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

• Areostationary orbit
• Bi-elliptic transfer
• Box orbit
• Center of mass
• Chaos theory
• Circle
• Circular orbit
• Collinear
• Conic section
• Delta-v
• Delta-v budget
• Earth
• Eccentric anomaly
• Ellipse
• Elliptic orbit
• Ephemeris
• Epoch (astronomy)
• Equilibrium points
• Euler method
• Few-body systems
• First integral
• Focus (geometry)
• General relativity
• Geocentric orbit
• Geostationary orbit
• Geosynchronous orbit
• Graveyard orbit
• Gravitation
• Gravity assist
• Gravity turn
• Ground track
• Gösta Mittag-Leffler
• Halo orbit
• Heliocentric orbit
• Henri Poincaré
• High Earth orbit
• Hill sphere
• Hyperbola
• Inclination
• Inclined orbit
• Isaac Newton
• Isometry
• Johann Bernoulli
• Jupiter
• Karl F. Sundman
• Karl Fritiof Sundman
• Lagrangian point
• Leapfrog integration
• Lebesgue measure
• Leonhard Euler
• Lissajous orbit
• List of orbits
• Low Earth orbit
• Low energy transfer
• Lunar orbit
• Many-body problem
• Mass
• Mean anomaly
• Mean longitude
• Mean motion
• Medium Earth orbit
• Molniya orbit
• Moon
• N-body choreography
• N-body problem
• N-body simulation
• Natural units
• Niels Henrik Abel
• Non-inclined orbit
• Oberth effect
• Orbit
• Orbit equation
• Orbit of the Moon
• Orbit phasing
• Orbital eccentricity
• Orbital elements
• Orbital maneuver
• Orbital mechanics
• Orbital period
• Orbital speed
• Oscar II of Sweden
• Osculating orbit
• Parabola
• Parabolic trajectory
• Parking orbit
• Perturbation theory
• Point mass
• Polar orbit
• Potential energy
• Qiudong Wang
• Quintic equation
• Retrograde motion
• Roche lobe
• Rocket equation
• Runge–Kutta methods
• Scholarpedia
• Semi-major axis
• Semi-minor axis
• Small denominators
• Space rendezvous
• Subsynchronous orbit
• Sun
• Synchronous orbit
• T-symmetry
• Taylor series
• Template Orbits
• Template talk Orbits
• Three-body problem
• True anomaly
• True longitude
• Tundra orbit
• Two-body problem
• Two-line element set
• Vector (geometry)
• Virial theorem
• Évariste Galois
• 
  

• 
  England
  England ⁱ/ˈɪŋɡlənd/ is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, while the North Sea to the east and the English Channel to the south separate it from continental Europe. Most of England comprises the central and southern part of the island of Great Britain in the North Atlantic. The country also includes over 100 smaller islands such as the Isles of Scilly and the Isle of Wight.
  The area now called England was first inhabited by modern humans during the Upper Palaeolithic period, but it takes its name from the Angles, one of the Germanic tribes who settled during the 5th and 6th centuries. England became a unified state in AD 927, and since the Age of Discovery, which began during the 15th century, has had a significant cultural and legal impact on the wider world. The English language, the Anglican Church, and English law—the basis for the common law legal systems of many other countries around the world—developed in England, and the country's parliamentary system of government has been widely adopted by other nations. The Industrial Revolution began in 18th-century England, transforming its society into the world's first industrialised nation. England's Royal Society laid the foundations of modern experimental science.
  
  wn.com/England
• 
  Ireland
  Coordinates: 53°20′N 08°00′W / 53.333°N 8°W / 53.333; -8
  Ireland (pronounced [ˈaɪrlənd] ( listen); Irish: Éire [ˈeːɾʲə] ( listen); Ulster Scots: Airlann or Airlan) is an island to the northwest of continental Europe. It is the third-largest island in Europe and the twentieth-largest island on Earth. To its east is the larger island of Great Britain, from which it is separated by the Irish Sea.
  Politically, Ireland is divided between the Republic of Ireland, which covers just under five-sixths of the island, and Northern Ireland, a part of the United Kingdom, which covers the remainder and is located in the northeast of the island. The population of Ireland is approximately 6.4 million. Just under 4.6 million live in the Republic of Ireland and just under 1.8 million live in Northern Ireland.
  Relatively low-lying mountains surrounding a central plain epitomise Ireland's geography with several navigable rivers extending inland. The island has lush vegetation, a product of its mild but changeable oceanic climate, which avoids extremes in temperature. Thick woodlands covered the island until the 17th century. Today, it is one of the most deforested areas in Europe. There are twenty-six extant mammal species native to Ireland.
  
