University of Cambridge
The University of Cambridge is a collegiate public research university in Cambridge, United Kingdom. Founded in 1209 and granted a Royal Charter by King Henry III in 1231, Cambridge is the second-oldest university in the English-speaking world and the world's fourth-oldest surviving university; the university grew out of an association of scholars who left the University of Oxford after a dispute with the townspeople. The two'ancient universities' share many common features and are referred to jointly as'Oxbridge'; the history and influence of the University of Cambridge has made it one of the most prestigious universities in the world. Cambridge is formed from a variety of institutions which include 31 constituent Colleges and over 100 academic departments organised into six schools. Cambridge University Press, a department of the university, is the world's oldest publishing house and the second-largest university press in the world; the university operates eight cultural and scientific museums, including the Fitzwilliam Museum, as well as a botanic garden.
Cambridge's libraries hold a total of around 15 million books, eight million of which are in Cambridge University Library, a legal deposit library. In the fiscal year ending 31 July 2018, the university had a total income of £1.965 billion, of which £515.5 million was from research grants and contracts. In the financial year ending 2017, the central university and colleges had combined net assets of around £11.8 billion, the largest of any university in the country. However, the true extent of Cambridge's wealth is much higher as many colleges hold their historic main sites, which date as far back as the 13th century, at depreceated valuations. Furthermore, many of the wealthiest colleges do not account for “heritage assets” such as works of art, libraries or artefacts, whose value many college accounts describe as “immaterial”; the university is linked with the development of the high-tech business cluster known as'Silicon Fen'. It is a member of numerous associations and forms part of the'golden triangle' of English universities and Cambridge University Health Partners, an academic health science centre.
As of 2018, Cambridge is the top-ranked university in the United Kingdom according to all major league tables. As of September 2017, Cambridge is ranked the world's second best university by the Times Higher Education World University Rankings, is ranked 3rd worldwide by Academic Ranking of World Universities, 6th by QS, 7th by US News. According to the Times Higher Education ranking, no other institution in the world ranks in the top 10 for as many subjects; the university has educated many notable alumni, including eminent mathematicians, politicians, philosophers, writers and foreign Heads of State. As of March 2019, 118 Nobel Laureates, 11 Fields Medalists, 7 Turing Award winners and 15 British Prime Ministers have been affiliated with Cambridge as students, faculty or research staff. By the late 12th century, the Cambridge area had a scholarly and ecclesiastical reputation, due to monks from the nearby bishopric church of Ely. However, it was an incident at Oxford, most to have led to the establishment of the university: two Oxford scholars were hanged by the town authorities for the death of a woman, without consulting the ecclesiastical authorities, who would take precedence in such a case, but were at that time in conflict with King John.
The University of Oxford went into suspension in protest, most scholars moved to cities such as Paris and Cambridge. After the University of Oxford reformed several years enough scholars remained in Cambridge to form the nucleus of the new university. In order to claim precedence, it is common for Cambridge to trace its founding to the 1231 charter from King Henry III granting it the right to discipline its own members and an exemption from some taxes. A bull in 1233 from Pope Gregory IX gave graduates from Cambridge the right to teach "everywhere in Christendom". After Cambridge was described as a studium generale in a letter from Pope Nicholas IV in 1290, confirmed as such in a bull by Pope John XXII in 1318, it became common for researchers from other European medieval universities to visit Cambridge to study or to give lecture courses; the colleges at the University of Cambridge were an incidental feature of the system. No college is as old as the university itself; the colleges were endowed fellowships of scholars.
There were institutions without endowments, called hostels. The hostels were absorbed by the colleges over the centuries, but they have left some traces, such as the name of Garret Hostel Lane. Hugh Balsham, Bishop of Ely, founded Peterhouse, Cambridge's first college, in 1284. Many colleges were founded during the 14th and 15th centuries, but colleges continued to be established until modern times, although there was a gap of 204 years between the founding of Sidney Sussex in 1596 and that of Downing in 1800; the most established college is Robinson, built in the late 1970s. However, Homerton College only achieved full university college status in March 2010, making it the newest full college. In medieval times, many colleges were founded so that their members would pray for the souls of the founders, were associated with chapels or abbeys; the colleges' focus changed in 1536 with the Dissolution of the Monasteries. King Henry VIII ordered the university to disband its Faculty of Canon Law and to stop teaching "scholastic philosophy".
