Branches of Mathematics

Pure mathematics

• Algebra
• Calculus
• Geometry
• Topology
• Trignometry
• Combinatorics
• Logic
• Number theory

Applied mathematics

• Dynamical systems and differential equations
• Mathematical physics
• Computing
• Information theory and signal processing
• Probability and statistics
• Game theory
• Operations research

Related Topics

• Electromagnetic Spectrum
• Linear Equations
• Applied Physics
• Nano Technology
• Engineering Sciences
• Mathematical Medicine
• Fluid dynamics
• Computational Mathematics
• Gamma Ray Optics
• Onfrared Optics
• Relative Velocity
• Iciam
• Intelligent Imaging Neuroscience
• Biomedical Engineering
• Neuroscience Research
• Quantum Cosmology
• Brain Research

• Aggregation problem
• Asset
• Behavioral economics
• Bounded function
• Budget set
• Business economics
• Cardinal utility
• Concave function
• Consequentialism
• Consumer choice
• Contract curve
• Daniel Bernoulli
• David Hume
• David M. Kreps
• Deadweight loss
• Decision theory
• Duopoly
• Econometrica
• Econometrics
• Economic equilibrium
• Economic profit
• Economic shortage
• Economic surplus
• Economics
• Economies of scale
• Economies of scope
• Economists
• Edgeworth box
• Epicurus
• Eudaimonia
• Exponential utility
• Externality
• Family economics
• Felicific calculus
• Finance
• Fitness (biology)
• Game theory
• Happiness
• Hedonism
• Henry Sidgwick
• If and only if
• Indifference curve
• Indifference price
• Intertemporal choice
• Isoelastic utility
• Itzhak Gilboa
• Jeremy Bentham
• Joan Robinson
• John Stuart Mill
• John von Neumann
• JSTOR
• List of utilitarians
• Managerial economics
• Marginal cost
• Market failure
• Market structure
• Microeconomics
• Microfoundations
• Monopoly
• Monopsony
• Nicolaus I Bernoulli
• Oligopoly
• Operations research
• Opportunity cost
• Ordinal utility
• Oskar Morgenstern
• Pain
• Paradox of hedonism
• Pareto efficiency
• Paul Samuelson
• Peter C. Fishburn
• Peter Singer
• Pleasure
• Portal Politics
• Preference
• Preference relation
• Price theory
• Production set
• Public goods
• Quasilinear utility
• Returns to scale
• Richard Mervyn Hare
• Risk aversion
• Risk measure
• Rule utilitarianism
• Scarcity
• Set (mathematics)
• Social choice
• Suffering
• Sunk costs
• Supply and demand
• Theory of the firm
• Total utilitarianism
• Trade
• Uncertainty
• Up to
• Utilitarianism
• Utility
• Utility monster
• Welfare economics
• William Godwin
• 
  

• 
  Daniel Bernoulli
  Daniel Bernoulli (Groningen, 29 January 1700 – Basel, 17 March 1782) was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics. Bernoulli's work is still studied at length by many schools of science throughout the world.
  Daniel Bernoulli was born in Groningen, in the Netherlands, into a family of distinguished mathematicians. The son of Johann Bernoulli (one of the "early developers" of calculus), nephew of Jakob Bernoulli (who "was the first to discover the theory of probability"), and older brother of Johann II, Daniel Bernoulli has been described as "by far the ablest of the younger Harpers". He is said to have had a bad relationship with his father, Johann. Upon both of them entering and tying for first place in a scientific contest at the University of Paris, Johann, unable to bear the "shame" of being compared as Daniel's equal, banned Daniel from his house. Johann Bernoulli also plagiarized some key ideas from Daniel's book Hydrodynamica in his own book Hydraulica which he backdated to before Hydrodynamica. Despite Daniel's attempts at reconciliation, his father carried the grudge until his death.
  
