1.
Budapest
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Budapest is the capital and most populous city of Hungary, one of the largest cities in the European Union and sometimes described as the primate city of Hungary. It has an area of 525 square kilometres and a population of about 1.8 million within the limits in 2016. Budapest became a single city occupying both banks of the Danube river with the unification of Buda and Óbuda on the west bank, the history of Budapest began with Aquincum, originally a Celtic settlement that became the Roman capital of Lower Pannonia. Hungarians arrived in the territory in the 9th century and their first settlement was pillaged by the Mongols in 1241–1242. The re-established town became one of the centres of Renaissance humanist culture by the 15th century, following the Battle of Mohács and nearly 150 years of Ottoman rule, the region entered a new age of prosperity, and Budapest became a global city after its unification in 1873. It also became the co-capital of the Austro-Hungarian Empire, a power that dissolved in 1918. Budapest was the point of the Hungarian Revolution of 1848, the Hungarian Republic of Councils in 1919, the Battle of Budapest in 1945. Budapest is an Alpha- global city, with strengths in arts, commerce, design, education, entertainment, fashion, finance, healthcare, media, services, research, and tourism. Its business district hosts the Budapest Stock Exchange and the headquarters of the largest national and international banks and it is the highest ranked Central and Eastern European city on Innovation Cities Top 100 index. Budapest attracts 4.4 million international tourists per year, making it the 25th most popular city in the world, further famous landmarks include Andrássy Avenue, St. It has around 80 geothermal springs, the worlds largest thermal water system, second largest synagogue. Budapest is home to the headquarters of the European Institute of Innovation and Technology, the European Police College, over 40 colleges and universities are located in Budapest, including the Eötvös Loránd University, Central European University and Budapest University of Technology and Economics. Budapest is the combination of the city names Buda and Pest, One of the first documented occurrences of the combined name Buda-Pest was in 1831 in the book Világ, written by Count István Széchenyi. The origins of the names Buda and Pest are obscure, according to chronicles from the Middle Ages, the name Buda comes from the name of its founder, Bleda, brother of the Hunnic ruler Attila. The theory that Buda was named after a person is also supported by modern scholars, an alternative explanation suggests that Buda derives from the Slavic word вода, voda, a translation of the Latin name Aquincum, which was the main Roman settlement in the region. There are also theories about the origin of the name Pest. One of the states that the word Pest comes from the Roman times. According to another theory, Pest originates from the Slavic word for cave, or oven, the first settlement on the territory of Budapest was built by Celts before 1 AD
2.
San Diego
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San Diego is a major city in California, United States. It is in San Diego County, on the coast of the Pacific Ocean in Southern California, approximately 120 miles south of Los Angeles and immediately adjacent to the border with Mexico. With an estimated population of 1,394,928 as of July 1,2015, San Diego is the eighth-largest city in the United States and second-largest in California. It is part of the San Diego–Tijuana conurbation, the second-largest transborder agglomeration between the US and a country after Detroit–Windsor, with a population of 4,922,723 people. San Diego has been called the birthplace of California, historically home to the Kumeyaay people, San Diego was the first site visited by Europeans on what is now the West Coast of the United States. Upon landing in San Diego Bay in 1542, Juan Rodríguez Cabrillo claimed the area for Spain, the Presidio and Mission San Diego de Alcalá, founded in 1769, formed the first European settlement in what is now California. In 1821, San Diego became part of the newly independent Mexico, in 1850, California became part of the United States following the Mexican–American War and the admission of California to the union. The city is the seat of San Diego County and is the center of the region as well as the San Diego–Tijuana metropolitan area. San Diegos main economic engines are military and defense-related activities, tourism, international trade, the presence of the University of California, San Diego, with the affiliated UCSD Medical Center, has helped make the area a center of research in biotechnology. The original inhabitants of the region are now known as the San Dieguito, the area of San Diego has been inhabited by the Kumeyaay people. The first European to visit the region was Portuguese-born explorer Juan Rodríguez Cabrillo sailing under the flag of Castile, sailing his flagship San Salvador from Navidad, New Spain, Cabrillo claimed the bay for the Spanish Empire in 1542, and named the site San Miguel. In November 1602, Sebastián Vizcaíno was sent to map the California coast, in May 1769, Gaspar de Portolà established the Fort Presidio of San Diego on a hill near the San Diego River. It was the first settlement by Europeans in what is now the state of California, in July of the same year, Mission San Diego de Alcalá was founded by Franciscan friars under Junípero Serra. By 1797, the mission boasted the largest native population in Alta California, with over 1,400 neophytes living in, Mission San Diego was the southern anchor in California of the historic mission trail El Camino Real. Both the Presidio and the Mission are National Historic Landmarks, in 1821, Mexico won its independence from Spain, and San Diego became part of the Mexican territory of Alta California. In 1822, Mexico began attempting to extend its authority over the territory of Alta California. The fort on Presidio Hill was gradually abandoned, while the town of San Diego grew up on the land below Presidio Hill. The Mission was secularized by the Mexican government in 1833, the 432 residents of the town petitioned the governor to form a pueblo, and Juan María Osuna was elected the first alcalde, defeating Pío Pico in the vote
3.
California
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California is the most populous state in the United States and the third most extensive by area. Located on the western coast of the U. S, California is bordered by the other U. S. states of Oregon, Nevada, and Arizona and shares an international border with the Mexican state of Baja California. Los Angeles is Californias most populous city, and the second largest after New York City. The Los Angeles Area and the San Francisco Bay Area are the nations second- and fifth-most populous urban regions, California also has the nations most populous county, Los Angeles County, and its largest county by area, San Bernardino County. The Central Valley, an agricultural area, dominates the states center. What is now California was first settled by various Native American tribes before being explored by a number of European expeditions during the 16th and 17th centuries, the Spanish Empire then claimed it as part of Alta California in their New Spain colony. The area became a part of Mexico in 1821 following its war for independence. The western portion of Alta California then was organized as the State of California, the California Gold Rush starting in 1848 led to dramatic social and demographic changes, with large-scale emigration from the east and abroad with an accompanying economic boom. If it were a country, California would be the 6th largest economy in the world, fifty-eight percent of the states economy is centered on finance, government, real estate services, technology, and professional, scientific and technical business services. Although it accounts for only 1.5 percent of the states economy, the story of Calafia is recorded in a 1510 work The Adventures of Esplandián, written as a sequel to Amadis de Gaula by Spanish adventure writer Garci Rodríguez de Montalvo. The kingdom of Queen Calafia, according to Montalvo, was said to be a land inhabited by griffins and other strange beasts. This conventional wisdom that California was an island, with maps drawn to reflect this belief, shortened forms of the states name include CA, Cal. Calif. and US-CA. Settled by successive waves of arrivals during the last 10,000 years, various estimates of the native population range from 100,000 to 300,000. The Indigenous peoples of California included more than 70 distinct groups of Native Americans, ranging from large, settled populations living on the coast to groups in the interior. California groups also were diverse in their organization with bands, tribes, villages. Trade, intermarriage and military alliances fostered many social and economic relationships among the diverse groups, the first European effort to explore the coast as far north as the Russian River was a Spanish sailing expedition, led by Portuguese captain Juan Rodríguez Cabrillo, in 1542. Some 37 years later English explorer Francis Drake also explored and claimed a portion of the California coast in 1579. Spanish traders made unintended visits with the Manila galleons on their trips from the Philippines beginning in 1565
4.
Czechoslovakia
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From 1939 to 1945, following its forced division and partial incorporation into Nazi Germany, the state did not de facto exist but its government-in-exile continued to operate. From 1948 to 1990, Czechoslovakia was part of the Soviet bloc with a command economy and its economic status was formalized in membership of Comecon from 1949, and its defense status in the Warsaw Pact of May 1955. A period of liberalization in 1968, known as the Prague Spring, was forcibly ended when the Soviet Union, assisted by several other Warsaw Pact countries. In 1993, Czechoslovakia split into the two states of the Czech Republic and Slovakia. Form of state 1918–1938, A democratic republic, 1938–1939, After annexation of Sudetenland by Nazi Germany in 1938, the region gradually turned into a state with loosened connections among the Czech, Slovak, and Ruthenian parts. A large strip of southern Slovakia and Carpatho-Ukraine was annexed by Hungary, 1939–1945, The region was split into the Protectorate of Bohemia and Moravia and the Slovak Republic. A government-in-exile continued to exist in London, supported by the United Kingdom, United States and its Allies, after the German invasion of Russia, Czechoslovakia adhered to the Declaration by United Nations and was a founding member of the United Nations. 1946–1948, The country was governed by a government with communist ministers, including the prime minister. Carpathian Ruthenia was ceded to the Soviet Union, 1948–1989, The country became a socialist state under Soviet domination with a centrally planned economy. In 1960, the country became a socialist republic, the Czechoslovak Socialist Republic. It was a state of the Soviet Union. 1989–1990, The federal republic consisted of the Czech Socialist Republic, 1990–1992, Following the Velvet Revolution, the state was renamed the Czech and Slovak Federal Republic, consisting of the Czech Republic and the Slovak Republic. Neighbours Austria 1918–1938, 1945–1992 Germany Hungary Poland Romania 1918–1938 Soviet Union 1945–1991 Ukraine 1991–1992 Topography The country was of irregular terrain. The western area was part of the north-central European uplands, the eastern region was composed of the northern reaches of the Carpathian Mountains and lands of the Danube River basin. Climate The weather is mild winters and mild summers, influenced by the Atlantic Ocean from the west, Baltic Sea from the north, and Mediterranean Sea from the south. The area was long a part of the Austro Hungarian Empire until the Empire collapsed at the end of World War I, the new state was founded by Tomáš Garrigue Masaryk, who served as its first president from 14 November 1918 to 14 December 1935. He was succeeded by his ally, Edvard Beneš. The roots of Czech nationalism go back to the 19th century, nationalism became a mass movement in the last half of the 19th century
5.