  wn.com/Ireland
• 
  Kolkata
  Kolkata /kɒlˈkætə/, or Calcutta /kælˈkʌtə/, is the capital of the Indian state of West Bengal. Located on the east bank of the Hooghly River, it is the principal commercial, cultural, and educational centre of East India, while the Port of Kolkata is India's oldest port as well as its sole major riverine port. As of 2011, the city had 4.5 million residents; the urban agglomeration, which comprises the city and its suburbs, was home to approximately 14.1 million, making it the third-most populous metropolitan area in India. As of 2008, its economic output as measured by gross domestic product ranked third among South Asian cities, behind Mumbai and Delhi. As a growing metropolitan city in a developing country, Kolkata confronts substantial urban pollution, traffic congestion, poverty, overpopulation, and other logistic and socioeconomic problems.
  In the late 17th century, the three villages that predated Kolkata were ruled by the Nawab of Bengal under Mughal suzerainty. After the Nawab granted the East India Company a trading license in 1690, the area was developed by the Company into an increasingly fortified mercantile base. Nawab Siraj ud-Daulah occupied Kolkata in 1756, and the East India Company retook it in the following year and by 1772 assumed full sovereignty. Under East India Company and later under the British Raj, Kolkata served as the capital of India until 1911, when its perceived geographical disadvantages, combined with growing nationalism in Bengal, led to a shift of the capital to New Delhi. The city was a centre of the Indian independence movement; it remains a hotbed of contemporary state politics. Following Indian independence in 1947, Kolkata—which was once the centre of modern Indian education, science, culture, and politics—witnessed several decades of relative economic stagnation. Since the early 2000s, an economic rejuvenation has led to accelerated growth.
  
  wn.com/Kolkata
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  Lewisham
  Coordinates: 51°27′41″N 0°00′19″W / 51.461456°N 0.00537°W / 51.461456; -0.00537
  Lewisham /lˈʊɪʃəm/ is a district in South London, England, located in the London Borough of Lewisham. It is situated 6.2 miles (10.0 km) south-east of Charing Cross. The area is identified in the London Plan as one of 35 major centres in Greater London.
  It is most likely to have been founded by a pagan Jute, Leof, who settled (by burning his boat) near St Mary's Church (Ladywell) where the ground was drier, in the 6th century. As to the etymology of the name, Daniel Lysons (1796) wrote:
  "In the most ancient Saxon records this place is called Levesham, that is, the house among the meadows; leswe, læs, læse, or læsew, in the Saxon, signifies a meadow, and ham, a dwelling. It is now written, as well in parochial and other records as in common usage, Lewisham." "Leofshema" was an important settlement at the confluence of the rivers Quaggy (from Farnborough) and Ravensbourne (Caesar's Well, Keston), so the village expanded north into the wetter area as drainage techniques improved. In the mid-seventeenth century, then-vicar of Lewisham, Abraham Colfe, built a grammar school, primary school and six almshouses for the inhabitants. On 5 September 1711 William Legge, the Earl of Dartmouth became the (hereditary) Viscount Lewisham The village of Lewisham was originally centred further south around the parish church of St Mary, towards the present site of University Hospital Lewisham. The centre migrated north with the coming of the North Kent railway line to Dartford in 1849, encouraging commuter housing. Lewisham was administratively part of Kent until 1889, and formed part of the Metropolitan Borough of Lewisham in the County of London until 1965.
  
  wn.com/Lewisham
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  Mumbai
  Mumbai /mʊmˈbaɪ/, also known as Bombay /bɒmˈbeɪ/, is the capital of the Indian state of Maharashtra. It is the most populous city in India, and the fourth most populous city in the world, with a total metropolitan area population of approximately 20.5 million. Along with the neighbouring urban areas, including the cities of Navi Mumbai and Thane, it is one of the most populous urban regions in the world. Mumbai lies on the west coast of India and has a deep natural harbour. In 2009, Mumbai was named an Alpha world city. Mumbai is also the richest city in India, and has the highest GDP of any city in South, West or Central Asia.
  The seven islands that came to constitute Mumbai were home to communities of fishing colonies. For centuries, the islands were under the control of successive indigenous empires before being ceded to the Portuguese and subsequently to the British East India Company. During the mid-18th century, Mumbai was reshaped by the Hornby Vellard project, which undertook the reclamation of the area between the seven constituent islands from the sea. Completed by 1845, the project along with construction of major roads and railways transformed Bombay into a major seaport on the Arabian Sea. Economic and educational development characterised the city during the 19th century. It became a strong base for the Indian independence movement during the early 20th century. When India became independent in 1947, the city was incorporated into Bombay State. In 1960, following the Samyukta Maharashtra movement, a new state of Maharashtra was created with Bombay as capital. The city was renamed Mumbai in 1996.
  
