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

• 37500 Yens
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• 
  

• 
  Boston
  Boston (pronounced /ˈbɒstən/ or locally /ˈbɔstən/ ( listen)) is the capital of and largest city in Massachusetts, and is one of the oldest cities in the United States. The largest city in New England, Boston is regarded as the unofficial "Capital of New England" for its economic and cultural impact on the entire New England region. The city proper, covering only 48.43 square miles, had a population of 617,594 according to the 2010 U.S. Census. Boston is also the anchor of a substantially larger metropolitan area called Greater Boston, home to 4.5 million people and the tenth-largest metropolitan area in the country. Greater Boston as a commuting region is home to 7.6 million people, making it the fifth-largest Combined Statistical Area in the United States.
  In 1630, Puritan colonists from England founded the city on the Shawmut Peninsula. During the late 18th century, Boston was the location of several major events during the American Revolution, including the Boston Massacre and the Boston Tea Party. Several early battles of the American Revolution, such as the Battle of Bunker Hill and the Siege of Boston, occurred within the city and surrounding areas. Through land reclamation and municipal annexation, Boston has expanded beyond the peninsula. After American independence was attained Boston became a major shipping port and manufacturing center, and its rich history now helps attract many tourists, with Faneuil Hall alone attracting over 20 million every year. The city was the site of several firsts, including America's first public school, Boston Latin School (1635), and the first subway system in the United States (1897).
  
  wn.com/Boston
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  Chicago
  Chicago (ⁱ/ʃɪˈkɑːɡoʊ/ or /ʃɪˈkɔːɡoʊ/) is the largest city in the US state of Illinois and the third most populous city in the United States after New York City and Los Angeles. The city has around 2.7 million residents. Its metropolitan area, sometimes called "Chicagoland", is the third largest in the United States, with an estimated 9.8 million people. Chicago is the county seat of Cook County, though a small portion also extends into DuPage County.
  Chicago was incorporated as a city in 1837, near a portage between the Great Lakes and the Mississippi River watershed. Today, Chicago is listed as an alpha+ global city by the Globalization and World Cities Research Network, and ranks seventh in the world on the 2012 Global Cities Index. The city retains its status as an international hub for finance, industry, telecommunications and infrastructure, with O'Hare International Airport being the second busiest airport in the world in terms of traffic movements. In 2008^[update], the city hosted 45.6 million domestic and overseas visitors. Among metropolitan areas, Chicago has the 4th largest Gross Domestic Product (GDP) in the world, ranking just behind Tokyo, New York City, and Los Angeles. Chicago is one of the most important Worldwide Centers of Commerce and trade.
  
  wn.com/Chicago
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  Cleveland, Ohio
  Cleveland ( /ˈkliːvlənd/) is a city in the U.S. state of Ohio and is the county seat of Cuyahoga County, the most populous county in the state. The city is located in northeastern Ohio on the southern shore of Lake Erie, approximately 60 miles (97 km) west of the Pennsylvania border. It was founded in 1796 near the mouth of the Cuyahoga River, and became a manufacturing center owing to its location on the lake shore, as well as being connected to numerous canals and railroad lines. Cleveland's economy has diversified sectors that include manufacturing, financial services, healthcare, and biomedical. Cleveland is home to the Rock and Roll Hall of Fame.
  As of the 2010 Census, the city proper had a total population of 396,815 and was the 45th largest city in the United States, and the second largest city in Ohio. It is the center of Greater Cleveland, the largest metropolitan area in Ohio. The Cleveland-Elyria-Mentor Metropolitan Statistical Area in 2011 ranked as the 28th largest in the United States with 2,068,283 people. Cleveland is part of the larger Cleveland-Akron-Elyria Combined Statistical Area, which in 2011 had a population of 2,871,084, and ranked as the country's 15th largest.
  
  wn.com/Cleveland,_Ohio
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  DeKalb, Illinois
  DeKalb /dɨˈkælb/ is a city in DeKalb County, Illinois, United States. The population was 43,862 according to the 2010 census. The city is named after decorated German war hero Johann De Kalb, who died during the American Revolutionary War.
  Founded in 1837, DeKalb remained a small community until the arrival of the Chicago and North Western Transportation Company in 1853. DeKalb's central location brought easier shipping of crops and access to larger markets. Agriculture was the primary economic activity until 1873-4 when farmer Joseph Glidden developed barbed wire and began commercial mass production of his new invention. Glidden sold half of his interest to hardware merchant Isaac L. Ellwood and together the two formed the Barb Fence Company.
  Two months after Glidden filed his application for a patent, lumber salesman Jacob Haish also applied for a patent and on June 25, 1874 ran interference papers against Glidden's patent. After several years of legal wrangling, in 1877 Glidden's patent won and Glidden was declared the "Father of Barbed Wire".
  