United States
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Forty-eight of the fifty states and the federal district are contiguous and located in North America between Canada and Mexico. The state of Alaska is in the northwest corner of North America, bordered by Canada to the east, the state of Hawaii is an archipelago in the mid-Pacific Ocean. The U. S. territories are scattered about the Pacific Ocean, the geography, climate and wildlife of the country are extremely diverse. At 3.8 million square miles and with over 324 million people, the United States is the worlds third- or fourth-largest country by area, third-largest by land area. It is one of the worlds most ethnically diverse and multicultural nations, paleo-Indians migrated from Asia to the North American mainland at least 15,000 years ago. European colonization began in the 16th century, the United States emerged from 13 British colonies along the East Coast. Numerous disputes between Great Britain and the following the Seven Years War led to the American Revolution. On July 4,1776, during the course of the American Revolutionary War, the war ended in 1783 with recognition of the independence of the United States by Great Britain, representing the first successful war of independence against a European power. The current constitution was adopted in 1788, after the Articles of Confederation, the first ten amendments, collectively named the Bill of Rights, were ratified in 1791 and designed to guarantee many fundamental civil liberties. During the second half of the 19th century, the American Civil War led to the end of slavery in the country. By the end of century, the United States extended into the Pacific Ocean. The Spanish–American War and World War I confirmed the status as a global military power. The end of the Cold War and the dissolution of the Soviet Union in 1991 left the United States as the sole superpower. The U. S. is a member of the United Nations, World Bank, International Monetary Fund, Organization of American States. The United States is a developed country, with the worlds largest economy by nominal GDP. It ranks highly in several measures of performance, including average wage, human development, per capita GDP. While the U. S. economy is considered post-industrial, characterized by the dominance of services and knowledge economy, the United States is a prominent political and cultural force internationally, and a leader in scientific research and technological innovations. In 1507, the German cartographer Martin Waldseemüller produced a map on which he named the lands of the Western Hemisphere America after the Italian explorer and cartographer Amerigo Vespucci
6.
Canada
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Canada is a country in the northern half of North America. Canadas border with the United States is the worlds longest binational land border, the majority of the country has a cold or severely cold winter climate, but southerly areas are warm in summer. Canada is sparsely populated, the majority of its territory being dominated by forest and tundra. It is highly urbanized with 82 per cent of the 35.15 million people concentrated in large and medium-sized cities, One third of the population lives in the three largest cities, Toronto, Montreal and Vancouver. Its capital is Ottawa, and other urban areas include Calgary, Edmonton, Quebec City, Winnipeg. Various aboriginal peoples had inhabited what is now Canada for thousands of years prior to European colonization. Pursuant to the British North America Act, on July 1,1867, the colonies of Canada, New Brunswick and this began an accretion of provinces and territories to the mostly self-governing Dominion to the present ten provinces and three territories forming modern Canada. With the Constitution Act 1982, Canada took over authority, removing the last remaining ties of legal dependence on the Parliament of the United Kingdom. Canada is a parliamentary democracy and a constitutional monarchy, with Queen Elizabeth II being the head of state. The country is officially bilingual at the federal level and it is one of the worlds most ethnically diverse and multicultural nations, the product of large-scale immigration from many other countries. Its advanced economy is the eleventh largest in the world, relying chiefly upon its abundant natural resources, Canadas long and complex relationship with the United States has had a significant impact on its economy and culture. Canada is a country and has the tenth highest nominal per capita income globally as well as the ninth highest ranking in the Human Development Index. It ranks among the highest in international measurements of government transparency, civil liberties, quality of life, economic freedom, Canada is an influential nation in the world, primarily due to its inclusive values, years of prosperity and stability, stable economy, and efficient military. While a variety of theories have been postulated for the origins of Canada. In 1535, indigenous inhabitants of the present-day Quebec City region used the word to direct French explorer Jacques Cartier to the village of Stadacona, from the 16th to the early 18th century Canada referred to the part of New France that lay along the St. Lawrence River. In 1791, the area became two British colonies called Upper Canada and Lower Canada collectively named The Canadas, until their union as the British Province of Canada in 1841. Upon Confederation in 1867, Canada was adopted as the name for the new country at the London Conference. The transition away from the use of Dominion was formally reflected in 1982 with the passage of the Canada Act, later that year, the name of national holiday was changed from Dominion Day to Canada Day
7.
Hungarian Americans
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Hungarian Americans are Americans of Hungarian descent. In 1583, a Hungarian poet Stephanus Parmenius joined Humphrey Gilberts expedition to North America with the intention of writing a chronicle of the voyage, Parmenius reached Newfoundland, likely becoming the first Hungarian in the New World. Hungarians have long settled in the New World, such as Michael de Kovats, Hungarians have maintained a constant state of emigration to the United States since then, however, they are best known for three principle waves of emigration. He is widely remembered today as the Father of California Viticulture or the Father of Modern Winemaking in California, lajos Kossuth gave a seven-month speaking tour of the US in 1851 and 1852 to great acclaim as a champion of liberty, thereby unleashing a brief outburst of pro-Hungarian emotions. He left embittered because his refusal to oppose slavery alienated his natural constituency, by 1860,2,710 Hungarians lived in the US, and at least 99 of them fought in the Civil War. Their motivations were not so much antislavery as a belief in democracy, a taste for adventure, validation of their military credentials, and solidarity with their American neighbors. Unlike the educated classes who formed the core of the 1849 wave, the majority of the 2 million immigrants from the Kingdom of Hungary were not ethnic Hungarians but belonged to the Slavic, Romanian or German minorities. An increase of immigration from Hungary was also observed after World War II and The Holocaust, the circumstances of the third wave of emigration had much in common with the first wave. In 1956, Hungary was again under the power of a state, this time the Soviet Union. There was a renewed economic migration after the end of communism in Hungary during the 1990s to 2000s, other places with over 10% are Fairport Harbor, Ohio and West Pike Run Township, Pennsylvania. About one hundred other municipalities have more than 5% of Hungarian-American residents, Wallingford, Connecticut, has a vibrant Hungarian-American Club and community. In entertainment, Szőke Szakáll, known as S. Z. Sakall, was a Hungarian film character actor and he was in many films including In the Good Old Summertime, Lullaby of Broadway, Christmas in Connecticut and Casablanca in which he played Carl, the head waiter. The comic style of Ernie Kovacs influenced numerous television programs for years to come. The Fox Film Corporation was formed by William Fox, actress Vilma Bánky starred in numerous silent films opposite Hollywood legends such as Rudolph Valentino and Ronald Colman. Actress Drew Barrymores mother is Hungarian, actor Tony Curtis has been in over 100 films, including his iconic roles in Some Like It Hot and The Defiant Ones. Actress Jessica Szohr of Gossip Girl is of partial Hungarian descent, actor Peter Lorre became famous after his role as a murderer in Fritz Langs M and went on to play many antagonistic villain roles. Legendary actor Béla Lugosi played Count Dracula in the stage version, actress Ilona Massey was frequently billed as the new Dietrich and famously played the role of a femme fatale in Love Happy. Sex symbol Zsa Zsa Gabor was perhaps known for her status as a socialite
8.
McGill University
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McGill University is a public research university in Montreal, Quebec, Canada. It was established in 1821 by royal charter, issued by King George IV of Great Britain, the University bears the name of James McGill, a prominent Montreal merchant from Scotland whose bequest in 1813 formed the universitys precursor, McGill College. Its academic units are organized into 11 main Faculties and Schools, McGill offers degrees and diplomas in over 300 fields of study, with the highest average admission requirements of any Canadian university. Most students are enrolled in the five largest faculties, namely Arts, Science, Medicine, Engineering, tuition fees vary significantly between in-province, out-of-province, and international students, as well as between faculties. Scholarships are generous, yet highly competitive and relatively difficult to attain, throughout its long history, McGill alumni were instrumental in inventing or initially organizing football, basketball, and ice hockey. In 1816 the RIAL was authorized to operate two new Royal Grammar Schools, in Quebec City and in Montreal and this was an important first step in the creation of nondenominational schools. When James McGill died in 1813 his bequest was administered by the RIAL, the original two Royal Grammar Schools closed in 1846 and by the mid-19th century the RIAL lost control of the other 82 grammar schools it had administered. Its sole remaining purpose was to administer the McGill bequest on behalf of the private college, since the revised Royal Charter of 1852, The Trustees of the RIAL comprise the Board of Governors of McGill University. James McGill, born in Glasgow, Scotland on 6 October 1744, was a merchant in Quebec. Between 1811 and 1813, he drew up a will leaving his Burnside estate, a 19-hectare tract of rural land and 10,000 pounds to the Royal Institution for the Advancement of Learning. As a condition of the bequest, the land and funds had to be used for the establishment of a University or College, for the purposes of Education and the Advancement of Learning in the said Province. On March 31,1821, after protracted battles with the Desrivières family. The Charter provided that the College should be deemed and taken as a University, the Faculty of Medicine granted its first degree, a Doctor of Medicine and Surgery, in 1833, this was also the first medical degree to be awarded in Canada. The Faculty of Medicine remained the only functioning faculty until 1843 when the Faculty of Arts commenced teaching in the newly constructed Arts Building. The university also historically has strong linkage with The Canadian Grenadier Guards and this title is marked upon the stone that stands before the Arts building, from where the Guards step off annually to commemorate Remembrance Day. The Faculty of Law was founded in 1848 which is also the oldest of its kind in the nation,48 years later, the school of architecture at McGill University was founded. Sir John William Dawson, McGills principal from 1855 to 1893, is credited with transforming the school into a modern university. He recruited the aid of Montreals wealthiest citizens, many of whom donated property and their names adorn many of the campuss prominent buildings
9.