In response, colleges changed
Jutland known as the Cimbric or Cimbrian Peninsula, is a peninsula of Northern Europe that forms the continental portion of Denmark and part of northern Germany. The names are derived from the Cimbri, respectively; as the rest of Denmark, Jutland's terrain is flat, with a elevated ridge down the central parts and hilly terrains in the east. West Jutland is characterised by open lands, heaths and peat bogs, while East Jutland is more fertile with lakes and lush forests. Southwest Jutland is characterised by the Wadden Sea, a large unique international coastal region stretching through Denmark and the Netherlands. Jutland is a peninsula bounded by the North Sea to the west, the Skagerrak to the north, the Kattegat and Baltic Sea to the east and Germany to the south. Geographically and Jutland comprises the regions of South Jutland, West Jutland, East Jutland and North Jutland. Since the mid-20th century, it has become common to design an area as Central Jutland, but its definition varies a lot.
There are several historical subdivisions and regional names, some of which are still encountered today. They include Nørrejyllland, Sydjylland and others. Politically, Jutland comprises the three contemporary Danish Administrative Regions of North Jutland Region, Central Denmark Region and the Region of Southern Denmark, along with portions of the German state of Schleswig-Holstein; the Danish part of Jutland is divided into three administrative regions: North Jutland Region, Central Denmark Region and Region of Southern Denmark. The northernmost part of Jutland is separated from the mainland by the Limfjord, a narrow stretch of water bisecting the peninsula from coast to coast; the Limfjord was a long brackish water inlet, but a breaching North Sea flood in 1825 created a coast to coast connection. This area is called the North Jutlandic Island, Vendsyssel-Thy or Jutland north of the Limfjord; the islands of Læsø, Anholt and Samsø in Kattegat and Als at the rim of the Baltic Sea are administratively and tied to Jutland, although the latter two are regarded as traditional districts of their own.
Inhabitants of Als, known as Alsinger, would agree to be South Jutlanders, but not Jutlanders. The Danish Wadden Sea Islands and the German North Frisian Islands stretch along the southwest coast of Jutland in the German Bight; the largest cities in the Danish section of Jutland are as follows: Aarhus Aalborg Esbjerg Randers Kolding Horsens Vejle Herning Silkeborg FredericiaAarhus, Billund, Kolding, Vejle and Haderslev, along with a number of smaller towns, make up the suggested East Jutland metropolitan area, more densely populated than the rest of Jutland, although far from forming one consistent city. Administratively, Danish Jutland comprises three of Denmark's five regions, namely Nordjylland and the western half of Southern Denmark, which includes Funen; the five administrative regions came into effect on 1 January 2007, following a structural reform. The southern third of the peninsula is made up of the German Bundesland of Schleswig-Holstein; the German parts are not seen as Jutland proper, but described more abstract as part of the Jutlandic Peninsula, Cimbrian Peninsula or Jutland-Schleswig-Holstein.
Schleswig-Holstein has two historical parts: the former duchies of Schleswig and Holstein, both of which have passed back and forth between Danish and German rulers. The last adjustment of the Danish–German border followed the Schleswig Plebiscites in 1920 and resulted in Denmark regaining Northern Schleswig; the historical southern border of Jutland was the river Eider, which forms the border between the former duchies of Schleswig and Holstein, as well as the border between the Danish and German realms from c. 850 to 1864. Although most of Schleswig-Holstein is geographically part of the peninsula, most German residents there would not identify themselves with Jutland or as Jutlanders, but rather with Schleswig-Holstein; the medieval law Code of Jutland applied to Schleswig until 1900, when it was replaced by the Prussian Civil Code. Some used clauses of the Jutlandic Code still apply north of the Eider; the largest cities in the German part of the Jutland Peninsula are Flensburg. Geologically the Mid Jutland Region and the North Jutland Region as well as the Capital Region of Denmark are located in the north of Denmark, rising because of post-glacial rebound.