  wn.com/DeKalb,_Illinois
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  Illinois
  Illinois (ⁱ/ˌɪlɨˈnɔɪ/ IL-i-NOY) is the 25th most extensive and the 5th most populous of the 50 United States, and is often noted as a microcosm of the entire country. With Chicago in the northeast, small industrial cities and great agricultural productivity in central and northern Illinois, and natural resources like coal, timber, and petroleum in the south, Illinois has a broad economic base. Illinois is a major transportation hub. The Port of Chicago connects the state to other global ports from the Great Lakes, via the Saint Lawrence Seaway, to the Atlantic Ocean; as well as the Great Lakes to the Mississippi River, via the Illinois River. For decades, O'Hare International Airport has ranked as one of the world's busiest airports. Illinois has long had a reputation as a bellwether both in social and cultural terms and politics.
  Although the state's largest population centers today are in northern Illinois, originally the state's population grew from south to north, with settlers arriving from Kentucky in the 1810s. In 1818, Illinois achieved statehood. Chicago was founded in the 1830s on the banks of the Chicago River, one of the few natural harbors on southern Lake Michigan. Railroads and John Deere's invention of the self-scouring steel plow turned Illinois' rich prairie into some of the world's most productive and valuable farmlands, attracting immigrant farmers from Germany and Sweden. By 1900, the growth of industrial jobs in the northern cities and coal mining in the central and southern areas attracted immigrants from Eastern and Southern Europe. Illinois was an important manufacturing center during both world wars. The Great Migration established a large community of African Americans in Chicago that created the city's famous jazz and blues cultures.
  
  wn.com/Illinois
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  Japan
  Japan ⁱ/dʒəˈpæn/ (Japanese: 日本 Nihon or Nippon; formally 日本国  Nippon-koku or Nihon-koku, literally the State of Japan) is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south. The characters that make up Japan's name mean "sun-origin", which is why Japan is sometimes referred to as the "Land of the Rising Sun".
  Japan is an archipelago of 6,852 islands. The four largest islands are Honshū, Hokkaidō, Kyūshū and Shikoku, together accounting for ninety-seven percent of Japan's land area. Japan has the world's tenth-largest population, with over 127 million people. The Greater Tokyo Area, which includes the de facto capital city of Tokyo and several surrounding prefectures, is the largest metropolitan area in the world, with over 30 million residents.
  Archaeological research indicates that people lived in Japan as early as the Upper Paleolithic period. The first written mention of Japan is in Chinese history texts from the 1st century AD. Influence from other nations followed by long periods of isolation has characterized Japan's history. In the late 19th and early 20th centuries, victory in the First Sino-Japanese War, the Russo-Japanese War and World War I allowed Japan to expand its empire during a period of increasing militarism. The Second Sino-Japanese War of 1937 expanded into part of World War II in 1941, which came to an end in 1945 following the atomic bombings of Hiroshima and Nagasaki. Since adopting its revised constitution in 1947, Japan has maintained a unitary constitutional monarchy with an emperor and an elected parliament called the Diet.
  
  wn.com/Japan
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  Los Angeles
  Los Angeles (ⁱ/lɒs ˈændʒələs/ loss-AN-jə-ləs; Spanish: [los ˈaŋxeles], which is written Los Ángeles; British pronounciation /lɒs ˈændʒəliːz/ loss-AN-jə-leez) with a population at the 2010 United States Census of 3,792,621, is the most populous city in the state of California, and the second most populous in the United States, after New York City. It has an area of 468.67 square miles (1,213.8 km²), and is located in Southern California. Often known by its initials L.A., the city is the focal point of the larger Los Angeles-Long Beach-Santa Ana metropolitan statistical area and Greater Los Angeles Area region, which contain 12,828,837 and nearly 18 million people respectively as of 2010, making it one of the most populous metropolitan areas in the world and the second largest in the United States. Los Angeles is also the seat of Los Angeles County, the most populated and one of the most ethnically diverse counties in the United States, while the entire Los Angeles area itself has been recognized as the most diverse of the nation's largest cities. The city's inhabitants are referred to as "Angelenos".
  
  wn.com/Los_Angeles
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  Louisville, Kentucky
  Louisville (ⁱ/ˈluːiːvɪl/, local ⁱ/ˈluːəvəl/ or ⁱ/ˈlʌvəl/) is the largest city in the U.S. state of Kentucky, and the county seat of Jefferson County. Since 2003, the city's borders have been coterminous with those of the county because of a city-county merger. The city's total consolidated population at the 2010 census was 741,096 (Louisville's balance total, 597,337, excludes semi-autonomous towns and is the population listed in most sources and national rankings). An important internal shipping port in the 19th century, Louisville today is best known as the location of the Kentucky Derby, the first of three annual thoroughbred horse races making up the Triple Crown.
  Louisville is southeasterly situated along the border between Kentucky and Indiana, the Ohio River, in north-central Kentucky at the Falls of the Ohio. The Louisville metropolitan area is often referred to as Kentuckiana because it includes counties in Southern Indiana. A resident of Louisville is referred to as a Louisvillian. Although situated in a Southern state, Louisville is influenced by both Southern and Midwestern culture. It is sometimes referred to as either one of the most northernmost Southern cities or as on of the southernmost Northern cities in the United States along with St. Louis, Missouri and Washington, D.C.
  