Carnegie Mellon University
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Carnegie Mellon University is a private research university in Pittsburgh, Pennsylvania. Founded in 1900 by Andrew Carnegie as the Carnegie Technical Schools, in 1967, the Carnegie Institute of Technology merged with the Mellon Institute of Industrial Research to form Carnegie Mellon University. The universitys 140-acre main campus is 3 miles from Downtown Pittsburgh, john Heinz III College of Information Systems and Public Policy, and the School of Computer Science. The university also has campuses in Qatar and Silicon Valley, with degree-granting programs in six continents, Carnegie Mellon consistently ranks in the top 25 in the national U. S. News & World Report rankings. It is home to the world’s first degree-granting Robotics and Drama programs, the university spent $242 million on research in 2015. Carnegie Mellon counts 13,650 students from 114 countries, over 100,000 living alumni, Carnegies vision was to open a vocational training school for the sons and daughters of working-class Pittsburghers. Carnegie was inspired for the design of his school by the Pratt Institute in Brooklyn, in 1912 the institution changed its name to Carnegie Institute of Technology and began offering four-year degrees. The Mellon Institute of Industrial Research was founded in 1913 by banker and industrialist brothers Andrew, Mellon in honor of their father, Thomas Mellon, the patriarch of the Mellon family. The Institute began as an organization which performed work for government. In 1927, the Mellon Institute incorporated as an independent nonprofit, in 1938, the Mellon Institutes iconic building was completed and it moved to its new, and current, location on Fifth Avenue. In 1967, with support from Paul Mellon, Carnegie Tech merged with the Mellon Institute of Industrial Research to become Carnegie Mellon University, Carnegie Mellons coordinate womens college, the Margaret Morrison Carnegie College closed in 1973 and merged its academic programs with the rest of the university. The industrial research mission of the Mellon Institute survived the merger as the Carnegie Mellon Research Institute and continued doing work on contract to industry, CMRI closed in 2001 and its programs were subsumed by other parts of the university or spun off into independent entities. Carnegie Mellons 140-acre main campus is three miles from downtown Pittsburgh, between Schenley Park and the Squirrel Hill, Shadyside, and Oakland neighborhoods, Carnegie Mellon is bordered to the west by the campus of the University of Pittsburgh. Carnegie Mellon owns 81 buildings in the Oakland and Squirrel Hill neighborhoods of Pittsburgh, for decades the center of student life on campus was Skibo Hall, the Universitys student union. Built in the 1950s, Skibo Halls design was typical of Mid-Century Modern architecture, the original Skibo was razed in the summer of 1994 and replaced by a new student union that is fully wi-fi enabled. Known as University Center, the building was dedicated in 1996, in 2014, Carnegie Mellon re-dedicated the University Center as the Cohon University Center in recognition of the eighth president of the university, Jared Cohon. A large grassy area known as the Cut forms the backbone of the campus, the Cut was formed by filling in a ravine with soil from a nearby hill that was leveled to build the College of Fine Arts building. The northwestern part of the campus was acquired from the United States Bureau of Mines in the 1980s, the sculpture was controversial for its placement, the general lack of input that the campus community had, and its aesthetic appeal
10.
National Medal of Science
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The twelve member presidential Committee on the National Medal of Science is responsible for selecting award recipients and is administered by the National Science Foundation. The National Medal of Science was established on August 25,1959, the medal was originally to honor scientists in the fields of the physical, biological, mathematical, or engineering sciences. The Committee on the National Medal of Science was established on August 23,1961, on January 7,1979, the American Association for the Advancement of Science passed a resolution proposing that the medal be expanded to include the social and behavioral sciences. In response, Senator Ted Kennedy introduced the Science and Technology Equal Opportunities Act into the Senate on March 7,1979, President Jimmy Carters signature enacted this change as Public Law 96-516 on December 12,1980. The first National Medal of Science was awarded on February 18,1963, the first woman to receive a National Medal of Science was Barbara McClintock, who was awarded for her work on plant genetics in 1970. Although Public Law 86-209 provides for 20 recipients of the medal per year, it is typical for approximately 8–15 accomplished scientists, there have been a number of years where no National Medals of Science were awarded. Those years include,1985,1984,1980,1978,1977,1972 and 1971, the awards ceremony is organized by the Office of Science and Technology Policy. It takes place at the White House and is presided by the sitting United States president, each year the National Science Foundation sends out a call to the scientific community for the nomination of new candidates for the National Medal of Science. Individuals are nominated by their peers with each nomination requiring three letters of support from individuals in science and technology, the nomination of a candidate is effective for three years, at the end of three years, the candidates peers are allowed to renominate the candidate. The Committee makes their recommendations to the President for the final awarding decision, the National Medal of Science depicts Man, surrounded by earth, sea, and sky, contemplating and struggling to understand Nature. The crystal in his hand represents the order and also suggests the basic unit of living things. The formula being outlined in the sand symbolizes scientific abstraction
11.
Mathematics
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Mathematics is the study of topics such as quantity, structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope, Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof, when mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry, rigorous arguments first appeared in Greek mathematics, most notably in Euclids Elements. Galileo Galilei said, The universe cannot be read until we have learned the language and it is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth, carl Friedrich Gauss referred to mathematics as the Queen of the Sciences. Benjamin Peirce called mathematics the science that draws necessary conclusions, David Hilbert said of mathematics, We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules, rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise. Albert Einstein stated that as far as the laws of mathematics refer to reality, they are not certain, Mathematics is essential in many fields, including natural science, engineering, medicine, finance and the social sciences. Applied mathematics has led to entirely new mathematical disciplines, such as statistics, Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, the history of mathematics can be seen as an ever-increasing series of abstractions. The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns, in Babylonian mathematics elementary arithmetic first appears in the archaeological record. Numeracy pre-dated writing and numeral systems have many and diverse. Between 600 and 300 BC the Ancient Greeks began a study of mathematics in its own right with Greek mathematics. Mathematics has since been extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today, the overwhelming majority of works in this ocean contain new mathematical theorems and their proofs. The word máthēma is derived from μανθάνω, while the modern Greek equivalent is μαθαίνω, in Greece, the word for mathematics came to have the narrower and more technical meaning mathematical study even in Classical times
12.
University of Michigan
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The University of Michigan, frequently referred to simply as Michigan, is a public research university in Ann Arbor, Michigan, United States. Founded in 1817 in Detroit as the Catholepistemiad, or University of Michigania,20 years before the Michigan Territory became a state, in 1821, the university was officially renamed the University of Michigan. It moved to Ann Arbor in 1837 onto 40 acres of what is now known as Central Campus, the University was a founding member of the Association of American Universities. Considered one of the foremost research universities in the United States, Michigans body of living alumni comprises more than 540,000 people, one of the largest alumni bases of any university in the world. Besides academic life, Michigans athletic teams compete in Division I of the NCAA and are known as the Wolverines. They are members of the Big Ten Conference, the University of Michigan was established in Detroit on August 26,1817 as the Catholepistemiad, or University of Michigania, by the governor and judges of Michigan Territory. Judge Augustus B. Woodward specifically invited The Rev. John Monteith and Father Gabriel Richard, Monteith became its first President and held seven of the professorships, and Richard was Vice President and held the other six professorships. Concurrently, Ann Arbor had set aside 40 acres in the hopes of being selected as the state capital, but when Lansing was chosen as the state capital, the city offered the land for a university. What would become the university moved to Ann Arbor in 1837 thanks to Governor Stevens T. Mason, the original 40 acres was the basis of the present Central Campus. The first classes in Ann Arbor were held in 1841, with six freshmen, eleven students graduated in the first commencement in 1845. By 1866, enrollment increased to 1,205 students, many of whom were Civil War veterans, Women were first admitted in 1870. U-M also became the first American university to use the method of study. Among the early students in the School of Medicine was Jose Celso Barbosa, who in 1880 graduated as valedictorian and he returned to Puerto Rico to practice medicine and also served in high-ranking posts in the government. In 1920 the university reorganized the College of Engineering and formed a committee of 100 industrialists to guide academic research initiatives. The university became a choice for bright Jewish students from New York in the 1920s and 1930s. Because of its standards, U-M gained the nickname Harvard of the West. During World War II, U-Ms research supported military efforts, such as U. S. Navy projects in proximity fuzes, PT boats, and radar jamming. After the war, enrollment expanded rapidly and by 1950, it reached 21,000, as the Cold War and the Space Race took hold, U-M received numerous government grants for strategic research and helped to develop peacetime uses for nuclear energy
13.
Ann Arbor, Michigan
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Ann Arbor is a city in the U. S. state of Michigan and the county seat of Washtenaw County. The 2010 census recorded its population to be 113,934, the citys population was estimated at 117,070 as of July 2015 by the U. S. Census Bureau. The Ann Arbor Metropolitan Statistical Area includes all of Washtenaw County, the city is also part of the larger Detroit–Ann Arbor–Flint, MI Combined Statistical Area with a population of 5,318,744. Ann Arbor was founded in 1824, named for wives of the villages founders, the University of Michigan moved from Detroit to Ann Arbor in 1837, and the city grew at a rapid rate in the early to mid-20th century. During the 1960s and 1970s, the city gained a reputation as a center for left-wing politics, Ann Arbor became a focal point for political activism and anti-Vietnam War movement, as well as various student movements. Ann Arbor is home to the University of Michigan, one of the foremost research universities in the United States, the university shapes Ann Arbors economy significantly as it employs about 30,000 workers, including about 12,000 in the medical center. The citys economy is centered on high technology, with several companies drawn to the area by the universitys research and development infrastructure. In about 1774, the Potawatomi founded two villages in the area of what is now Ann Arbor, Ann Arbor was founded in 1824 by land speculators John Allen and Elisha Walker Rumsey. On 25 May 1824, the plat was registered with Wayne County as Annarbour. Allen and Rumsey decided to name it for their wives, both named Ann, and for the stands of Bur Oak in the 640 acres of land purchased for $800 from the federal government at $1.25 per acre. The local Ojibwa named the settlement kaw-goosh-kaw-nick, after the sound of Allens sawmill, Ann Arbor became the seat of Washtenaw County in 1827, and was incorporated as a village in 1833. The Ann Arbor Land Company, a group of speculators, set aside 40 acres of undeveloped land and offered it to the state of Michigan as the site of the state capital, but lost the bid to Lansing. In 1837, the property was accepted instead as the site of the University of Michigan, since the universitys establishment in the city in 1837, the histories of the University of Michigan and Ann Arbor have been closely linked. Throughout the 1840s and the 1850s settlers continued to come to Ann Arbor, while the earlier settlers were primarily of British ancestry, the newer settlers also consisted of Germans, Irish, and African-Americans. In 1851, Ann Arbor was chartered as a city, though the city showed a drop in population during the Depression of 1873. It was not until the early 1880s that Ann Arbor again saw robust growth, with new immigrants coming from Greece, Italy, Russia, Ann Arbor saw increased growth in manufacturing, particularly in milling. Ann Arbors Jewish community also grew after the turn of the 20th century, during the 1960s and 1970s, the city gained a reputation as an important center for liberal politics. Ann Arbor also became a locus for left-wing activism and anti-Vietnam War movement, during the ensuing 15 years, many countercultural and New Left enterprises sprang up and developed large constituencies within the city
14.