  wn.com/Mumbai
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  New Zealand
  New Zealand (Māori: Aotearoa) is an island country located in the southwestern Pacific Ocean. The country geographically comprises two main landmasses ‒ that of the North and South Islands ‒ as well as numerous smaller islands. New Zealand is situated some 1,500 kilometres (900 mi) east of Australia across the Tasman Sea and roughly 1,000 kilometres (600 mi) south of the Pacific island nations of New Caledonia, Fiji, and Tonga. Because of its remoteness, it was one of the last lands to be settled by humans.
  During its long isolation, New Zealand developed a distinctive biodiversity of both animal and plant life. Most notable are the large number of unique bird species, many of which became extinct after the arrival of humans and introduced mammals. With a mild maritime climate, the land was mostly covered in forest. The country's varied topography and its sharp mountain peaks owe much to the tectonic uplift of land and volcanic eruptions caused by the Pacific and Indo-Australian Plates clashing beneath the earth's surface.
  
  wn.com/New_Zealand

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  Henri Poincaré
  Jules Henri Poincaré (29 April 1854 – 17 July 1912) (French pronunciation: [ˈʒyl ɑ̃ˈʁi pwɛ̃nkaˈʁe]) was a French mathematician, theoretical physicist, engineer, and a philosopher of science. He is often described as a polymath, and in mathematics as The Last Universalist, since he excelled in all fields of the discipline as it existed during his lifetime.
  As a mathematician and physicist, he made many original fundamental contributions to pure and applied mathematics, mathematical physics, and celestial mechanics. He was responsible for formulating the Poincaré conjecture, which was one of the most famous unsolved problems in mathematics until it was solved in 2002–2003. In his research on the three-body problem, Poincaré became the first person to discover a chaotic deterministic system which laid the foundations of modern chaos theory. He is also considered to be one of the founders of the field of topology.
  Poincaré made clear importance of paying attention to the invariance of laws of physics under different transformations, and was the first to present the Lorentz transformations in their modern symmetrical form. Poincaré discovered the remaining relativistic velocity transformations and recorded them in a letter to Dutch physicist Hendrik Lorentz (1853–1928) in 1905. Thus he obtained perfect invariance of all of Maxwell's equations, an important step in the formulation of the theory of special relativity.
  
  wn.com/Henri_Poincaré
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  Isaac Newton
  Sir Isaac Newton PRS MP (25 December 1642 – 20 March 1727 [NS: 4 January 1643 – 31 March 1727]) was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived." His monograph Philosophiæ Naturalis Principia Mathematica, published in 1687, lays the foundations for most of classical mechanics. In this work, Newton described universal gravitation and the three laws of motion, which dominated the scientific view of the physical universe for the next three centuries. Newton showed that the motions of objects on Earth and of celestial bodies are governed by the same set of natural laws, by demonstrating the consistency between Kepler's laws of planetary motion and his theory of gravitation, thus removing the last doubts about heliocentrism and advancing the Scientific Revolution.
  
  wn.com/Isaac_Newton
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  Johann Bernoulli
  Johann Bernoulli (27 July 1667 – 1 January 1748; also known as Jean or John) was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is known for his contributions to infinitesimal calculus and educated Leonhard Euler in his youth.
  Johann was born in Basel, the son of Nikolaus Bernoulli, an apothecary, and his wife, Margaretha Schonauer and began studying medicine at Basel University. His father desired that he study business so that he might take over the family spice trade, but Johann Bernoulli disliked business and convinced his father to allow him to study medicine instead. However, Johann Bernoulli did not enjoy medicine either and began studying mathematics on the side with his older brother Jacob. Throughout Johann Bernoulli’s education at Basel University the Bernoulli brothers worked together spending much of their time studying the newly discovered infinitesimal calculus. They were among the first mathematicians to not only study and understand calculus but to apply it to various problems.
  
  wn.com/Johann_Bernoulli
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  Leonhard Euler
  Leonhard Euler (German pronunciation: [ˈɔʏlɐ], ( Swiss German pronunciation (help·info)) ( Standard German pronunciation (help·info)) English approximation, "Oiler"; 15 April 1707 – 18 September 1783) was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function. He is also renowned for his work in mechanics, fluid dynamics, optics, and astronomy.
  Euler spent most of his adult life in St. Petersburg, Russia, and in Berlin, Prussia. He is considered to be the preeminent mathematician of the 18th century, and one of the greatest of all time. He is also one of the most prolific mathematicians ever; his collected works fill 60–80 quarto volumes. A statement attributed to Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is the master of us all."
  