  wn.com/Louisville,_Kentucky
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  Minneapolis
  Minneapolis (pronunciation: ⁱ/ˌmɪniːˈæpəlɪs/), nicknamed "City of Lakes" and the "Mill City", is the county seat of Hennepin County, the largest city in the state of Minnesota, and the 48th largest in the United States. Its name is attributed to the city's first schoolteacher, who combined mni, the Dakota word for water, and polis, the Greek word for city.
  As of the 2010 Census, the population of the city of Minneapolis is 382,578. Minneapolis lies on both banks of the Mississippi River, just north of the river's confluence with the Minnesota River, and adjoins Saint Paul, the state's capital. Known as the Twin Cities, Minneapolis-Saint Paul is the 16th-largest metropolitan area in the U.S., with approximately 3.3 million residents. The city is abundantly rich in water, with over twenty lakes and wetlands, the Mississippi river, creeks and waterfalls, many connected by parkways in the Chain of Lakes and the Grand Rounds National Scenic Byway. Among cities of similar densities, Minneapolis has the most dedicated parkland. It was once the world's flour milling capital and a hub for timber, and today is the primary business center between Chicago and Seattle, with Minneapolis proper containing the fifth highest concentration of Fortune 500 companies. It has cultural organizations that draw creative people and audiences to the city for theater, visual art, writing, and music. The community's diverse population has a long tradition of charitable support through progressive public social programs and VOLAGs, as well as private and corporate philanthropy.
  
  wn.com/Minneapolis
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  Northern Hemisphere
  Coordinates: 45°0′0″N 0°0′0″E / 45°N 0°E / 45; 0
  The Northern Hemisphere is the half of a planet that is north of its equator—the word hemisphere literally means “half sphere”. It is also that half of the celestial sphere north of the celestial equator. Earth's northern hemisphere contains most of the planet's land, and roughly 90% of its human population. See also Arctic, Temperate zone, Tropics, Seasons and Climate
  Due to the Earth's axial tilt, winter lasts from the winter solstice (typically December 22) to the vernal equinox (typically March 20), while summer lasts from the summer solstice (typically June 21) through to the autumnal equinox (typically September 21).
  The Arctic is the region north of the Arctic Circle. Its climate is characterized by cold winters and cool summers. Precipitation mostly comes in the form of snow. The Arctic experiences some days in summer when the Sun never sets, and some days during the winter when it never rises. The duration of these phases varies from one day for locations right on the Arctic Circle to several months near the North Pole.
  
  wn.com/Northern_Hemisphere
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  Pittsburgh
  Pittsburgh ( /ˈpɪtsbərɡ/, PITS-burg) is the second largest city in the U.S. Commonwealth of Pennsylvania and the county seat of Allegheny County. Regionally, it anchors the largest urban area of both Appalachia and the Ohio River Valley. Nationally, it is the 22nd largest urban area in the United States. The population of the city in 2010 was 305,704, while that of the seven-county metropolitan area stood at 2,356,285.Downtown Pittsburgh retains substantial economic influence, ranking at 25th in the nation for jobs within the urban core and 6th in job density. The characteristic shape of Pittsburgh's central business district is a triangular tract carved by the confluence of the Allegheny and Monongahela rivers, which form the Ohio River. The city features 151 high-rise buildings, 446 bridges, two inclined railways, and a pre-revolutionary fortification. Pittsburgh is known colloquially as "the City of Bridges" and "the Steel City" for its many bridges and former steel manufacturing base.
  
  wn.com/Pittsburgh
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  San Diego
  San Diego /ˌsæn diːˈeɪɡoʊ/ is the eighth-largest city in the United States and second-largest city in California. The city is located on the coast of the Pacific Ocean in Southern California, immediately adjacent to the Mexican border. The birthplace of California, San Diego is known for its mild year-round climate, natural deep-water harbor, extensive beaches, long association with the U.S. Navy, and recent emergence as a healthcare and biotechnology enclave. The population was 1,301,617 at the 2010 census.
  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 Cabrillo claimed the entire area for Spain, forming the basis for the settlement of Alta California 200 years later. The Presidio and Mission of San Diego, founded in 1769, were the first European settlement in what is now California. In 1821, San Diego became part of newly independent Mexico, and in 1850, became part of the United States following the Mexican-American War and the admission of California to the union.
  
  wn.com/San_Diego
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  St. Louis, Missouri
  St. Louis /seɪnt ˈluːɪs/ (French: Saint-Louis or St-Louis, [sɛ̃ lwi] ( listen)) is an independent city on the eastern border of Missouri, United States, and is the second-largest city in the state. With a population of 318,069 in July 2011, it was the 58th-largest U.S. city at the 2010 U.S. Census. The Metropolitan Statistical Area (MSA) population of 2,812,896 is the 18th-largest in the country. The Greater St. Louis combined statistical area's (CSA) population of 2,878,255 is the 16th-largest CSA in the country, the fourth-largest in the Midwest. The Greater St. Louis area is the largest metropolitan area in Missouri.
  The city of St. Louis was founded in 1764 by Pierre Laclède and Auguste Chouteau, and after the Louisiana Purchase, it became a major port on the Mississippi River. Its population expanded after the American Civil War, and it became the fourth-largest city in the United States in the late 19th century. It seceded from St. Louis County in March 1877, allowing it to become an independent city and limiting its political boundaries. In 1904, it hosted the 1904 World's Fair and the 1904 Olympic Games. The city's population peaked in 1950, then began a long decline that reversed only at the beginning of the 21st century.
  