Harvard University
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Although never formally affiliated with any denomination, the early College primarily trained Congregationalist and Unitarian clergy. Its curriculum and student body were gradually secularized during the 18th century, james Bryant Conant led the university through the Great Depression and World War II and began to reform the curriculum and liberalize admissions after the war. The undergraduate college became coeducational after its 1977 merger with Radcliffe College, Harvards $34.5 billion financial endowment is the largest of any academic institution. Harvard is a large, highly residential research university, the nominal cost of attendance is high, but the Universitys large endowment allows it to offer generous financial aid packages. Harvards alumni include eight U. S. presidents, several heads of state,62 living billionaires,359 Rhodes Scholars. To date, some 130 Nobel laureates,18 Fields Medalists, Harvard was formed in 1636 by vote of the Great and General Court of the Massachusetts Bay Colony. In 1638, it obtained British North Americas first known printing press, in 1639 it was named Harvard College after deceased clergyman John Harvard an alumnus of the University of Cambridge who had left the school £779 and his scholars library of some 400 volumes. The charter creating the Harvard Corporation was granted in 1650 and it offered a classic curriculum on the English university model—many leaders in the colony had attended the University of Cambridge—but conformed to the tenets of Puritanism. It was never affiliated with any denomination, but many of its earliest graduates went on to become clergymen in Congregational. The leading Boston divine Increase Mather served as president from 1685 to 1701, in 1708, John Leverett became the first president who was not also a clergyman, which marked a turning of the college toward intellectual independence from Puritanism. When the Hollis Professor of Divinity David Tappan died in 1803 and the president of Harvard Joseph Willard died a year later, in 1804, in 1846, the natural history lectures of Louis Agassiz were acclaimed both in New York and on the campus at Harvard College. Agassizs approach was distinctly idealist and posited Americans participation in the Divine Nature, agassizs perspective on science combined observation with intuition and the assumption that a person can grasp the divine plan in all phenomena. When it came to explaining life-forms, Agassiz resorted to matters of shape based on an archetype for his evidence. Charles W. Eliot, president 1869–1909, eliminated the position of Christianity from the curriculum while opening it to student self-direction. While Eliot was the most crucial figure in the secularization of American higher education, he was motivated not by a desire to secularize education, during the 20th century, Harvards international reputation grew as a burgeoning endowment and prominent professors expanded the universitys scope. Rapid enrollment growth continued as new schools were begun and the undergraduate College expanded. Radcliffe College, established in 1879 as sister school of Harvard College, Harvard became a founding member of the Association of American Universities in 1900. In the early 20th century, the student body was predominately old-stock, high-status Protestants, especially Episcopalians, Congregationalists, by the 1970s it was much more diversified
15.
Edward B. Curtis
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Edward Baldwin Curtis is an American mathematician. Edward Curtis received his bachelors degree from Harvard University in 1954, after graduate study from 1958 to 1959 at the University of Oxford, he returned to Harvard and earned a Ph. D. there in 1962. His thesis The Lower Central Series for Free Group Complexes was supervised by Raoul Bott, Curtis became an instructor at the Massachusetts Institute of Technology, assistant professor, and associate professor. In 1970 he became a professor at the University of Washington in Seattle and his research interests include graph theory and flow networks. In 1967 for his studies on algebraic topology he received a Guggenheim Fellowship, the Lower Central Series for Free Group Complexes. With James A. Morrow, Inverse problems for electrical networks, mary Ellis Woodring and Susan Park Norton, Reports of the President and the Treasurer 1967 and 1968
16.
Robert MacPherson (mathematician)
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Robert Duncan MacPherson is an American mathematician at the Institute for Advanced Study and Princeton University. He is best known for the invention of intersection homology with Mark Goresky, MacPherson previously taught at Brown University, the University of Paris, and the Massachusetts Institute of Technology. In 1983 he gave an address at the International Congress of Mathematicians in Warsaw. Educated at Swarthmore College and Harvard University, MacPherson received his Ph. D. from Harvard in 1970 and his thesis, written under the direction of Raoul Bott, was entitled Singularities of Maps and Characteristic Classes. Among his many Ph. D students are Kari Vilonen and Mark Goresky, in 1992 MacPherson was awarded the NAS Award in Mathematics from the National Academy of Sciences. In 2002 he and Goresky were awarded the Leroy P. Steele Prize by the American Mathematical Society, in 2012 he became a fellow of the American Mathematical Society. Goresky, Mark, MacPherson, Robert, La dualité de Poincaré pour les espaces singuliers, mR0440533 Goresky, Mark, MacPherson, Robert, Intersection homology theory, Topology 19, no. Doi,10. 1016/0040-938390003-8 MR0572580 Goresky, Mark, MacPherson, Robert, doi,10. 1007/BF01389130 MR0696691 Robert MacPherson at the Mathematics Genealogy Project IAS page, including links to publications and CV The work of Robert MacPherson
17.
Stephen Smale
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Stephen Smale is an American mathematician from Flint, Michigan. His research concerns topology, dynamical systems and mathematical economics and he was awarded the Fields Medal in 1966 and spent more than three decades on the mathematics faculty of the University of California, Berkeley. Smale entered the University of Michigan in 1948, initially, he was a good student, placing into an honors calculus sequence taught by Bob Thrall and earning himself As. However, his sophomore and junior years were marred with mediocre grades, mostly Bs, Cs, however, with some luck, Smale was accepted as a graduate student at the University of Michigans mathematics department. Yet again, Smale performed poorly in his first years, earning a C average as a graduate student and it was only when the department chair, Hildebrandt, threatened to kick Smale out that he began to work hard. Smale finally earned his Ph. D. in 1957, under Raoul Bott, Smale began his career as an instructor at the college at the University of Chicago. In 1958, he astounded the world with a proof of a sphere eversion. After having made great strides in topology, he turned to the study of dynamical systems. His first contribution is the Smale horseshoe that started significant research in dynamical systems and he also outlined a research program carried out by many others. Smale is also known for injecting Morse theory into mathematical economics, in 1998 he compiled a list of 18 problems in mathematics to be solved in the 21st century, known as Smales problems. This list was compiled in the spirit of Hilberts famous list of problems produced in 1900, in fact, Smales list contains some of the original Hilbert problems, including the Riemann hypothesis and the second half of Hilberts sixteenth problem, both of which are still unsolved. Earlier in his career, Smale was involved in controversy over remarks he made regarding his work habits while proving the higher-dimensional Poincaré conjecture and he said that his best work had been done on the beaches of Rio. This led to the withholding of his grant money from the NSF and he has been politically active in various movements in the past, such as the Free Speech movement and the movement against the Vietnam War. At one time he was subpoenaed by the House Un-American Activities Committee, in 1960 Smale was appointed an associate professor of mathematics at the University of California, Berkeley, moving to a professorship at Columbia University the following year. In 1964 he returned to a professorship at UC Berkeley where he has spent the part of his career. He retired from UC Berkeley in 1995 and took up a post as professor at the City University of Hong Kong and he also amassed over the years one of the finest private mineral collections in existence. Many of Smales mineral specimens can be seen in the book—The Smale Collection, since 2002 Smale is a Professor at the Toyota Technological Institute at Chicago, starting August 1,2009, he is also a Distinguished University Professor at the City University of Hong Kong. In 2007, Smale was awarded the Wolf Prize in mathematics, generalized Poincarés conjecture in dimensions greater than four
18.
Fellow of the Royal Society
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As of 2016, there are around 1600 living Fellows, Foreign and Honorary Members. Fellowship of the Royal Society has been described by The Guardian newspaper as “the equivalent of a lifetime achievement Oscar” with several institutions celebrating their announcement each year. Up to 60 new Fellows, honorary and foreign members are elected annually usually in May, each candidate is considered on their merits and can be proposed from any sector of the scientific community. Fellows are elected for life on the basis of excellence in science and are entitled to use the post-nominal letters FRS, see Category, Fellows of the Royal Society and Category, Female Fellows of the Royal Society. Every year, Fellows elect up to ten new Foreign Members, like Fellows, Foreign Members are elected for life through peer review on the basis of excellence in science. As of 2016 there are around 165 Foreign Members, who are entitled to use the post-nominal ForMemRS, see Category, Foreign Members of the Royal Society. Honorary Fellows include Bill Bryson, Melvyn Bragg, Robin Saxby, David Sainsbury, Baron Sainsbury of Turville, Honorary Fellows are entitled to use the post nominal letters HonFRS. Others including John Maddox, Patrick Moore and Lisa Jardine were elected as honorary fellows, statute 12 is a legacy mechanism for electing members before official honorary membership existed in 1997. Fellows elected under statute 12 include David Attenborough and John Palmer, prime Ministers of the United Kingdom such as Margaret Thatcher, Neville Chamberlain, H. H. Asquith were elected under statute 12, see Category, Fellows of the Royal Society. The Council of the Royal Society can recommend members of the British Royal Family for election as Royal Fellows of the Royal Society. As of 2016 there are five royal fellows, Charles, Prince of Wales, Anne, Princess Royal, Prince Edward, Duke of Kent, Prince William, Duke of Cambridge and Prince Andrew, Duke of York. Her Majesty the Queen, Elizabeth II is not a Royal Fellow, Prince Philip, Duke of Edinburgh was elected under statute 12, not as a Royal Fellow. The election of new fellows is announced annually in May, after their nomination, each candidate for Fellowship or Foreign Membership is nominated by two Fellows of the Royal Society, who sign a certificate of proposal. Previously, nominations required at least five fellows to support each nomination by the proposer, the certificate of election includes a statement of the principal grounds on which the proposal is being made. There is no limit on the number of nominations each year. In 2015, there were 654 candidates for election as Fellows and 106 candidates for Foreign Membership. The final list of up to 52 Fellowship candidates and up to 10 Foreign Membership candidates is confirmed by the Council in April, a candidate is elected if he or she secures two-thirds of votes of those Fellows present and voting. A further maximum of six can be ‘Honorary’, ‘General’ or ‘Royal’ Fellows, nominations for Fellowship are peer reviewed by sectional committees, each with fifteen members and a chair
19.