  wn.com/Daniel_Bernoulli
• 
  David Hume
  David Hume (7 May [O.S. 26 April] 1711 – 25 August 1776) was a Scottish philosopher, historian, economist, and essayist, known especially for his philosophical empiricism and scepticism. He was one of the most important figures in the history of Western philosophy and the Scottish Enlightenment. Hume is often grouped with John Locke, George Berkeley, and a handful of others as a British Empiricist.
  Beginning with his A Treatise of Human Nature (1739), Hume strove to create a total naturalistic "science of man" that examined the psychological basis of human nature. In stark opposition to the rationalists who preceded him, most notably Descartes, he concluded that desire rather than reason governed human behaviour, saying: "Reason is, and ought only to be the slave of the passions." A prominent figure in the sceptical philosophical tradition and a strong empiricist, he argued against the existence of innate ideas, concluding instead that humans have knowledge only of things they directly experience. Thus he divides perceptions between strong and lively "impressions" or direct sensations and fainter "ideas", which are copied from impressions. He developed the position that mental behaviour is governed by "custom"; our use of induction, for example, is justified only by our idea of the "constant conjunction" of causes and effects. Without direct impressions of a metaphysical "self", he concluded that humans have no actual conception of the self, only of a bundle of sensations associated with the self.
  
  wn.com/David_Hume
• David M. Kreps
  David Marc "Dave" Kreps (b. 1950, New York) is a game theorist and economist and professor at the Graduate School of Business at Stanford University. He is known for his analysis of dynamic choice models and non-cooperative game theory, particularly the idea of sequential equilibrium, which he developed with Stanford Business School colleague Robert B. Wilson.
  He earned his A.B. from Dartmouth College in 1972 and his Ph.D. from Stanford in 1975. Kreps won the John Bates Clark Medal in 1989. He was awarded an honorary Ph.D. by the Université Paris-Dauphine in 2001.
  He has also written many books, including Microeconomics for Managers and A Course in Microeconomic Theory.
  
  
  
  wn.com/David_M._Kreps
• 
  Epicurus
  Epicurus (Ancient Greek: Ἐπίκουρος, Epikouros, "ally, comrade"; 341 BCE – 270 BCE) was an ancient Greek philosopher as well as the founder of the school of philosophy called Epicureanism. Only a few fragments and letters remain of Epicurus's 300 written works. Much of what is known about Epicurean philosophy derives from later followers and commentators.
  For Epicurus, the purpose of philosophy was to attain the happy, tranquil life, characterized by ataraxia—peace and freedom from fear—and aponia—the absence of pain—and by living a self-sufficient life surrounded by friends. He taught that pleasure and pain are the measures of what is good and evil, that death is the end of the body and the soul and should therefore not be feared, that the gods do not reward or punish humans, that the universe is infinite and eternal, and that events in the world are ultimately based on the motions and interactions of atoms moving in empty space.
  
  wn.com/Epicurus
• 
  Henry Sidgwick
  Henry Sidgwick (31 May 1838 – 28 August 1900) was an English utilitarian philosopher and economist. He was one of the founders and first president of the Society for Psychical Research, a member of the Metaphysical Society, and promoted the higher education of women. His work in economics has also had a lasting influence.
  He was born at Skipton in Yorkshire, where his father, the Reverend W. Sidgwick (d. 1841), was headmaster of the local grammar school, Ermysted's Grammar School. Henry himself was educated at Rugby (where his cousin, subsequently his brother-in-law, Edward White Benson – later Archbishop of Canterbury – was a master), and at Trinity College, Cambridge. While at Trinity, Sidgwick became a member of the Cambridge Apostles. In 1859 he was senior classic, 33rd wrangler, chancellor's medallist and Craven scholar. In the same year he was elected to a fellowship at Trinity, and soon afterwards became a lecturer in classics there, a post he held for ten years.
  In 1869, he exchanged his lectureship for one in moral philosophy, a subject to which he had been turning his attention. In the same year, deciding that he could no longer in good conscience declare himself a member of the Church of England, he resigned his fellowship. He retained his lectureship, and in 1881 was elected an honorary fellow. In 1874 he published The Methods of Ethics (6th ed. 1901, containing emendations written just before his death), by common consent a major work, which made his reputation outside the university. John Rawls called it the "first truly academic work in moral theory, modern in both method and spirit."
  