Jutland has been one of the three lands of Denmark, the other two being Scania and Zealand. Before that, according to Ptolemy, Jutland or the Cimbric Chersonese was the home of Teutons and Charudes. Many Angles and Jutes migrated from Continental Europe to Great Britain starting in c. 450 AD. The Angles themselves gave their name to the new emerging kingdoms called England. Saxons and Frisii migrated to the region in the early part of the Christian era. To protect themselves from invasion by the Christian Frankish emperors, beginning in the 5th century, the pagan Danes initiated the Danevirke, a defensi
In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x. In the simplest case, the logarithm counts repeated multiplication of the same factor; the logarithm of x to base b is denoted as logb . More exponentiation allows any positive real number to be raised to any real power, always producing a positive result, so the logarithm for any two positive real numbers b and x where b is not equal to 1, is always a unique real number y. More explicitly, the defining relation between exponentiation and logarithm is: log b = y if b y = x. For example, log2 64 = 6, as 26 = 64; the logarithm to base 10 is called the common logarithm and has many applications in science and engineering. The natural logarithm has the number e as its base; the binary logarithm uses base 2 and is used in computer science. Logarithms were introduced by John Napier in the early 17th century as a means to simplify calculations.
They were adopted by navigators, scientists and others to perform computations more using slide rules and logarithm tables. Tedious multi-digit multiplication steps can be replaced by table look-ups and simpler addition because of the fact—important in its own right—that the logarithm of a product is the sum of the logarithms of the factors: log b = log b x + log b y, provided that b, x and y are all positive and b ≠ 1; the present-day notion of logarithms comes from Leonhard Euler, who connected them to the exponential function in the 18th century. Logarithmic scales reduce wide-ranging quantities to tiny scopes. For example, the decibel is a unit used to express ratio as logarithms for signal power and amplitude. In chemistry, pH is a logarithmic measure for the acidity of an aqueous solution. Logarithms are commonplace in scientific formulae, in measurements of the complexity of algorithms and of geometric objects called fractals, they help describing frequency ratios of musical intervals, appear in formulas counting prime numbers or approximating factorials, inform some models in psychophysics, can aid in forensic accounting.
In the same way as the logarithm reverses exponentiation, the complex logarithm is the inverse function of the exponential function applied to complex numbers. The discrete logarithm is another variant. Addition and exponentiation are three fundamental arithmetic operations. Addition, the simplest of these, can be undone by subtraction: adding, say, 2 to 3 gives 5; the process of adding 2 can be undone by subtracting 2: 5 − 2 = 3. Multiplication, the next-simplest operation, can be undone by division: doubling a number x, i.e. multiplying x by 2, the result is 2x. To get back x, it is necessary to divide by 2. For example 2 ⋅ 3 = 6 and the process of multiplying by 2 is undone by dividing by 2: 6 / 2 = 3; the idea and purpose of logarithms is to undo a fundamental arithmetic operation, namely raising a number to a certain power, an operation known as exponentiation. For example, raising 2 to the third power yields 8, because 8 is the product of three factors of 2: 2 3 = 2 × 2 × 2 = 8 The logarithm of 8 is 3, reflecting the fact that 2 was raised to the third power to get 8.
This subsection contains a short overview of the exponentiation operation, fundamental to understanding logarithms. Raising b to the n-th power, where n is a natural number, is done by multiplying n factors equal to b; the n-th power of b is written bn, so that b n = b × b × ⋯ × b ⏟ n factors Exponentiation may be extended to by, where b is a positive number and the exponent y is any real number. For example, b − 1 is the reciprocal of b. Raising b to the power 1/2 is the square root of b. More raising b to a rational power p/q, where p and q are integers, is given by b p / q = b p q, the q-th root of bp. Any irrational number y can be approximated to arbitrary precision by rational numbers; this can be used to compute the y-th power of b: for example 2 ≈ 1.414... and
Copenhagen is the capital and most populous city of Denmark. As of July 2018, the city has a population of 777,218, it forms the core of the wider urban area of the Copenhagen metropolitan area. Copenhagen is situated on the eastern coast of the island of Zealand; the Øresund Bridge connects the two cities by road. A Viking fishing village established in the 10th century in the vicinity of what is now Gammel Strand, Copenhagen became the capital of Denmark in the early 15th century. Beginning in the 17th century it consolidated its position as a regional centre of power with its institutions and armed forces. After suffering from the effects of plague and fire in the 18th century, the city underwent a period of redevelopment; this included construction of the prestigious district of Frederiksstaden and founding of such cultural institutions as the Royal Theatre and the Royal Academy of Fine Arts. After further disasters in the early 19th century when Horatio Nelson attacked the Dano-Norwegian fleet and bombarded the city, rebuilding during the Danish Golden Age brought a Neoclassical look to Copenhagen's architecture.