Hungarians
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Hungarians, also known as Magyars, are a nation and ethnic group who speak Hungarian and are primarily associated with Hungary. There are around 13. 1–14.7 million Hungarians, of whom 8. 5–9.8 million live in todays Hungary, the Hungarians own ethnonym to denote themselves in the Early Middle Ages is uncertain. The Magyars/Hungarians probably belonged to the Onogur tribal alliance, and it is possible that they became its ethnic majority, in the Early Middle Ages the Hungarians had many names, including Ungherese, Ungar, and Hungarus. The H- prefix is an addition of Medieval Latin, another possible explanation comes from the Old Russian Yugra. It may refer to the Hungarians during a time when they dwelt east of the Ural Mountains along the borders of Europe. The Hungarian people refer to themselves by the demonym Magyar rather than Hungarian, Magyar is Finno-Ugric from the Old Hungarian mogyër. Magyar possibly derived from the name of the most prominent Hungarian tribe, the tribal name Megyer became Magyar in reference to the Hungarian people as a whole. Magyar may also derive from the Hunnic Muageris or Mugel, the Greek cognate of Tourkia was used by the scholar and Byzantine Emperor Constantine VII Porphyrogenitus in his De Administrando Imperio of c. AD950, though in his use, Turks always referred to Magyars, the historical Latin phrase Natio Hungarica had a wider meaning because it once referred to all nobles of the Kingdom of Hungary, regardless of their ethnicity. During the 4th millennium BC, the Uralic-speaking peoples who were living in the central, some dispersed towards the west and northwest and came into contact with Iranian speakers who were spreading northwards. From at least 2000 BC onwards, the Ugrian speakers became distinguished from the rest of the Uralic community, judging by evidence from burial mounds and settlement sites, they interacted with the Indo-Iranian Andronovo culture. In the 4th and 5th centuries AD, the Hungarians moved from the west of the Ural Mountains to the area between the southern Ural Mountains and the Volga River known as Bashkiria and Perm Krai. In the early 8th century, some of the Hungarians moved to the Don River to an area between the Volga, Don and the Seversky Donets rivers, meanwhile, the descendants of those Hungarians who stayed in Bashkiria remained there as late as 1241. The Hungarians around the Don River were subordinates of the Khazar khaganate and their neighbours were the archaeological Saltov Culture, i. e. Bulgars and the Alans, from whom they learned gardening, elements of cattle breeding and of agriculture. Tradition holds that the Hungarians were organized in a confederacy of seven tribes, the names of the seven tribes were, Jenő, Kér, Keszi, Kürt-Gyarmat, Megyer, Nyék, and Tarján. Around 830, a rebellion broke out in the Khazar khaganate, as a result, three Kabar tribes of the Khazars joined the Hungarians and moved to what the Hungarians call the Etelköz, the territory between the Carpathians and the Dnieper River. The Hungarians faced their first attack by the Pechenegs around 854, the new neighbours of the Hungarians were the Varangians and the eastern Slavs. In 895/896, under the leadership of Árpád, some Hungarians crossed the Carpathians, the tribe called Magyar was the leading tribe of the Hungarian alliance that conquered the centre of the basin
20.
Americans
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Americans are citizens of the United States of America. The country is home to people of different national origins. As a result, Americans do not equate their nationality with ethnicity, although citizens make up the majority of Americans, non-citizen residents, dual citizens, and expatriates may also claim an American identity. See Names for United States citizens. S, virgin Islands and Northern Mariana Islands in the 20th century. It also includes influences of African-American culture, westward expansion integrated the Creoles and Cajuns of Louisiana and the Hispanos of the Southwest and brought close contact with the culture of Mexico. Large-scale immigration in the late 19th and early 20th centuries from Southern and Eastern Europe introduced a variety of elements, immigration from Asia, Africa, and Latin America has also had impact. A cultural melting pot, or pluralistic salad bowl, describes the way in which generations of Americans have celebrated and exchanged distinctive cultural characteristics, in addition to the United States, Americans and people of American descent can be found internationally. As many as seven million Americans are estimated to be living abroad, the United States of America is a diverse country, racially, and ethnically. Some other race is also an option in the census and other surveys, people of European descent, or White Americans, constitute the majority of the 308 million people living in the United States, with 72. 4% of the population in the 2010 United States Census. They are considered people who trace their ancestry to the peoples of Europe, the Middle East. Of those reporting to be White American,7,487,133 reported to be Multiracial, with largest combination being white, additionally, there are 29,184,290 White Hispanics or Latinos. Non-Hispanic Whites are the majority in 46 states, there are four minority-majority states, California, Texas, New Mexico, and Hawaii. In addition, the District of Columbia has a non-white majority, the state with the highest percentage of non-Hispanic White Americans is Maine. The largest continental ancestral group of Americans are that of Europeans who have origins in any of the peoples of Europe. This includes people via African, North American, Caribbean, Central American or South American and Oceanian nations that have a large European diaspora, the Spanish were the first Europeans to establish a continuous presence in what is now the United States. Martín de Argüelles born 1566, San Agustín, La Florida, was the first person of European descent born in what is now the United States. Twenty-one years later, Virginia Dare born 1587 Roanoke Island in present-day North Carolina, was the first child born in the Thirteen Colonies to English parents. 8% of the total population, Hispanic or Latino Americans constitute the largest ethnic minority in the United States. They form the second largest group after non-Hispanic Whites in the United States, hispanic/Latino Americans are very racially diverse, and as a result form an ethnic category, rather than a race
21.
Mathematician
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A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems. Mathematics is concerned with numbers, data, quantity, structure, space, models, one of the earliest known mathematicians was Thales of Miletus, he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, 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, and 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 works on applied mathematics. Because of a dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked. Science and mathematics in the Islamic world during the Middle Ages followed various models and it was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. 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 working under Muslim rule in medieval times is that they were often polymaths. Examples include the work on optics, maths and astronomy of Ibn al-Haytham, the Renaissance brought an increased emphasis on mathematics and science to Europe. As time passed, many gravitated towards universities. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the “regurgitation of knowledge” to “encourag productive thinking. ”Thus, seminars, overall, science became the focus of universities in the 19th and 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. ”Mathematicians usually cover a breadth of topics within mathematics in their undergraduate education, and then 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 an understanding of mathematics, the students, who pass, are permitted to work on a doctoral dissertation. Mathematicians involved with solving problems with applications in life are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their knowledge and professional methodology. With professional focus on a variety of problems, theoretical systems
22.
Geometry
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Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer, Geometry arose independently in a number of early cultures as a practical way for dealing with lengths, areas, and volumes. Geometry began to see elements of mathematical science emerging in the West as early as the 6th century BC. By the 3rd century BC, geometry was put into a form by Euclid, whose treatment, Euclids Elements. Geometry arose independently in India, with texts providing rules for geometric constructions appearing as early as the 3rd century BC, islamic scientists preserved Greek ideas and expanded on them during the Middle Ages. By the early 17th century, geometry had been put on a solid footing by mathematicians such as René Descartes. Since then, and into modern times, geometry has expanded into non-Euclidean geometry and manifolds, while geometry has evolved significantly throughout the years, there are some general concepts that are more or less fundamental to geometry. These include the concepts of points, lines, planes, surfaces, angles, contemporary geometry has many subfields, Euclidean geometry is geometry in its classical sense. The mandatory educational curriculum of the majority of nations includes the study of points, lines, planes, angles, triangles, congruence, similarity, solid figures, circles, Euclidean geometry also has applications in computer science, crystallography, and various branches of modern mathematics. Differential geometry uses techniques of calculus and linear algebra to problems in geometry. It has applications in physics, including in general relativity, topology is the field concerned with the properties of geometric objects that are unchanged by continuous mappings. In practice, this often means dealing with large-scale properties of spaces, convex geometry investigates convex shapes in the Euclidean space and its more abstract analogues, often using techniques of real analysis. It has close connections to convex analysis, optimization and functional analysis, algebraic geometry studies geometry through the use of multivariate polynomials and other algebraic techniques. It has applications in areas, including cryptography and string theory. Discrete geometry is concerned mainly with questions of relative position of simple objects, such as points. It shares many methods and principles with combinatorics, Geometry has applications to many fields, including art, architecture, physics, as well as to other branches of mathematics. The earliest recorded beginnings of geometry can be traced to ancient Mesopotamia, the earliest known texts on geometry are the Egyptian Rhind Papyrus and Moscow Papyrus, the Babylonian clay tablets such as Plimpton 322. For example, the Moscow Papyrus gives a formula for calculating the volume of a truncated pyramid, later clay tablets demonstrate that Babylonian astronomers implemented trapezoid procedures for computing Jupiters position and motion within time-velocity space
23.