  wn.com/Leonhard_Euler
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  Niels Henrik Abel
  Niels Henrik Abel (5 August 1802 – 6 April 1829) was a Norwegian mathematician who proved the impossibility of solving the quintic equation by radicals. The Abel Prize is named for him.
  Niels Henrik Abel was born in Nedstrand, Norway, as second child to Søren Georg Abel and Anne Marie Simonsen. When he was born, the family was living at the rectory at Finnøy. Much suggests that Niels Henrik was born in the neighboring parish, as his parents were guests of the bailiff in Nedstrand in July / August of his year of birth.
  Niels Henrik Abel's father, Søren Georg Abel, had a degree in theology and philosophy and served as pastor at Finnøy. Søren's father, Niels's grandfather, Hans Mathias Abel, was also a pastor, at Gjerstad near Risør. Søren had spent his childhood at Gjerstad, and had also served as chaplain there; and after his father's death in 1804, Søren was appointed pastor at Gjerstad and the family moved there.
  Anne Marie Simonsen was from Risør; her father, Niels Henrik Saxild Simonsen, was a tradesman and merchant ship-owner, and said to be the richest person in Risør. Anne Marie had grown up with two stepmothers, in relative luxurious surroundings. At Gjerstad rectory, she enjoyed arranging balls and social gatherings. Much suggests she was early on an alcoholic and took little interest in the upbringing of the children. Niels Henrik and his brothers were given their schooling by their father, with handwritten books to read. Interestingly, an addition table in a book of mathematics reads: 1+0=0.
  
  wn.com/Niels_Henrik_Abel
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  Oscar II of Sweden
  Oscar II (21 January 1829 – 8 December 1907), baptised Oscar Fredrik was King of Sweden from 1872 until his death and King of Norway from 1872 until 1905. The third son of King Oscar I of Sweden and Josephine of Leuchtenberg, he was a descendant of Gustav I of Sweden through his mother.
  At his birth in Stockholm, Oscar Fredrik was created Duke of Östergötland. He entered the navy at the age of eleven, and was appointed junior lieutenant in July 1845. Later he studied at Uppsala University, where he distinguished himself in mathematics. On 13 December 1848, he was made an honorary member of the Royal Swedish Academy of Sciences.
  On 6 June 1857 he married in Wiesbaden-Biebrich, Germany, Princess Sophia Wilhelmina, youngest daughter of Duke William of Nassau.
  From 1859, when his father died, he was first in line to the Swedish throne after his oldest brother King Charles, who then had no male heirs (his son had died in infancy in 1854). His middle brother Gustaf had died in 1852.
  He succeeded his brother Charles XV and IV on 18 September 1872, and was crowned as king of Norway in the Nidaros Cathedral in Trondheim on 18 July 1873. At the accession he adopted as his motto Brödrafolkens väl / Broderfolkenes Vel ("The Welfare of the Brother Peoples"). While the King and the Royal Court resided mostly in Sweden, Oscar made the effort of learning to be fluent in Norwegian and from the very beginning he realized the essential difficulties in the maintenance of the union between the two countries.
  
  wn.com/Oscar_II_of_Sweden
• Qiudong Wang
  Qiudong Wang is an Associate Professor at the Department of Mathematics, the University of Arizona. In 1982 he received a B.S. at Nanjing University and in 1994 a Ph.D. at the University of Cincinnati.
  Wang is best known for his paper The global solution of the n-body problem, in which he generalised Karl F. Sundman's results from 1912 to a system of more than three bodies.
  
  
  
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  Évariste Galois
  Évariste Galois (French pronunciation: [evaʁist ɡalwa]) (25 October 1811 – 31 May 1832) was a French mathematician born in Bourg-la-Reine. While still in his teens, he was able to determine a necessary and sufficient condition for a polynomial to be solvable by radicals, thereby solving a long-standing problem. His work laid the foundations for Galois theory and group theory, two major branches of abstract algebra, and the subfield of Galois connections. He was the first to use the word "group" (French: groupe) as a technical term in mathematics to represent a group of permutations. A radical Republican during the monarchy of Louis Philippe in France, he died from wounds suffered in a duel under questionable circumstances at the age of twenty.
  Galois was born on 25 October 1811 to Nicolas-Gabriel Galois and Adélaïde-Marie (born Demante). His father was a Republican and was head of Bourg-la-Reine's liberal party. He became mayor of the village after Louis XVIII returned to the throne in 1814. His mother, the daughter of a jurist, was a fluent reader of Latin and classical literature and was responsible for her son's education for his first twelve years. At the age of 10, Galois was offered a place at the college of Reims, but his mother preferred to keep him at home.
  
  wn.com/Évariste_Galois