  wn.com/St._Louis,_Missouri
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  São Paulo
  São Paulo (/ˌsaʊ ˈpaʊloʊ/; Portuguese pronunciation: [sɐ̃w ˈpawlu] ( listen); Saint Paul;), popularly known as Sampa, is the largest city in Brazil, the largest city in the southern hemisphere and Americas, and the world's seventh largest city by population. The metropolis is anchor to the São Paulo metropolitan area, ranked as the second most populous metropolitan area in the Americas and among the five largest metropolitan areas on the planet. São Paulo is the capital of the state of São Paulo, which is the most populous Brazilian state, and exerts strong regional influence in commerce and finance as well as arts and entertainment. São Paulo maintains strong international influence and is considered an Alpha- World City. The name of the city honors Saint Paul.
  The metropolis has significant cultural, economic and political influence both nationally and internationally. It houses several important monuments, parks and museums such as the Latin American Memorial, the Museum of the Portuguese Language, São Paulo Museum of Art and the Ibirapuera Park. The Paulista Avenue is the most important financial center of São Paulo. The city holds many high profile events, like the São Paulo Art Biennial, the Brazil Grand Prix Formula 1 Sao Paulo, Sao Paulo Fashion Week, ATP Brasil Open, and the São Paulo Indy 300.
  
  wn.com/São_Paulo
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  Toronto, ON
  Toronto (/təˈrɒntoʊ/, colloquially /ˈtrɒnoʊ/) is the largest city in Canada and the provincial capital of Ontario. It is located in Southern Ontario on the northwestern shore of Lake Ontario. A relatively modern city, Toronto's history dates back to the late-18th century, when its land was first purchased by the British monarchy from the Mississaugas of the New Credit. The settlement was later established as the Town of York and proclaimed as the new capital of Upper Canada by its lieutenant-governor, John Graves Simcoe. In 1834, York was incorporated as a city and renamed to its present name. The city was ransacked in the Battle of York during the War of 1812 and damaged in two great fires in 1849 and in 1904. Since its incorporation, Toronto has repeatedly expanded its borders through amalgamation with surrounding municipalities, most recently in 1998.
  With over 2.6 million residents, it is the fifth most populous city in North America. Its metropolitan area has over 5.5 million residents. Toronto is at the heart of the Greater Toronto Area (GTA), and is part of a densely populated region in Southern Ontario known as the Golden Horseshoe, which has a population of nearly 9 million people as of 2011. The census metropolitan area (CMA) had a population of 5,583,064, and the Greater Toronto Area had a population of 6,054,191 in the 2011 Census. Its cosmopolitan and international population reflects its role as an important destination for immigrants to Canada. Toronto is one of the world's most diverse cities by percentage of non-native-born residents, with about 49% of the population born outside Canada. Toronto is also consistently rated as one of the world's most livable cities by the Economist Intelligence Unit and the Mercer Quality of Living Survey.
  
  wn.com/Toronto,_ON
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  United Kingdom
  The United Kingdom of Great Britain and Northern Ireland (commonly known as the United Kingdom, the UK, or Britain) is a sovereign state located off the north-western coast of continental Europe. The country includes the island of Great Britain, the north-eastern part of the island of Ireland and many smaller islands. Northern Ireland is the only part of the UK that shares a land border with another sovereign state—the Republic of Ireland. Apart from this land border the UK is surrounded by the Atlantic Ocean, the North Sea, the English Channel and the Irish Sea.
  The United Kingdom is a unitary state governed under a constitutional monarchy and a parliamentary system, with its seat of government in the capital city of London. It is a country in its own right and consists of four countries: England, Northern Ireland, Scotland and Wales. There are three devolved administrations, each with varying powers, based in Belfast, Edinburgh and Cardiff, the capitals of Northern Ireland, Scotland, and Wales. Associated with the UK, but not constitutionally part of it, are three Crown Dependencies. The United Kingdom has fourteen overseas territories. These are remnants of the British Empire which, at its height in 1922, encompassed almost a quarter of the world's land surface and was the largest empire in history. British influence can still be observed in the language, culture and legal systems of many of its former territories.
  