Morse theory
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In another context, a Morse function can also mean an anharmonic oscillator, see Morse potential. In mathematics, specifically in topology, Morse theory enables one to analyze the topology of a manifold by studying differentiable functions on that manifold. According to the insights of Marston Morse, a typical differentiable function on a manifold will reflect the topology quite directly. Morse theory allows one to find CW structures and handle decompositions on manifolds, before Morse, Arthur Cayley and James Clerk Maxwell had developed some of the ideas of Morse theory in the context of topography. Morse originally applied his theory to geodesics and these techniques were used in Raoul Botts proof of his periodicity theorem. The analogue of Morse theory for complex manifolds is Picard–Lefschetz theory, consider, for purposes of illustration, a mountainous landscape M. If f is the function M → R sending each point to its elevation, each connected component of a contour line is either a point, a simple closed curve, or a closed curve with a double point. Contour lines may also have points of order, but these are unstable. Double points in contour lines occur at points, or passes. Saddle points are points where the surrounding landscape curves up in one direction, imagine flooding this landscape with water. Then, the covered by water when the water reaches an elevation of a is f−1(−∞, a]. Consider how the topology of this changes as the water rises. It appears, intuitively, that it does not change except when a passes the height of a point, that is. In other words, it does not change except when the water either starts filling a basin, covers a saddle, to each of these three types of critical points – basins, passes, and peaks – one associates a number called the index. Intuitively speaking, the index of a point b is the number of independent directions around b in which f decreases. Therefore, the indices of basins, passes, and peaks are 0,1, rigorously, the index of a critical point is the dimension of the negative-definite submatrix of the hessian matrix calculated at that point. In case of smooth maps, the matrix turns out to be a symmetric matrix. Starting from the bottom of the torus, let p, q, r, and s be the four points of index 0,1,1
24.
Canadian Armed Forces
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This unified institution consists of sea, land, and air elements referred to as the Royal Canadian Navy, Canadian Army, and Royal Canadian Air Force. Under the National Defence Act, the Canadian Armed Forces are an entity separate and distinct from the Department of National Defence, the Commander-in-Chief of the Canadian Armed Forces is the reigning Canadian monarch, Queen Elizabeth II, who is represented by the Governor General of Canada. The Canadian Armed Forces is led by the Chief of the Defence Staff, during the Cold War, a principal focus of Canadian defence policy was contributing to the security of Europe in the face of the Soviet military threat. Toward that end, Canadian ground and air forces were based in Europe from the early 1950s until the early 1990s, Canadian defence policy today is based on the Canada First Defence Strategy, introduced in 2008. Based on that strategy, the Canadian military is oriented and being equipped to carry out six core missions within Canada, in North America and globally. Prior to Confederation in 1867, residents of the colonies in what is now Canada served as members of French and British forces. Thereafter, the Royal Canadian Navy was formed, and, with the advent of military aviation and these forces were organised under the Department of Militia and Defence, and split into the Permanent and Non-Permanent Active Militias—frequently shortened to simply The Militia. By 1923, the department was merged into the Department of National Defence, the first overseas deployment of Canadian military forces occurred during the Second Boer War, when several units were raised to serve under British command. Similarly, when the United Kingdom entered into conflict with Germany in the First World War, the Canadian Crown-in-Council then decided to send its forces into the Second World War, as well as the Korean War. Since 1947, Canadian military units have participated in more than 200 operations worldwide, Canada maintained an aircraft carrier from 1957 to 1970 during the Cold War, which never saw combat but participated in patrols during the Cuban Missile Crisis. At the end of the Second World War, Canada possessed the fourth-largest air force and fifth-largest naval surface fleet in the world, conscription for overseas service was introduced only near the end of the war, and only 2,400 conscripts actually made it into battle. Originally, Canada was thought to have had the third-largest navy in the world and its roots, however, lie in colonial militia groups that served alongside garrisons of the French and British armies and navies, a structure that remained in place until the early 20th century. After the 1980s, the use of the Canadian Armed Forces name gave way to Canadian Forces, land Forces during this period also deployed in support of peacekeeping operations within United Nations sanctioned conflicts. The nature of the Canadian Forces has continued to evolve and they have been deployed in Afghanistan until 2011, under the NATO-led United Nations International Security Assistance Force, at the request of the Government of Afghanistan. The Armed Forces are today funded by approximately $20, the number of primary reserve personnel is expected to go up to 30,000 by 2020, and the number of active to at least 70,000. In addition,5000 rangers and 19,000 supplementary personnel will be serving, if this happens the total strength would be around 124,000. These individuals serve on numerous CF bases located in all regions of the country, and are governed by the Queens Regulations and Orders, the 2006 renewal and re-equipment effort has resulted in the acquisition of specific equipment to support the mission in Afghanistan. It has also encompassed initiatives to renew certain so-called core capabilities, in addition, new systems have also been acquired for the Armed Forces
25.
Europe
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Europe is a continent that comprises the westernmost part of Eurasia. Europe is bordered by the Arctic Ocean to the north, the Atlantic Ocean to the west, yet the non-oceanic borders of Europe—a concept dating back to classical antiquity—are arbitrary. Europe covers about 10,180,000 square kilometres, or 2% of the Earths surface, politically, Europe is divided into about fifty sovereign states of which the Russian Federation is the largest and most populous, spanning 39% of the continent and comprising 15% of its population. Europe had a population of about 740 million as of 2015. Further from the sea, seasonal differences are more noticeable than close to the coast, Europe, in particular ancient Greece, was the birthplace of Western civilization. The fall of the Western Roman Empire, during the period, marked the end of ancient history. Renaissance humanism, exploration, art, and science led to the modern era, from the Age of Discovery onwards, Europe played a predominant role in global affairs. Between the 16th and 20th centuries, European powers controlled at times the Americas, most of Africa, Oceania. The Industrial Revolution, which began in Great Britain at the end of the 18th century, gave rise to economic, cultural, and social change in Western Europe. During the Cold War, Europe was divided along the Iron Curtain between NATO in the west and the Warsaw Pact in the east, until the revolutions of 1989 and fall of the Berlin Wall. In 1955, the Council of Europe was formed following a speech by Sir Winston Churchill and it includes all states except for Belarus, Kazakhstan and Vatican City. Further European integration by some states led to the formation of the European Union, the EU originated in Western Europe but has been expanding eastward since the fall of the Soviet Union in 1991. The European Anthem is Ode to Joy and states celebrate peace, in classical Greek mythology, Europa is the name of either a Phoenician princess or of a queen of Crete. The name contains the elements εὐρύς, wide, broad and ὤψ eye, broad has been an epithet of Earth herself in the reconstructed Proto-Indo-European religion and the poetry devoted to it. For the second part also the divine attributes of grey-eyed Athena or ox-eyed Hera. The same naming motive according to cartographic convention appears in Greek Ανατολή, Martin Litchfield West stated that phonologically, the match between Europas name and any form of the Semitic word is very poor. Next to these there is also a Proto-Indo-European root *h1regʷos, meaning darkness. Most major world languages use words derived from Eurṓpē or Europa to refer to the continent, in some Turkic languages the originally Persian name Frangistan is used casually in referring to much of Europe, besides official names such as Avrupa or Evropa
26.
World War II
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World War II, also known as the Second World War, was a global war that lasted from 1939 to 1945, although related conflicts began earlier. It involved the vast majority of the worlds countries—including all of the great powers—eventually forming two opposing alliances, the Allies and the Axis. It was the most widespread war in history, and directly involved more than 100 million people from over 30 countries. Marked by mass deaths of civilians, including the Holocaust and the bombing of industrial and population centres. These made World War II the deadliest conflict in human history, from late 1939 to early 1941, in a series of campaigns and treaties, Germany conquered or controlled much of continental Europe, and formed the Axis alliance with Italy and Japan. Under the Molotov–Ribbentrop Pact of August 1939, Germany and the Soviet Union partitioned and annexed territories of their European neighbours, Poland, Finland, Romania and the Baltic states. In December 1941, Japan attacked the United States and European colonies in the Pacific Ocean, and quickly conquered much of the Western Pacific. The Axis advance halted in 1942 when Japan lost the critical Battle of Midway, near Hawaii, in 1944, the Western Allies invaded German-occupied France, while the Soviet Union regained all of its territorial losses and invaded Germany and its allies. During 1944 and 1945 the Japanese suffered major reverses in mainland Asia in South Central China and Burma, while the Allies crippled the Japanese Navy, thus ended the war in Asia, cementing the total victory of the Allies. World War II altered the political alignment and social structure of the world, the United Nations was established to foster international co-operation and prevent future conflicts. The victorious great powers—the United States, the Soviet Union, China, the United Kingdom, the Soviet Union and the United States emerged as rival superpowers, setting the stage for the Cold War, which lasted for the next 46 years. Meanwhile, the influence of European great powers waned, while the decolonisation of Asia, most countries whose industries had been damaged moved towards economic recovery. Political integration, especially in Europe, emerged as an effort to end pre-war enmities, the start of the war in Europe is generally held to be 1 September 1939, beginning with the German invasion of Poland, Britain and France declared war on Germany two days later. The dates for the beginning of war in the Pacific include the start of the Second Sino-Japanese War on 7 July 1937, or even the Japanese invasion of Manchuria on 19 September 1931. Others follow the British historian A. J. P. Taylor, who held that the Sino-Japanese War and war in Europe and its colonies occurred simultaneously and this article uses the conventional dating. Other starting dates sometimes used for World War II include the Italian invasion of Abyssinia on 3 October 1935. The British historian Antony Beevor views the beginning of World War II as the Battles of Khalkhin Gol fought between Japan and the forces of Mongolia and the Soviet Union from May to September 1939, the exact date of the wars end is also not universally agreed upon. It was generally accepted at the time that the war ended with the armistice of 14 August 1945, rather than the formal surrender of Japan
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Montreal
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Montreal, officially Montréal, is the most populous municipality in the Canadian province of Quebec and the 2nd-most populous in Canada as a whole. Originally called Ville-Marie, or City of Mary, it is believed to be named after Mount Royal, the city has a distinct four-season continental climate, with warm-to-hot summers and cold, snowy winters. In 2016, Montreal had a population of 1,704,694, Montreals metropolitan area had a population of 4,098,927 and a population of 1,958,257 in the urban agglomeration, with all of the municipalities on the Island of Montreal included. Legally a French-speaking city,60. 5% of Montrealers speak French at home,21. 2% speak English and 19. 8% speak neither, Montreal is one of the most bilingual cities in Quebec and Canada, with 56% of the population able to speak both official languages. Montreal is the second-largest primarily French-speaking city in the world after Paris, historically the commercial capital of Canada, it was surpassed in population and economic strength by Toronto in the 1970s. It remains an important centre of commerce, aerospace, finance, pharmaceuticals, technology, design, education, culture, tourism, gaming, film, Montreal was also named a UNESCO City of Design. In 2009, Montreal was named North Americas leading host city for international events, according to the 2009 preliminary rankings of the International Congress. According to the 2015 Global Liveability Ranking by the Economist Intelligence Unit, in the 2017 edition of their Best Student Cities ranking, Quacquarelli Symonds ranked Montreal as the worlds best city to study abroad. Also, Montreal has 11 universities with 170,000 students enrolled, the Greater Montréal region has the highest number of university students per capita among all metropolitan areas in North America. It is the only Canadian city to have held the Summer Olympics, currently, the city hosts the Canadian Grand Prix of Formula One, the Montreal International Jazz Festival and the Just for Laughs festival. In 2012, Montreal was ranked as a Beta+ world city, in Kanien’kéha, or Mohawk language, the island is called Tiohtià, ke Tsi or Ka-wé-no-te. In Anishinaabemowin, or Ojibwe language, the land is called Mooniyaang, though the city was first named by French colonizers Ville Marie, or City of Mary, its current name comes from Mount Royal, the triple-peaked hill in the heart of the city. The most popular theory is that the name derives from Mont Réal, Cartiers 1535 diary entry, naming the mountain, according to the Commission de toponymie du Québec and the Geographical Names Board of Canada, Canadian place names have only one official form. Thus, Montreal is officially spelled with an accent over the e in both English and French. In practice, this is limited to governmental uses. English-speaking Montrealers, including English-language media, regularly omit the accent when writing in English, archaeological evidence demonstrates that First Nations native people occupied the island of Montreal as early as 4,000 years ago. By the year AD1000, they had started to cultivate maize, within a few hundred years, they had built fortified villages. Archeologists have found evidence of their habitation there and at locations in the valley since at least the 14th century
28.