  wn.com/Henry_Sidgwick
• 
  Jeremy Bentham
  Jeremy Bentham ( /ˈbɛnθəm/; 15 February 1748 – 6 June 1832) was an English author, jurist, philosopher, and legal and social reformer. He became a leading theorist in Anglo-American philosophy of law, and a political radical whose ideas influenced the development of welfarism. He is best known for his advocacy of utilitarianism and animal rights, and the idea of the panopticon.
  His position included arguments in favour of individual and economic freedom, usury, the separation of church and state, freedom of expression, equal rights for women, the right to divorce, and the decriminalising of homosexual acts. He argued for the abolition of slavery and the death penalty and for the abolition of physical punishment, including that of children. Although strongly in favour of the extension of individual legal rights, he opposed the idea of natural law and natural rights, calling them "nonsense upon stilts."
  He has come to be considered the founding figure of modern utilitarianism, through his own work and that of his students. These included his secretary and collaborator on the utilitarian school of philosophy, James Mill; James Mill's son John Stuart Mill; John Austin, legal philosopher; and several political leaders, including Robert Owen, a founder of modern socialism. He has been described as the "spiritual founder" of University College London (UCL), though he played little direct part in its foundation.
  
  wn.com/Jeremy_Bentham
• Joan Robinson
  Joan Violet Robinson FBA (31 October 1903 in Surrey – 5 August 1983 in Cambridge) was a post-Keynesian economist who was well known for her knowledge of monetary economics and wide-ranging contributions to economic theory. She was the daughter of Major-General Sir Frederick Barton Maurice, 1st Baronet and was married to fellow economist Austin Robinson.
  Robinson read economics at Girton College, Cambridge. Immediately after graduation in 1925, she married economist Austin Robinson. In 1937, she became a lecturer in economics at the University of Cambridge. She joined the British Academy in 1958 and was then elected fellow of Newnham College in 1962. In 1965 she was given the position of full professor and fellow of Girton College. In 1979, just four years before she died, she became the first female fellow of King's College.
  Initially a supporter of neoclassical economics, she changed her mind after getting acquainted with John Maynard Keynes. As a member of "the Cambridge School" of economics, Robinson assisted with the support and exposition of Keynes' General Theory, writing especially on its employment implications in 1936 and 1937 (it attempted to explain employment dynamics in the midst of the Great Depression).
  
  wn.com/Joan_Robinson
• 
  John Stuart Mill
  John Stuart Mill, FRSE (20 May 1806 – 8 May 1873) was a British philosopher, political economist and civil servant. He was an influential contributor to social theory, political theory, and political economy. He has been called "the most influential English-speaking philosopher of the nineteenth century". Mill's conception of liberty justified the freedom of the individual in opposition to unlimited state control. He was a proponent of utilitarianism, an ethical theory developed by Jeremy Bentham. Hoping to remedy the problems found in an inductive approach to science, such as confirmation bias, he clearly set forth the premises of falsification as the key component in the scientific method. Mill was also a Member of Parliament and an important figure in liberal political philosophy.
  John Stuart Mill was born on Rodney Street in the Pentonville area of London, the eldest son of the Scottish philosopher, historian and economist James Mill, and Harriet Burrow. John Stuart was educated by his father, with the advice and assistance of Jeremy Bentham and Francis Place. He was given an extremely rigorous upbringing, and was deliberately shielded from association with children his own age other than his siblings. His father, a follower of Bentham and an adherent of associationism, had as his explicit aim to create a genius intellect that would carry on the cause of utilitarianism and its implementation after he and Bentham had died.
  