  wn.com/United_Kingdom
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  Washington, D.C.
  Washington, D.C., formally the District of Columbia and commonly referred to as Washington, "the District", or simply D.C., is the capital of the United States. On July 16, 1790, the United States Congress approved the creation of a federal district to become the national capital as permitted by the U.S. Constitution. The District is therefore not a part of any U.S. state. It was formed from land along the Potomac River donated by the states of Maryland and Virginia; however, the Virginia portion was returned by Congress in 1846.
  A new capital city named after George Washington was founded in 1791 to the east of the preexisting port of Georgetown. Congress consolidated the City of Washington, Georgetown, and the remaining unincorporated area within the District under a single municipal government in 1871. The city shares its name with the U.S. state of Washington, located on the country's Pacific coast.
  Washington, D.C., had an estimated population of 617,996 in 2011. The city was the 24th most populous place in the United States as of 2010. Commuters from the surrounding Maryland and Virginia suburbs raise the city's population to over one million during the workweek. The Washington Metropolitan Area, of which the District is a part, has a population of nearly 5.6 million, the seventh-largest metropolitan area in the country.
  
  wn.com/Washington,_D.C.
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  Windsor, ON
  Windsor is the southernmost city in Canada and is located in Southwestern Ontario at the western end of the heavily populated Quebec City–Windsor Corridor. It is within the Essex, Ontario Census division, although administratively separated from the county government. Separated by the Detroit River, Windsor is located south of Detroit, Michigan in the United States. Windsor is known as The City of Roses and residents are known as Windsorites.
  Prior to European exploration and settlement, the Windsor area was inhabited by the First Nations and Native American people. Windsor was settled by the French in 1749 as an agricultural settlement. It is the oldest continually inhabited European settlement in Canada west of Montreal. The area was first named Petite Côte ("Little Coast" - as opposed to the longer coastline on the Detroit side of the river). Later it was called La Côte de Misère ("Poverty Coast") because of the sandy soils near LaSalle.
  Windsor's French Canadian heritage is reflected in many French street names, such as Ouellette, Pelissier, François, Pierre, Langlois, Marentette, and Lauzon. The current street system of Windsor (a grid with elongated blocks) reflects the Canadien method of agricultural land division, where the farms were long and narrow, fronting along the river. Today, the north-south street name often indicates the name of the family that at one time farmed the land. The street system of outlying areas is consistent with the British system for granting land concessions. There is a significant French-speaking minority in Windsor and the surrounding area, particularly in the Lakeshore, Tecumseh and LaSalle areas.
  
  wn.com/Windsor,_ON

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  Bela Bartok
  Béla Viktor János Bartók ( /ˈbɑrtɒk/; Hungarian pronunciation: [ˈbeːlɒ ˈbɒrtoːk]; March 25, 1881 – September 26, 1945) was a Hungarian composer and pianist. He is considered one of the most important composers of the 20th century and is regarded, along with Liszt, as Hungary's greatest composer (Gillies 2001). Through his collection and analytical study of folk music, he was one of the founders of ethnomusicology.
  Béla Bartók was born in the small Banatian town of Nagyszentmiklós in the Kingdom of Hungary, Austria-Hungary (since 1920 Sânnicolau Mare, Romania) on March 25, 1881. Bartók's family reflected some of the ethno-cultural diversities of the country. His father, Béla Sr., considered himself thoroughly Hungarian, because on his father's side the Bartók family was a Hungarian lower noble family, originating from Borsod county (Móser 2006a, 44; Bartók 1981, 13), though his mother was from a Roman Catholic Serbian family (Bayley 2001, 16). His mother, Paula (born Paula Voit), had German as a mother tongue, but was ethnically of "mixed Hungarian" origin: Her maiden name Voit is German, probably of Saxon origin from Upper Hungary (Since 1920 in Czechoslovakia, since 1993 in Slovakia), though she spoke Hungarian fluently.^{[citation needed]} Among her closest forefathers there were family names like Polereczky (Magyarized Polish or Slovak) and Fegyveres (Magyar). Béla displayed notable musical talent very early in life: according to his mother, he could distinguish between different dance rhythms that she played on the piano before he learned to speak in complete sentences (Gillies 1990, 6). By the age of four, he was able to play 40 pieces on the piano; his mother began formally teaching him the next year.
  
  wn.com/Bela_Bartok
• 
  Bill Laswell
  Bill Laswell (born February 12, 1955 in Salem, Illinois and raised in Albion, Michigan) is an American bassist, producer and record label owner.
  Laswell ranks among the most prolific of modern musicians, being involved in hundreds of recordings with many collaborators from all over the world. Laswell's music draws upon many different genres, most notably funk, various world music, jazz, dub and ambient styles. He has also played or produced music from the noisier, more aggressive end of the rock spectrum, such as hardcore punk and metal.
  According to music critic Chris Brazier, "Laswell’s pet concept is 'collision music' which involves bringing together musicians from wildly divergent but complementary spheres and seeing what comes out." The credo of one record label run by Laswell, and which typifies much of his work, is “Nothing Is True, Everything Is Permitted”. Though projects arranged by Laswell may be credited under the same name and often feature the same roster of musicians, the styles and themes explored on different albums can vary dramatically: Material began as a noisy dance music project, but subsequent releases have been centered around hip hop, jazz, or backing spoken word readings by beat generation icon William S. Burroughs. Similarly, most versions of Praxis have featured guitarist Buckethead, but have explored different permutations with each new album.
  