Electrical engineering
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Electrical engineering is a field of engineering that generally deals with the study and application of electricity, electronics, and electromagnetism. This field first became an occupation in the later half of the 19th century after commercialization of the electric telegraph, the telephone. Subsequently, broadcasting and recording media made electronics part of daily life, the invention of the transistor, and later the integrated circuit, brought down the cost of electronics to the point they can be used in almost any household object. Electrical engineers typically hold a degree in engineering or electronic engineering. Practicing engineers may have professional certification and be members of a professional body, such bodies include the Institute of Electrical and Electronics Engineers and the Institution of Engineering and Technology. Electrical engineers work in a wide range of industries and the skills required are likewise variable. These range from basic circuit theory to the management skills required of a project manager, the tools and equipment that an individual engineer may need are similarly variable, ranging from a simple voltmeter to a top end analyzer to sophisticated design and manufacturing software. Electricity has been a subject of scientific interest since at least the early 17th century and he also designed the versorium, a device that detected the presence of statically charged objects. In the 19th century, research into the subject started to intensify, Electrical engineering became a profession in the later 19th century. Practitioners had created an electric telegraph network and the first professional electrical engineering institutions were founded in the UK. Over 50 years later, he joined the new Society of Telegraph Engineers where he was regarded by other members as the first of their cohort, Practical applications and advances in such fields created an increasing need for standardised units of measure. They led to the standardization of the units volt, ampere, coulomb, ohm, farad. This was achieved at a conference in Chicago in 1893. During these years, the study of electricity was considered to be a subfield of physics. Thats because early electrical technology was electromechanical in nature, the Technische Universität Darmstadt founded the worlds first department of electrical engineering in 1882. The first course in engineering was taught in 1883 in Cornell’s Sibley College of Mechanical Engineering. It was not until about 1885 that Cornell President Andrew Dickson White established the first Department of Electrical Engineering in the United States, in the same year, University College London founded the first chair of electrical engineering in Great Britain. Professor Mendell P. Weinbach at University of Missouri soon followed suit by establishing the engineering department in 1886
29.
Doctor of Philosophy
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A Doctor of Philosophy is a type of doctoral degree awarded by universities in many countries. Ph. D. s are awarded for a range of programs in the sciences, engineering. The Ph. D. is a degree in many fields. The completion of a Ph. D. is often a requirement for employment as a university professor, researcher, individuals with an earned doctorate can use the title of Doctor with their name and use the post-nominal letters Ph. D. The requirements to earn a Ph. D. degree vary considerably according to the country, institution, a person who attains a doctorate of philosophy is automatically awarded the academic title of doctor. A student attaining this level may be granted a Candidate of Philosophy degree at some institutions. A Ph. D. candidate must submit a project, thesis or dissertation often consisting of a body of academic research. In many countries, a candidate must defend this work before a panel of examiners appointed by the university. Universities award other types of doctorates besides the Ph. D. such as the Doctor of Musical Arts, a degree for music performers and the Doctor of Education, in 2016, ELIA launched The Florence Principles on the Doctorate in the Arts. The Florence Principles have been endorsed are supported also by AEC, CILECT, CUMULUS, the degree is abbreviated PhD, from the Latin Philosophiae Doctor, pronounced as three separate letters. In the universities of Medieval Europe, study was organized in four faculties, the faculty of arts. All of these faculties awarded intermediate degrees and final degrees, the doctorates in the higher faculties were quite different from the current Ph. D. degree in that they were awarded for advanced scholarship, not original research. No dissertation or original work was required, only lengthy residency requirements, besides these degrees, there was the licentiate. According to Keith Allan Noble, the first doctoral degree was awarded in medieval Paris around 1150, the doctorate of philosophy developed in Germany as the terminal Teachers credential in the 17th century. Typically, upon completion, the candidate undergoes an oral examination, always public, starting in 2016, in Ukraine Doctor of Philosophy is the highest education level and the first science degree. PhD is awarded in recognition of a contribution to scientific knowledge. A PhD degree is a prerequisite for heading a university department in Ukraine, upon completion of a PhD, a PhD holder can elect to continue his studies and get a post-doctoral degree called Doctor of Sciences, which is the second and the highest science degree in Ukraine. Scandinavian countries were among the early adopters of a known as a doctorate of philosophy
30.
Pittsburgh
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Pittsburgh is a city in the Commonwealth of Pennsylvania in the United States, and is the county seat of Allegheny County. The city proper has a population of 304,391. The metropolitan population of 2,353,045 is the largest in both the Ohio Valley and Appalachia, the second-largest in Pennsylvania, and the 26th-largest in the U. S. The city features 30 skyscrapers, two inclines, a fortification and the Point State Park at the confluence of the rivers. Aside from steel, Pittsburgh has led in manufacturing of aluminum, glass, shipbuilding, petroleum, foods, sports, transportation, computing, autos, and electronics. For part of the 20th century, Pittsburgh was behind only New York and Chicago in corporate headquarters employment, Americas 1980s deindustrialization laid off area blue-collar workers and thousands of downtown white-collar workers when the longtime Pittsburgh-based world headquarters moved out. The area has served also as the federal agency headquarters for cyber defense, software engineering, robotics, energy research. The area is home to 68 colleges and universities, including research and development leaders Carnegie Mellon University, the region is a hub for Leadership in Energy and Environmental Design, sustainable energy, and energy extraction. Pittsburgh was named in 1758 by General John Forbes, in honor of British statesman William Pitt, 1st Earl of Chatham. The current pronunciation, which is unusual in English speaking countries, is almost certainly a result of a printing error in some copies of the City Charter of March 18,1816. The error was repeated commonly enough throughout the rest of the 19th century that the pronunciation was lost. After a public campaign the original spelling was restored by the United States Board on Geographic Names in 1911. The area of the Ohio headwaters was long inhabited by the Shawnee, the first known European to enter the region was the French explorer/trader Robert de La Salle from Quebec during his 1669 expedition down the Ohio River. European pioneers, primarily Dutch, followed in the early 18th century, Michael Bezallion was the first to describe the forks of the Ohio in a 1717 manuscript, and later that year European fur traders established area posts and settlements. In 1749, French soldiers from Quebec launched an expedition to the forks to unite Canada with French Louisiana via the rivers, during 1753–54, the British hastily built Fort Prince George before a larger French force drove them off. The French built Fort Duquesne based on LaSalles 1669 claims, the French and Indian War, the North American front of the Seven Years War, began with the future Pittsburgh as its center. British General Edward Braddock was dispatched with Major George Washington as his aide to take Fort Duquesne, the British and colonial force were defeated at Braddocks Field. General John Forbes finally took the forks in 1758, Forbes began construction on Fort Pitt, named after William Pitt the Elder while the settlement was named Pittsborough
31.
