioli. As time passed, many mathematicians gravitated towards universities. An emphasis on free thinking and experimentation had begun in Britain's oldest universities beginning in the seventeenth century at Oxford with the scientists Robert Hooke and Robert Boyle, at Cambridge where Isaac Newton was Lucasian Professor of Mathematics & Physics. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the “regurgitation of knowledge” to “encourag productive thinking.” In 1810, Humboldt convinced the King of Prussia to build a university in Berlin based on Friedrich Schleiermacher’s liberal ideas. Thus and laboratories started to evolve. British universities of this period adopted some approaches familiar to the Italian and German universities, but as they enjoyed substantial freedoms and autonomy the changes there had begun with the Age of Enlightenment, the same influences that inspired Humboldt.
The Universities of Oxford and Cambridge emphasized the importance of research, arguably more authentically implementing Humboldt’s idea of a university than German universities, which were subject to state authority. Overall, science became the focus of universities in the 20th centuries. Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge; the German university system fostered professional, bureaucratically regulated scientific research performed in well-equipped laboratories, instead of the kind of research done by private and individual scholars in Great Britain and France. In fact, Rüegg asserts that the German system is responsible for the development of the modern research university because it focused on the idea of “freedom of scientific research and study.” Mathematicians cover a breadth of topics within mathematics in their undergraduate education, proceed to specialize in topics of their own choice at the graduate level.
In some universities, a qualifying exam serves to test both the breadth and depth of a student's understanding of mathematics. Mathematicians involved with solving problems with applications in real life are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their specialized knowledge and professional methodology, approach many of the imposing problems presented in related scientific fields. With professional focus on a wide variety of problems, theoretical systems, localized constructs, applied mathematicians work in the study and formulation of mathematical models. Mathematicians and applied mathematicians are considered to be two of the STEM careers; the discipline of applied mathematics concerns