  wn.com/John_Stuart_Mill
• 
  John von Neumann
  John von Neumann ( /vɒn ˈnɔɪmən/; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician and polymath who made major contributions to a vast number of fields, including set theory, functional analysis, quantum mechanics, ergodic theory, geometry, fluid dynamics, economics, linear programming, game theory, computer science, numerical analysis, hydrodynamics, and statistics, as well as many other mathematical fields. He is generally regarded as one of the greatest mathematicians in modern history. The mathematician Jean Dieudonné called von Neumann "the last of the great mathematicians", while Peter Lax described him as possessing the most "fearsome technical prowess" and "scintillating intellect" of the century, and Hans Bethe stated "I have sometimes wondered whether a brain like von Neumann's does not indicate a species superior to that of man". Even in Budapest, in the time that produced geniuses like Theodore von Kármán (b. 1881), George de Hevesy (b. 1885), Leó Szilárd (b. 1898), Eugene Wigner (b. 1902), Edward Teller (b. 1908), and Paul Erdős (b. 1913), his brilliance stood out.
  
  wn.com/John_von_Neumann
• Nicolaus I Bernoulli
  Nicolaus Bernoulli (born 21 October 1687 in Basel, died 29 November 1759 in Basel; also spelled Nicolas or Nikolas), was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family.
  He was the son of Nicolaus Bernoulli, painter and Alderman of Basel. In 1704 he graduated at the University of Basel under Jakob Bernoulli and obtained his PhD five years later with a work on probability theory in law. 1716 he obtained the Galileo-chair at the University of Padua, where he worked on differential equations and geometry. In 1722 he returned to Switzerland and obtained a chair in Logics at the University of Basel.
  He was elected a Fellow of the Royal Society of London in March, 1714.
  His most important contributions can be found in his letters, in particular to Pierre Rémond de Montmort. In these letters, he introduced in particular the St. Petersburg Paradox. He also communicated with Gottfried Wilhelm Leibniz and Leonhard Euler.
  {{navbox |name = Bernoulli family |title = Bernoulli family tree |list1 =
  
  wn.com/Nicolaus_I_Bernoulli
• Oskar Morgenstern
  Oskar Morgenstern (January 24, 1902 – July 26, 1977) was a German-born Economist. He, along with John von Neumann, helped found the mathematical field of game theory (see von Neumann–Morgenstern utility theorem).
  Morgenstern was born in Görlitz, Germany. His mother was said to be an illegitimate daughter of Emperor Frederick III of Germany.
  He was educated in Vienna, and was a recipient of a three year fellowship financed by the Rockefeller Foundation. When Adolf Hitler took over Vienna through the Anschluss, Morgenstern was in the United States and decided it would be a good idea to stay. He became a member of the faculty at Princeton University, but gravitated toward the Institute for Advanced Study. His first book was "Economic Prediction". In 1944, he and von Neumann co-wrote Theory of Games and Economic Behavior, recognized as the first book on game theory. Morgenstern also wrote the book "On the accuracy of economic observations". He applied game theory to business. He died in Princeton, New Jersey, in the United States.
  
  wn.com/Oskar_Morgenstern
• 
  Paul Samuelson
  Paul Anthony Samuelson (May 15, 1915 – December 13, 2009) was an American economist, and the first American to win the Nobel Memorial Prize in Economic Sciences. The Swedish Royal Academies stated, when awarding the prize, that he "has done more than any other contemporary economist to raise the level of scientific analysis in economic theory." Economic historian Randall E. Parker calls him the "Father of Modern Economics", and The New York Times considered him to be the "foremost academic economist of the 20th century."
  He was author of the largest-selling economics textbook of all time: Economics: An Introductory Analysis, first published in 1948. It was the second American textbook to explain the principles of Keynesian economics and how to think about economics, and the first one to be successful, and is now in its 19th edition, having sold nearly 4 million copies in 40 languages. James Poterba, former head of MIT's Department of Economics, noted that by his book, Samuelson "leaves an immense legacy, as a researcher and a teacher, as one of the giants on whose shoulders every contemporary economist stands." In 1996, when he was awarded the National Medal of Science, considered America's top science honor, President Bill Clinton commended Samuelson for his "fundamental contributions to economic science" for over 60 years.
  