  wn.com/Bill_Laswell
• 
  Captain Beefheart
  Don Van Vliet ( /væn ˈvliːt/, born Don Glen Vliet; January 15, 1941 – December 17, 2010) was an American musician, singer-songwriter, artist and poet best known by the stage name Captain Beefheart. His musical work was conducted with a rotating ensemble of musicians called The Magic Band, active between 1965 and 1982, with whom he recorded 13 studio albums. Noted for his powerful singing voice with its wide range, Van Vliet also played the harmonica, saxophone and numerous other wind instruments. His music blended rock, blues and psychedelia with avant-garde and contemporary experimental composition. Beefheart was also known for exercising an almost dictatorial control over his supporting musicians, and for often constructing myths about his life.
  
  wn.com/Captain_Beefheart
• Cheer-Accident
  Cheer-Accident is an American indie rock ensemble headed by Thymme Jones. Jones took the name of the band from a Hallmark Cards shopping display, and first formed the group in 1981 with singer Jim Drummond and drummer Mike Greenlees.
  Cheer-Accident's first album, Life Isn't Like That, was released in 1986, after which Drummond and Greenlees left the group. They were replaced by bassist Chris Block and guitarist Jeff Libersher. The group's second release, 1988's Sever Roots, Tree Dies, which was produced and engineered by the Phil Bonnet.
  Their 1990 EP, Dumb Ask, was produced by Steve Albini, and following this the group signed to British label Neat Records. However, the album was pressed poorly and the group severed its ties to the label, and went back to recording for Complacency Records with Bonnet, who by that time had joined the group on guitar. Block left the band in 1992 and was replaced by Dan Forden, after which the group returned to the studio.
  In 1994, the group released The Why Album and helped start a local Chicago Public-access television show called Cool Clown Ground. Albini recorded the group's next release, Not a Food (recorded in July 1994 and eventually released in 1996). Shortly after these sessions, Forden left the band who was then replaced with Dylan Posa (formerly of The Flying Luttenbachers). By this time, Cheer-Accident members were collaborating regularly with other Chicago indie artists such as U.S. Maple, Bobby Conn, Gastr del Sol, and Smog.
  
  wn.com/Cheer-Accident
• Dazzling Killmen
  Dazzling Killmen was a math rock band from the St. Louis, Missouri area.
  The group, which formed in 1990, was composed of jazz students—drummer Blake Fleming, bassist Darin Gray, vocalist/guitarist Nick Sakes, and later on guitarist Tim Garrigan.
  The Dazzling Killmen caught the attention of Skin Graft Records. They released two full-length albums, as well as several 7" singles before breaking up in the fall of 1995, immediately prior to a planned tour of Japan with Jim O'Rourke.
  Today, its members are better-known for their later projects - Nick Sakes has been in bands Colossamite and Sicbay. Darin Gray was in Brise-Glace, and has performed and recorded with Jim O'Rourke and with Glenn Kotche in On Fillmore. Blake Fleming was in Laddio Bolocko, The Mars Volta and Electric Turn to Me. Tim Garrigan, now based in Brooklyn, is a solo performer.
  Lounge Ax Cassette-Only, Skin Graft Records
  Recuerda CD, Skin Graft Records (1996)
  
  wn.com/Dazzling_Killmen
• 
  Frank Zappa
  Frank Vincent Zappa (December 21, 1940 – December 4, 1993) was an American composer, singer-songwriter, electric guitarist, recording engineer, record producer and film director. In a career spanning more than 30 years, Zappa wrote rock, jazz, orchestral and musique concrète works. He also directed feature-length films and music videos, and designed album covers. Zappa produced almost all of the more than 60 albums he released with the band The Mothers of Invention and as a solo artist. While in his teens, he acquired a taste for percussion-based avant-garde composers such as Edgard Varèse and 1950s rhythm and blues music. He began writing classical music in high school, while at the same time playing drums in rhythm and blues bands; he later switched to electric guitar.
  He was a self-taught composer and performer, and his diverse musical influences led him to create music that was often impossible to categorize. His 1966 debut album with The Mothers of Invention, Freak Out!, combined songs in conventional rock and roll format with collective improvisations and studio-generated sound collages. His later albums shared this eclectic and experimental approach, irrespective of whether the fundamental format was one of rock, jazz or classical. His lyrics—often humorously—reflected his iconoclastic view of established social and political processes, structures and movements. He was a strident critic of mainstream education and organized religion, and a forthright and passionate advocate for freedom of speech, self-education, political participation and the abolition of censorship.
  