Following the Second World War, the Finger Plan fostered the development of housing and businesses along the five urban railway routes stretching out from the city centre. Since the turn of the 21st century, Copenhagen has seen strong urban and cultural development, facilitated by investment in its institutions and infrastructure; the city is the cultural and governmental centre of Denmark. Copenhagen's economy has seen rapid developments in the service sector through initiatives in information technology and clean technology. Since the completion of the Øresund Bridge, Copenhagen has become integrated with the Swedish province of Scania and its largest city, Malmö, forming the Øresund Region. With a number of bridges connecting the various districts, the cityscape is characterised by parks and waterfronts. Copenhagen's landmarks such as Tivoli Gardens, The Little Mermaid statue, the Amalienborg and Christiansborg palaces, Rosenborg Castle Gardens, Frederik's Church, many museums and nightclubs are significant tourist attractions.
The largest lake of Denmark, Arresø, lies around 27 miles northwest of the City Hall Square. Copenhagen is home to the University of Copenhagen, the Technical University of Denmark, Copenhagen Business School and the IT University of Copenhagen; the University of Copenhagen, founded in 1479, is the oldest university in Denmark. Copenhagen is home to the FC Brøndby football clubs; the annual Copenhagen Marathon was established in 1980. Copenhagen is one of the most bicycle-friendly cities in the world; the Copenhagen Metro launched in 2002 serves central Copenhagen while the Copenhagen S-train, the Lokaltog and the Coast Line network serves and connects central Copenhagen to outlying boroughs. To relieve traffic congestion, the Fehmarn Belt Fixed Link road and rail construction is planned, because the narrow 9-9.5 mile isthmus between Roskilde Fjord and Køge Bugt forms a traffic bottleneck. The Copenhagen-Ringsted Line will relieve traffic congestion in the corridor between Roskilde and Copenhagen.
Serving two million passengers a month, Copenhagen Airport, Kastrup, is the busiest airport in the Nordic countries. Copenhagen's name reflects its origin as a place of commerce; the original designation in Old Norse, from which Danish descends, was Kaupmannahǫfn, meaning "merchants' harbour". By the time Old Danish was spoken, the capital was called Køpmannæhafn, with the current name deriving from centuries of subsequent regular sound change. An exact English equivalent would be "chapman's haven". However, the English term for the city was adapted from Kopenhagen. Although the earliest historical records of Copenhagen are from the end of the 12th century, recent archaeological finds in connection with work on the city's metropolitan rail system revealed the remains of a large merchant's mansion near today's Kongens Nytorv from c. 1020. Excavations in Pilestræde have led to the discovery of a well from the late 12th century; the remains of an ancient church, with graves dating to the 11th century, have been unearthed near where Strøget meets Rådhuspladsen.
These finds indicate. Substantial discoveries of flint tools in the area provide evidence of human settlements dating to the Stone Age. Many historians believe the town dates to the late Viking Age, was founded by Sweyn I Forkbeard; the natural harbour and good herring stocks seem to have attracted fishermen and merchants to the area on a seasonal basis from the 11th century and more permanently in the 13th century. The first habitations were centred on Gammel Strand in the 11thcentury or earlier; the earliest written mention of the town was in the 12th century when Saxo Grammaticus in Gesta Danorum referred to it as Portus
Engineers, as practitioners of engineering, are professionals who invent, analyze and test machines, systems and materials to fulfill objectives and requirements while considering the limitations imposed by practicality, regulation and cost. The word engineer is derived from the Latin words ingenium; the foundational qualifications of an engineer include a four-year bachelor's degree in an engineering discipline, or in some jurisdictions, a master's degree in an engineering discipline plus four to six years of peer-reviewed professional practice and passage of engineering board examinations. The work of engineers forms the link between scientific discoveries and their subsequent applications to human and business needs and quality of life. In 1961, the Conference of Engineering Societies of Western Europe and the United States of America defined "professional engineer" as follows: A professional engineer is competent by virtue of his/her fundamental education and training to apply the scientific method and outlook to the analysis and solution of engineering problems.
