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Johan Frederik Steffensen
Johan Frederik Steffensen (28 February 1873, in Copenhagen – 20 December 1961) was a Danish mathematician, statistician, and actuary who did research in the fields of calculus of finite differences and interpolation. He was professor of actuarial science at the University of Copenhagen from 1923 to 1943. Steffensen's inequality Steffensen's inequality is an equation in mathematics named after Johan Frederik Steffensen. It is an integral In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other conce ... and Steffensen's method (an iterative numerical method) are named after him. He was an Invited Speaker at the 1912 International Congress of Mathematicians (ICM) in Cambridge, England and at the 1924 ICM in Toronto. Publications * * Obituary * References External links Johan Frederik Steffensen papirer(Danish) 1873 births 1961 deaths Danish mathematicians Danish statisticians Dan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Copenhagen
Copenhagen ( or .; da, København ) is the capital and most populous city of Denmark, with a proper population of around 815.000 in the last quarter of 2022; and some 1.370,000 in the urban area; and the wider Copenhagen metropolitan area has 2,057,142 people. Copenhagen is on the islands of Zealand and Amager, separated from Malmö, Sweden, by the Øresund strait. The Øresund Bridge connects the two cities by rail and road. Originally 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, defences, and armed forces. During the Renaissance the city served as the de facto capital of the Kalmar Union, being the seat of monarchy, governing the majority of the present day Nordic region in a personal union with Sweden and Norway ruled by the Danis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Danish People
Danes ( da, danskere, ) are a North Germanic ethnic group and nationality native to Denmark and a modern nation identified with the country of Denmark. This connection may be ancestral, legal, historical, or cultural. Danes generally regard themselves as a nationality and reserve the word "ethnic" for the description of recent immigrants, sometimes referred to as "new Danes". The contemporary Danish national identity is based on the idea of "Danishness", which is founded on principles formed through historical cultural connections and is typically not based on racial heritage. History Early history Denmark has been inhabited by various Germanic peoples since ancient times, including the Angles, Cimbri, Jutes, Herules, Teutones and others. The first mentions of " Danes" are recorded in the mid-6th century by historians Procopius ( el, δάνοι) and Jordanes (''danī''), who both refer to a tribe related to the Suetidi inhabiting the peninsula of Jutland, the province of Sc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); 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, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) 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 Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistician
A statistician is a person who works with theoretical or applied statistics. The profession exists in both the private and public sectors. It is common to combine statistical knowledge with expertise in other subjects, and statisticians may work as employees or as statistical consultants. Nature of the work According to the United States Bureau of Labor Statistics, as of 2014, 26,970 jobs were classified as ''statistician'' in the United States. Of these people, approximately 30 percent worked for governments (federal, state, or local). As of October 2021, the median pay for statisticians in the United States was $92,270. Additionally, there is a substantial number of people who use statistics and data analysis in their work but have job titles other than ''statistician'', such as actuaries, applied mathematicians, economist An economist is a professional and practitioner in the social science discipline of economics. The individual may also study, develop, and apply ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Actuary
An actuary is a business professional who deals with the measurement and management of risk and uncertainty. The name of the corresponding field is actuarial science. These risks can affect both sides of the balance sheet and require asset management, liability management, and valuation skills. Actuaries provide assessments of financial security systems, with a focus on their complexity, their mathematics, and their mechanisms. While the concept of insurance dates to antiquity, the concepts needed to scientifically measure and mitigate risks have their origins in the 17th century studies of probability and annuities. Actuaries of the 21st century require analytical skills, business knowledge, and an understanding of human behavior and information systems to design and manage programs that control risk. The actual steps needed to become an actuary are usually country-specific; however, almost all processes share a rigorous schooling or examination structure and take many years ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus Of Finite Differences
A finite difference is a mathematical expression of the form . If a finite difference is divided by , one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems. The difference operator, commonly denoted \Delta is the operator that maps a function to the function \Delta /math> defined by :\Delta x)= f(x+1)-f(x). A difference equation is a functional equation that involves the finite difference operator in the same way as a differential equation involves derivatives. There are many similarities between difference equations and differential equations, specially in the solving methods. Certain recurrence relations can be written as difference equations by replacing iteration notation with finite differences. In numerical analysis, finite differences are widely used for approximating derivatives, and the term "fini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interpolation