  wn.com/Frank_Zappa
• 
  Fred Frith
  Fred Frith (born 17 February 1949) is an English multi-instrumentalist, composer and improvisor.
  Probably best known for his guitar work, Frith first came to attention as one of the founding members of the English avant-rock group Henry Cow. Frith was also a member of Art Bears, Massacre and Skeleton Crew. He has collaborated with a number of prominent musicians, including Robert Wyatt, Derek Bailey, The Residents, Lol Coxhill, John Zorn, Brian Eno, Mike Patton, Lars Hollmer, Bill Laswell, Iva Bittová, Jad Fair, the ARTE Quartett and Bob Ostertag. He has also composed several long works, including Traffic Continues (1996, performed 1998 by Frith and Ensemble Modern) and Freedom in Fragments (1993, performed 1999 by Rova Saxophone Quartet). Frith produces most of his own music, and has also produced many albums by other musicians, including Curlew, The Muffins, Etron Fou Leloublan and Orthotonics.
  Frith is the subject of Nicolas Humbert and Werner Penzel's award-winning 1990 documentary film Step Across the Border. He also appears in the Canadian documentary Act of God, which is about the metaphysical effects of being struck by lightning. Frith has contributed to a number of music publications, including New Musical Express and Trouser Press, and has conducted improvising workshops across the world. Frith's career spans over three decades and he appears on over 400 albums. He still performs actively throughout the world.
  
  wn.com/Fred_Frith
• Fulflej
  Fulflej were a rock band from Richmond, Virginia, United States, formed in 1986 by guitarist/vocalist Jason Greschke and bassist Andre Phillips. They were signed to Scratchie Records.
  The band evolved from two previous projects. The first two incarnations were "The Un-Ones" with drummer Malcom Vaughn, hailing from Hampton, and then moving to Richmond to form "Rhithm Lyd" Other members briefly appearing in Rhithm Lyd were Phil Searcy and Katie Power. Rithim Lyd became Fulflej in Richmond Va with Drummer Matt Nelson. In 1996 Fulflej replaced Matt Nelson with drummer Ron Lowder.
  Their musical style blends punk and heavy metal with tinges of dream pop and shoegaze. They are often compared to other alternative rock acts such as The Smashing Pumpkins and Catherine.
  Though Fulflej had recorded more than enough material over the years, they have only put out two public releases: the "Microwave" EP (1995), and "Wack-Ass Tuba Riff" album (1996).
  Smashing Pumpkins members James Iha and D'arcy Wretzky were featured on the album, with Iha playing the E-Bow guitar on their track "Microwave", and Wretzky singing backup vocals on "Shells". Their song, "Shift Into Turbo" was featured in Turbo: A Power Rangers Movie, which came out the following year.
  
  wn.com/Fulflej
• 
  Igor Stravinsky
  Igor Fyodorovich Stravinsky (sometimes spelled Strawinsky or Stravinskii; Russian: Игорь Фёдорович Стравинский, transliterated: Igorʹ Fëdorovič Stravinskij; Russian pronunciation: [ˌiɡərʲ ˌfʲjodɐrɐvʲɪtɕ strɐˈvʲinskʲɪj]; 17 June [O.S. 5 June] 1882 – 6 April 1971) was a Russian, and later French and American composer, pianist and conductor. He is acknowledged by many as one of the most important and influential composers of the 20th century.
  Stravinsky's compositional career was notable for its stylistic diversity. He first achieved international fame with three ballets commissioned by the impresario Sergei Diaghilev and first performed in Paris by Diaghilev's Ballets Russes: The Firebird (1910), Petrushka (1911) and The Rite of Spring (1913). The Rite of Spring, which provoked a riot during its premiere, transformed the way in which subsequent composers thought about rhythmic structure and was largely responsible for Stravinsky's enduring reputation as a musical revolutionary who pushed the boundaries of musical design. His so-called Russian phase was followed in the 1920s by a period in which he turned to neoclassical music. The works from this period tended to make use of traditional musical forms (concerto grosso, fugue and symphony). They frequently concealed a vein of intense emotion beneath a surface appearance of detachment or austerity and often paid tribute to the music of earlier masters, for example J.S. Bach and Tchaikovsky. In the 1950s, Stravinsky adopted serial procedures. His compositions of this period shared traits with examples of his earlier output: rhythmic energy, the construction of extended melodic ideas out of a few two- or three-note cells and clarity of form, of instrumentation and of utterance.
  
  wn.com/Igor_Stravinsky
• Itamar Assumpção
  Itamar Assumpção (September 13, 1949 – June 12, 2003) was a Brazilian songwriter and composer who was born in Tietê, a city in the Brazilian state of São Paulo. Assumpção built a strong reputation in the Brazilian independent and alternative music scenes over two decades (1980s and 1990s), a situation that was especially the case in his home state of São Paulo.
  Itamar Assumpção was one of the biggest names and contributors in the "Vanguarda Paulistana" ("São Paulo Vanguard" in English), an alternative scene that dominated São Paulo in the very late 70s and the first half of the 80s. This movement united artists who operated involuntarily outside of the established commercial music industry during an era that pre-dated the Internet, the politics of downloading and the contemporary indie music scene. The "Vanguarda" was responsible for launching many new talents and establishing a foundation for autonomous, self-sufficient music production (and subsequent release) by artists such as Arrigo Barnabé and Grupo Rumo.
  