He/she is able to assume personal responsibility for the development and application of engineering science and knowledge, notably in research, construction, superintending, managing and in the education of the engineer. His/her work is predominantly intellectual and varied and not of a routine mental or physical character, it requires the exercise of original thought and judgement and the ability to supervise the technical and administrative work of others. His/her education will have been such as to make him/her capable of and continuously following progress in his/her branch of engineering science by consulting newly published works on a worldwide basis, assimilating such information and applying it independently. He/she is thus placed in a position to make contributions to the development of engineering science or its applications. His/her education and training will have been such that he/she will have acquired a broad and general appreciation of the engineering sciences as well as thorough insight into the special features of his/her own branch.
In due time he/she will be able to give authoritative technical advice and to assume responsibility for the direction of important tasks in his/her branch. Engineers develop new technological solutions. During the engineering design process, the responsibilities of the engineer may include defining problems and narrowing research, analyzing criteria and analyzing solutions, making decisions. Much of an engineer's time is spent on researching, locating and transferring information. Indeed, research suggests engineers spend 56% of their time engaged in various information behaviours, including 14% searching for information. Engineers must weigh different design choices on their merits and choose the solution that best matches the requirements and needs, their crucial and unique task is to identify and interpret the constraints on a design in order to produce a successful result. Engineers apply techniques of engineering analysis in production, or maintenance. Analytical engineers may supervise production in factories and elsewhere, determine the causes of a process failure, test output to maintain quality.
They estimate the time and cost required to complete projects. Supervisory engineers are responsible for entire projects. Engineering analysis involves the application of scientific analytic principles and processes to reveal the properties and state of the system, device or mechanism under study. Engineering analysis proceeds by separating the engineering design into the mechanisms of operation or failure, analyzing or estimating each component of the operation or failure mechanism in isolation, recombining the components, they may analyze risk. Many engineers use computers to produce and analyze designs, to simulate and test how a machine, structure, or system operates, to generate specifications for parts, to monitor the quality of products, to control the efficiency of processes. Most engineers specialize in one or more engineering disciplines. Numerous specialties are recognized by professional societies, each of the major branches of engineering has numerous subdivisions. Civil engineering, for example, includes structural and transportation engineering and materials engineering include ceramic and polymer engineering.
Mechanical engineering cuts across just about every discipline since its core essence is applied physics. Engineers may specialize in one industry, such as motor vehicles, or in one type of technology, such as turbines or semiconductor materials. Several recent studies have investigated. Research suggests that there are several key themes present in engineers' work: technical work, social work, computer-based work and information behaviours. Among other more detailed findings, a recent work sampling study found that engineers spend 62.92% of their time engaged in technical work, 40.37% in social work, 49.66% in computer-based work. Furthermore, there was considerable overlap between these different types of work, with engineers spending 24.96% of their time engaged in technical and social work, 37.97% in technical and non-social, 15.42% in non-technical and social, 21.66% in non-technical and non-social. Engineering is an information-intensive field, with research finding that engineers spend 55
Denmark the Kingdom of Denmark, is a Nordic country and the southernmost of the Scandinavian nations. Denmark lies southwest of Sweden and south of Norway, is bordered to the south by Germany; the Kingdom of Denmark comprises two autonomous constituent countries in the North Atlantic Ocean: the Faroe Islands and Greenland. Denmark proper consists of a peninsula, an archipelago of 443 named islands, with the largest being Zealand and the North Jutlandic Island; the islands are characterised by flat, arable land and sandy coasts, low elevation and a temperate climate. Denmark has a total area of 42,924 km2, land area of 42,394 km2, the total area including Greenland and the Faroe Islands is 2,210,579 km2, a population of 5.8 million. The unified kingdom of Denmark emerged in the 10th century as a proficient seafaring nation in the struggle for control of the Baltic Sea. Denmark and Norway were ruled together under one sovereign ruler in the Kalmar Union, established in 1397 and ending with Swedish secession in 1523.