Institute for Advanced Study
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The IAS is perhaps best known as the academic home of Albert Einstein, John von Neumann and Kurt Gödel, after their immigration to the United States. Although it is close to and collaborates with Princeton University, Rutgers University, Flexners guiding principle in founding the Institute was the pursuit of knowledge for its own sake. There are no programs or experimental facilities at the Institute. Research is never contracted or directed, it is left to each individual researcher to pursue their own goals and it is supported entirely by endowments, grants, and gifts, and is one of the eight American mathematics institutes funded by the National Science Foundation. It is the model for the eight members of the consortium Some Institutes for Advanced Study. The institute consists of four schools–Historical Studies, Mathematics, Natural Sciences, in 2016, the Institute has been in the news for a faculty housing project proposal. While the Institute owns the property on which it wants to build these houses, historians and archaeological evidence confirm the site witnessed Gen. George Washingtons arrival and charge on horseback across the battlefield during the January 3,1777 Battle of Princeton. The Institute was founded in 1930 by Abraham Flexner, together with philanthropists Louis Bamberger, Flexner is generally regarded as one of the most important figures in the history of American medicine and played a major role in the reform of medical education. This led to an interest in education generally and as early as 1890 he had founded a school which had no formal curriculum, exams. It was a success at preparing students for prestigious colleges. The Bamberger siblings wanted to use the proceeds from the sale of their department store in Newark, New Jersey, Flexner convinced them to put their money in the service of more abstract research. In 1932 Veblen resigned from Princeton and became the first professor in the new Institute for Advanced Study and he selected most of the original faculty and also helped the Institute acquire land in Princeton for both the original facility and future expansion. Flexner and Veblen set out to recruit the best mathematicians and physicists they could find, the rise of fascism and the associated anti-semitism forced many prominent mathematicians to flee Europe and some, such as Einstein and Hermann Weyl, found a home at the new institute. Weyl as a condition of accepting insisted that the Institute also appoint the thirty year old Austrian-Hungarian polymath John von Neumann, indeed, the IAS became the key lifeline for scholars fleeing Europe. Einstein was Flexners first coup and shortly after that he was followed by Veblens brilliant student James Alexander, Flexner was fortunate in the luminaries he directly recruited but also in the people that they brought along with them. Thus, by 1934 the fledgeling institute was led by six of the most prominent mathematicians in the world, in 1935 quantum physics pioneer Wolfgang Pauli became a faculty member. With the opening of the Institute for Advanced Study, Princeton replaced Göttingen as the center for mathematics in the twentieth century. Princeton Universitys science departments are less than two miles away and informal ties and collaboration between the two institutions occurred from the beginning and this helped start an incorrect impression that it was part of the University, one that has never been completely eradicated
32.
Electronic filter
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Electronic filters are circuits which perform signal processing functions, specifically to remove unwanted frequency components from the signal, to enhance wanted ones, or both. Electronic filters can be, passive or active analog or digital high-pass, low-pass, band-pass, band-stop, see the article on linear filters for details on their design and analysis. The oldest forms of filters are passive analog linear filters. These are known as RC and RL single-pole filters respectively, more complex multipole LC filters have also existed for many years, and their operation is well understood. Hybrid filters are possible, typically involving a combination of analog amplifiers with mechanical resonators or delay lines. Other devices such as CCD delay lines have also used as discrete-time filters. With the availability of digital processing, active digital filters have become common. Passive implementations of filters are based on combinations of resistors, inductors and capacitors. These types are known as passive filters, because they do not depend upon an external power supply and/or they do not contain active components such as transistors. Inductors block high-frequency signals and conduct low-frequency signals, while capacitors do the reverse, the inductors and capacitors are the reactive elements of the filter. The number of elements determines the order of the filter, in this context, an LC tuned circuit being used in a band-pass or band-stop filter is considered a single element even though it consists of two components. At high frequencies, sometimes the inductors consist of single loops or strips of metal. These inductive or capacitive pieces of metal are called stubs, the simplest passive filters, RC and RL filters, include only one reactive element, except hybrid LC filter which is characterized by inductance and capacitance integrated in one element. An L filter consists of two elements, one in series and one in parallel. Three-element filters can have a T or π topology and in either geometries, the components can be chosen symmetric or not, depending on the required frequency characteristics. The high-pass T filter in the illustration, has a low impedance at high frequencies. That means that it can be inserted in a line, resulting in the high frequencies being passed. Likewise, for the illustrated low-pass π filter, the circuit can be connected to a line, transmitting low frequencies
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Network synthesis filters
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Network synthesis is a method of designing signal processing filters. It has produced several important classes of filter including the Butterworth filter, the Chebyshev filter and it was originally intended to be applied to the design of passive linear analogue filters but its results can also be applied to implementations in active filters and digital filters. The essence of the method is to obtain the component values of the filter from a rational function representing the desired transfer function. The method can be viewed as the problem of network analysis. Network analysis starts with a network and by applying the various electric circuit theorems predicts the response of the network, network synthesis on the other hand, starts with a desired response and its methods produce a network that outputs, or approximates to, that response. Network synthesis was originally intended to produce filters of the formerly described as wave filters. That is, filters whose purpose is to pass waves of certain wavelengths while rejecting waves of other wavelengths, network synthesis starts out with a specification for the transfer function of the filter, H, as a function of complex frequency, s. In a digital implementation of a filter, H can be implemented directly, the advantages of the method are best understood by comparing it to the filter design methodology that was used before it, the image method. The image method considers the characteristics of a filter section in an infinite chain of identical sections. The filters produced by this method suffer from inaccuracies due to the theoretical termination impedance, with network synthesis filters, the terminations are included in the design from the start. The image method also requires an amount of experience on the part of the designer. The designer must first decide how many sections and of type should be used. This may not be what is required and there can be a number of iterations, the network synthesis method, on the other hand, starts out with the required function and generates as output the sections needed to build the corresponding filter. In general, the sections of a network synthesis filter are of identical topology, both methods make use of low-pass prototype filters followed by frequency transformations and impedance scaling to arrive at the final desired filter. The class of a filter refers to the class of polynomials from which the filter is mathematically derived, the order of the filter is the number of filter elements present in the filters ladder implementation. Generally speaking, the higher the order of the filter, the steeper the cut-off transition between passband and stopband, filters are often named after the mathematician or mathematics on which they are based rather than the discoverer or inventor of the filter. Butterworth filters are described as flat, meaning that the response in the frequency domain is the smoothest possible curve of any class of filter of the equivalent order. The Butterworth class of filter was first described in a 1930 paper by the British engineer Stephen Butterworth after whom it is named, the filter response is described by Butterworth polynomials, also due to Butterworth
34.
Passivity (engineering)
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Passivity is a property of engineering systems, used in a variety of engineering disciplines, but most commonly found in analog electronics and control systems. A passive component, depending on field, may be either a component that consumes energy, a component that is not passive is called an active component. An electronic circuit consisting entirely of passive components is called a passive circuit, used out-of-context and without a qualifier, the term passive is ambiguous. Typically, analog designers use this term to refer to incrementally passive components and systems, systems for which the small signal model is not passive are sometimes called locally active. Systems that can power about a time-variant unperturbed state are often called parametrically active. In control systems and circuit theory, a passive component or circuit is one that consumes energy. Circuit designers will sometimes refer to this class of components as dissipative, while many books give definitions for passivity, many of these contain subtle errors in how initial conditions are treated. Below is a correct, formal definition, taken from Wyatt et al, a system is considered passive if EA is finite for all initial states x. Otherwise, the system is considered active, roughly speaking, the inner product ⟨ v, i ⟩ is the instantaneous power, and EA is the upper bound on the integral of the instantaneous power. This upper bound is the energy in the system for the particular initial condition x. If, for all initial states of the system, the energy available is finite. In circuit design, informally, passive components refer to ones that are not capable of power gain, under this definition, passive components include capacitors, inductors, resistors, diodes, transformers, voltage sources, and current sources. They exclude devices like transistors, vacuum tubes, relays, tunnel diodes, formally, for a memoryless two-terminal element, this means that the current–voltage characteristic is monotonically increasing. For this reason, control systems and circuit network theorists refer to these devices as locally passive, incrementally passive, increasing, monotone increasing, or monotonic. This term is used colloquially in a number of contexts, A passive USB to PS/2 adapter consists of wires. An active USB to PS/2 adapter consists of logic to translate signals A passive mixer consists of just resistors, in audio work one can also find both passive and active converters between balanced and unbalanced lines. In some very informal settings, passivity may refer to the simplicity of the device, here, devices like diodes would be considered active, and only very simple devices like capacitors, inductors, and resistors are considered passive. In some cases, the linear element may be a more appropriate term than passive device
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Inductor
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An inductor, also called a coil or reactor, is a passive two-terminal electrical component that stores electrical energy in a magnetic field when electric current is flowing through it. An inductor typically consists of a conductor, such as a wire. When the current flowing through an inductor changes, the magnetic field induces a voltage in the conductor. According to Lenzs law, the direction of induced electromotive force opposes the change in current that created it, as a result, inductors oppose any changes in current through them. An inductor is characterized by its inductance, which is the ratio of the voltage to the rate of change of current, in the International System of Units, the unit of inductance is the henry. Inductors have values that range from 1 µH to 1 H. Many inductors have a core made of iron or ferrite inside the coil. Along with capacitors and resistors, inductors are one of the three passive linear circuit elements that make up electronic circuits, Inductors are widely used in alternating current electronic equipment, particularly in radio equipment. They are used to block AC while allowing DC to pass and they are also used in electronic filters to separate signals of different frequencies, and in combination with capacitors to make tuned circuits, used to tune radio and TV receivers. An electric current flowing through a conductor generates a magnetic field surrounding it, any changes of current and therefore in the magnetic flux through the cross-section of the inductor creates an opposing electromotive force in the conductor. An inductor is a component consisting of a wire or other conductor shaped to increase the flux through the circuit. Winding the wire into a coil increases the number of times the magnetic flux lines link the circuit, increasing the field, the more turns, the higher the inductance. The inductance also depends on the shape of the coil, separation of the turns, by adding a magnetic core made of a ferromagnetic material like iron inside the coil, the magnetizing field from the coil will induce magnetization in the material, increasing the magnetic flux. The high permeability of a core can increase the inductance of a coil by a factor of several thousand over what it would be without it. Any change in the current through an inductor creates a changing flux, for example, an inductor with an inductance of 1 henry produces an EMF of 1 volt when the current through the inductor changes at the rate of 1 ampere per second. This is usually taken to be the relation of the inductor. The dual of the inductor is the capacitor, which stores energy in a field rather than a magnetic field. Its current-voltage relation is obtained by exchanging current and voltage in the inductor equations, the polarity of the induced voltage is given by Lenzs law, which states that it will be such as to oppose the change in current