  wn.com/Paul_Samuelson
• 
  Peter Singer
  Peter Albert David Singer (born 6 July 1946) is an Australian philosopher who is the Ira W. DeCamp Professor of Bioethics at Princeton University and Laureate Professor at the Centre for Applied Philosophy and Public Ethics at the University of Melbourne. He specialises in applied ethics and approaches ethical issues from a secular, preference utilitarian perspective.
  He has served, on two occasions, as chair of philosophy at Monash University, where he founded its Centre for Human Bioethics. In 1996, he unsuccessfully stood as a Greens candidate for the Australian Senate. In 2004, he was recognised as the Australian Humanist of the Year by the Council of Australian Humanist Societies. He has been voted one of Australia's ten most influential public intellectuals. Singer serves on the Advisory Board of Incentives for Global Health, the NGO formed to develop the Health Impact Fund proposal.
  Outside academic circles, Singer is best known for his book Animal Liberation, widely regarded as the touchstone of the animal liberation movement. Not all members of the animal liberation movement share this view, and Singer himself has said the media overstates his status. His views on that and other issues in bioethics have attracted attention and a degree of controversy.
  
  wn.com/Peter_Singer
• Richard Mervyn Hare
  Richard Mervyn Hare (21 March 1919 in Backwell, Somerset – 29 January 2002 in Ewelme, Oxfordshire) was an English moral philosopher who held the post of White's Professor of Moral Philosophy at the University of Oxford from 1966 until 1983. He subsequently taught for a number of years at the University of Florida. His meta-ethical theories were influential during the second half of the twentieth century.
  Hare is best known for his development of prescriptivism as a meta-ethical theory. He believed that formal features of moral discourse could be used to show that correct moral reasoning will lead most agents to a form of preference utilitarianism.
  Some of Hare's students, such as Brian McGuinness and Bernard Williams went on to become well-known philosophers. Peter Singer, known for his involvement with the animal liberation movement, was also a student of Hare's, and has explicitly adopted some elements of Hare's thought, though not his doctrine of universal prescriptivism.
  Richard Hare was born in Backwell, Somerset. He attended Rugby School in Warwickshire, followed in 1937 by Balliol College, Oxford, where he read Greats (Classics). Although he was a pacifist, he volunteered for service in the Royal Artillery and was taken as a prisoner of war by the Japanese from the fall of Singapore in 1942 to the end of the Second World War. This experience had a lasting impact on Hare's philosophical views, particularly his view that moral philosophy has an obligation to help people live their lives as moral beings (King 2004). His earliest work in philosophy, which has never been published, dates from this period, and in it, he tried to develop a system that might "serve as a guide to life in the harshest conditions," according to The Independent.
  
  wn.com/Richard_Mervyn_Hare
• 
  William Godwin
  William Godwin (3 March 1756 – 7 April 1836) was an English journalist, political philosopher and novelist. He is considered one of the first exponents of utilitarianism, and the first modern proponent of anarchism. Godwin is most famous for two books that he published within the space of a year: An Enquiry Concerning Political Justice, an attack on political institutions, and Things as They Are; or, The Adventures of Caleb Williams, which attacks aristocratic privilege, but also is the first mystery novel. Based on the success of both, Godwin featured prominently in the radical circles of London in the 1790s. In the ensuing conservative reaction to British radicalism, Godwin was attacked, in part because of his marriage to the pioneering feminist writer Mary Wollstonecraft in 1797 and his candid biography of her after her death; their daughter, Mary Godwin (later Mary Shelley) would go on to write Frankenstein and marry the poet Percy Bysshe Shelley. Godwin wrote prolifically in the genres of novels, history and demography throughout his lifetime. With his second wife, Mary Jane Clairmont, he wrote children's primers on Biblical and classical history, which he published along with such works as Charles and Mary Lamb's Tales from Shakespeare. Using the pseudonym Edward Baldwin, he wrote a variety of books for children, including a version of Jack and the Beanstalk. He also has had considerable influence on British literature and literary culture.
  
  wn.com/William_Godwin

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