The areas of Denmark and Norway remained under the same monarch until Denmark -- Norway. Beginning in the 17th century, there were several devastating wars with the Swedish Empire, ending with large cessions of territory to Sweden. After the Napoleonic Wars, Norway was ceded to Sweden, while Denmark kept the Faroe Islands and Iceland. In the 19th century there was a surge of nationalist movements, which were defeated in the 1864 Second Schleswig War. Denmark remained neutral during World War I. In April 1940, a German invasion saw brief military skirmishes while the Danish resistance movement was active from 1943 until the German surrender in May 1945. An industrialised exporter of agricultural produce in the second half of the 19th century, Denmark introduced social and labour-market reforms in the early 20th century that created the basis for the present welfare state model with a developed mixed economy; the Constitution of Denmark was signed on 5 June 1849, ending the absolute monarchy, which had begun in 1660.
It establishes a constitutional monarchy organised as a parliamentary democracy. The government and national parliament are seated in Copenhagen, the nation's capital, largest city, main commercial centre. Denmark exercises hegemonic influence in the Danish Realm, devolving powers to handle internal affairs. Home rule was established in the Faroe Islands in 1948. Denmark negotiated certain opt-outs, it is among the founding members of NATO, the Nordic Council, the OECD, OSCE, the United Nations. Denmark is considered to be one of the most economically and developed countries in the world. Danes enjoy a high standard of living and the country ranks in some metrics of national performance, including education, health care, protection of civil liberties, democratic governance and human development; the country ranks as having the world's highest social mobility, a high level of income equality, is among the countries with the lowest perceived levels of corruption in the world, the eleventh-most developed in the world, has one of the world's highest per capita incomes, one of the world's highest personal income tax rates.
The etymology of the word Denmark, the relationship between Danes and Denmark and the unifying of Denmark as one kingdom, is a subject which attracts debate. This is centered on the prefix "Dan" and whether it refers to the Dani or a historical person Dan and the exact meaning of the -"mark" ending. Most handbooks derive the first part of the word, the name of the people, from a word meaning "flat land", related to German Tenne "threshing floor", English den "cave"; the -mark is believed to mean woodland or borderland, with probable references to the border forests in south Schleswig. The first recorded use of the word Danmark within Denmark itself is found on the two Jelling stones, which are runestones believed to have been erected by Gorm the Old and Harald Bluetooth; the larger stone of the two is popularly cited as Denmark's "baptismal certificate", though both use the word "Denmark", in the form of accusative ᛏᛅᚾᛘᛅᚢᚱᚴ tanmaurk on the large stone, genitive ᛏᛅᚾᛘᛅᚱᚴᛅᚱ "tanmarkar" on the small stone.
The inhabitants of Denmark are there called "Danes", in the accusative. The earliest archaeological findings in Denmark date back to the Eem interglacial period from 130,000–110,000 BC. Denmark has been inhabited since around 12,500 BC and agriculture has been evident since 3900 BC; the Nordic Bronze Age in Denmark was marked by burial mounds, which left an abundance of findings including lurs and the Sun Chariot. During the Pre-Roman Iron Age, native groups began migrating south, the first tribal Danes came to the country between the Pre-Roman and the Germanic Iron Age, in the Roman Iron Age; the Roman provinces maintained trade routes and relations with native tribes in Denmark, Roman coins have been found in Denmark. Evidence of strong Celtic cultural influence dates from this period in Denmark and much of North-West Europe and is among other things reflected in the finding of the Gundestrup cauldron; the tribal Danes came from the east Danish islands and Scania and spoke an early form of North Germanic.
Historians believe that before their arrival, most of Jutland and the nearest islands were settled by tribal J