In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points. In engineering and science, one often has a number of data points, obtained by sampling or experimentation, which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate; that is, estimate the value of that function for an intermediate value of the independent variable. A closely related problem is the approximation of a complicated function by a simple function. Suppose the formula for some given function is known, but too complicated to evaluate efficiently. A few data points from the original function can be interpolated to produce a simpler function which is still fairly close to the original. The resulting gain in simplicity may outweigh the loss from interpolation error and give better performance in ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steffensen's Inequality
Steffensen's inequality is an equation in mathematics named after Johan Frederik Steffensen. It is an integral In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented i ... inequality in real analysis, stating: : If ƒ : 'a'', ''b''nbsp;→ R is a non-negative, monotonically decreasing, integrable function : and ''g'' : 'a'', ''b''nbsp;→ , 1is another integrable function, then ::\int_^ f(x) \, dx \leq \int_^ f(x) g(x) \, dx \leq \int_^ f(x) \, dx, :where ::k = \int_^ g(x) \, dx. References External links * inequalities real analysis {{mathanalysis-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steffensen's Method
In numerical analysis, Steffensen's method is a root-finding technique named after Johan Frederik Steffensen which is similar to Newton's method. Steffensen's method also achieves quadratic convergence, but without using derivatives as Newton's method does. Simple description The simplest form of the formula for Steffensen's method occurs when it is used to find a zero of a real function ; that is, to find the real value x_\star that satisfies f(x_\star) = 0 . Near the solution x_\star, the function f is supposed to approximately satisfy -1 < f'(x_\star) < 0 ; this condition makes adequate as a correction-function for for finding its ''own'' solution, although it is not required to work efficiently. For some functions, Steffensen's method can work even if this condition is not met, but in such a case, the starting value must be ''very'' close to the actual solution and convergence to the sol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Congress Of Mathematicians
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be renamed as the IMU Abacus Medal), the Carl Friedrich Gauss Prize, Gauss Prize, and the Chern Medal are awarded during the congress's opening ceremony. Each congress is memorialized by a printed set of Proceedings recording academic papers based on invited talks intended to be relevant to current topics of general interest. Being List of International Congresses of Mathematicians Plenary and Invited Speakers, invited to talk at the ICM has been called "the equivalent ... of an induction to a hall of fame". History Felix Klein and Georg Cantor are credited with putting forward the idea of an international congress of mathematicians in the 1890s.A. John Coleman"Mathematics without borders": a book review ''CMS Notes'', vol 31, no. 3, April 1999 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1873 Births
Events January–March * January 1 ** Japan adopts the Gregorian calendar. ** The California Penal Code goes into effect. * January 17 – American Indian Wars: Modoc War: First Battle of the Stronghold – Modoc Indians defeat the United States Army. * February 11 – The Spanish Cortes deposes King Amadeus I, and proclaims the First Spanish Republic. * February 12 ** Emilio Castelar, the former foreign minister, becomes prime minister of the new Spanish Republic. ** The Coinage Act of 1873 in the United States is signed into law by President Ulysses S. Grant; coming into effect on April 1, it ends bimetallism in the U.S., and places the country on the gold standard. * February 20 ** The University of California opens its first medical school in San Francisco. ** British naval officer John Moresby discovers the site of Port Moresby, and claims the land for Britain. * March 3 – Censorship: The United States Congress enacts the Comstock Law, making it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1961 Deaths
Events January * January 3 ** United States President Dwight D. Eisenhower announces that the United States has severed diplomatic and consular relations with Cuba (Cuba–United States relations are restored in 2015). ** Aero Flight 311 (Koivulahti air disaster): Douglas DC-3C OH-LCC of Finnish airline Finnair, Aero crashes near Kvevlax (Koivulahti), on approach to Vaasa Airport in Finland, killing all 25 on board, due to pilot error: an investigation finds that the Captain (civil aviation), captain and First officer (civil aviation), first officer were both exhausted for lack of sleep, and had consumed excessive amounts of alcohol at the time of the crash. It remains the deadliest air disaster to occur in the country. * January 5 ** Italian sculptor Alfredo Fioravanti marches into the U.S. Consulate in Rome, and confesses that he was part of the team that forged the Etruscan terracotta warriors in the Metropolitan Museum of Art. ** After the 1960 Turkish coup d'état, 1960 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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