  wn.com/Itamar_Assumpção
• 
  John Cage
  John Milton Cage Jr. (September 5, 1912 – August 12, 1992) was an American composer, music theorist, writer, and artist. A pioneer of indeterminacy in music, electroacoustic music, and non-standard use of musical instruments, Cage was one of the leading figures of the post-war avant-garde. Critics have lauded him as one of the most influential American composers of the 20th century. He was also instrumental in the development of modern dance, mostly through his association with choreographer Merce Cunningham, who was also Cage's romantic partner for most of their lives.
  Cage is perhaps best known for his 1952 composition 4′33″, which is performed in the absence of deliberate sound; musicians who present the work do nothing aside from being present for the duration specified by the title. The content of the composition is not "four minutes and 33 seconds of silence," as is sometimes assumed, but rather the sounds of the environment heard by the audience during performance. The work's challenge to assumed definitions about musicianship and musical experience made it a popular and controversial topic both in musicology and the broader aesthetics of art and performance. Cage was also a pioneer of the prepared piano (a piano with its sound altered by objects placed between or on its strings or hammers), for which he wrote numerous dance-related works and a few concert pieces. The best known of these is Sonatas and Interludes (1946–48).
  
  wn.com/John_Cage
• 
  John Reis
  John Reis (b. 1969 and also known by the pseudonyms Speedo, Slasher, and The Swami) is an American musician, singer, guitarist, record label owner, and disc jockey. He is best known as the singer and guitarist for the rock band Rocket from the Crypt, which he formed and fronted (as Speedo) for the entirety of its career from 1990 to 2005. Prior to this he was the guitarist in the post-hardcore band Pitchfork, and also played in Drive Like Jehu during the early 1990s. In 1999 he formed the Hot Snakes, and in 2000 also formed the Sultans, in which (as Slasher) he sang and originally played bass before switching to rhythm guitar. He played in both these bands until their breakups in 2005 and 2007 respectively. He also released a solo recording under the name Back Off Cupids, which was recorded in 1994 but not released until 1999. Over the years he has performed in many other musical acts including Conservative Itch, Stacatto Reads, Custom Floor, and Beehive & the Barracudas. He is the owner of Swami Records, a label he founded in 1999 (he uses the title The Swami in this capacity). He frequently works with bands in a studio capacity and releases albums by many southern California groups through his label. He also hosts the "Swami Sound System" program on San Diego radio station 94.9 (KBZT) once a week on Saturday night. Reis remains an influential figure in the San Diego underground music community and is currently performing with a new band named The Night Marchers.
  
  wn.com/John_Reis
• 
  John Zorn
  John Zorn (born September 2, 1953 in New York City) is an American avant-garde composer, arranger, record producer, saxophonist and multi-instrumentalist. Zorn is a prolific artist: he has hundreds of album credits as performer, composer, or producer. He has had experience with a variety of genres including jazz, rock, hardcore punk, classical, extreme metal, klezmer, film, cartoon, popular, and improvised music. Zorn brings these styles to his work, which he refers to with the label avant-garde/experimental.
  Zorn has stated: "All the various styles are organically connected to one another. I'm an additive person - the entire storehouse of my knowledge informs everything I do. People are so obsessed with the surface that they can't see the connections, but they are there."
  Zorn has led the punk jazz band Naked City and the klezmer-influenced quartet Masada, composed Masada Songbooks (written concert music for classical ensembles), and has produced music for film and documentary.
  Zorn established himself within the New York City downtown music movement in the mid 1970s and has since composed and performed with a wide range of musicians working in diverse musical areas. By the early 1990s Zorn was working extensively in Japan, attracted by that culture's openness about borrowing and remixing ingredients from elsewhere, before returning to New York as a permanent base in the mid-1990s. Zorn has undertaken many tours of Europe, Asia, and the Middle East, often performing at festivals with varying ensembles to display his diverse output.
  
  wn.com/John_Zorn
• Lite (band)
  Lite is a Japanese instrumental rock band.
  Formed in 2003 in Tokyo, Lite played many gigs around Tokyo and self-released two demo CDs. They have released one mini-album, Lite, and one full-length album, Filmlets, through Transduction in the UK and Cargo in Europe.
  The band is made up of Nobuyuki Takeda (guitar), Kozo Kusumoto (guitar), Jun Izawa (bass), and Akinori Yamamoto (drums).
  Lite's sound combines the precision and musicianship of prog rock with the emotionally charged cinematic compositions of art rock, in a heavier, more modern package that they describe as “math rock”.
  They toured the UK and Ireland in 2006. In July 2007, they played at Fuji Rock Festival in Japan and followed that with another UK & Ireland tour in September, coinciding with a split release with Funanori (Kaori Tsuchida from The Go! Team and Mike Watt from the Minutemen). Titled "A Tiny Twofer", the split CD features three songs each. In May 2009, they made their American debut in New York City opening for Mike Watt's Missingmen.
  
  wn.com/Lite_(band)
• Mike Banfield
  Mike Banfield (b. Pittsburgh, Pennsylvania) is a rock guitarist.
  Banfield was a founding member of math rock pioneers Don Caballero, playing guitar with the band from 1991 to 1998. Prior to that, Banfield was a member of the popular State College, Pennsylvania band Slag. In 2006 he formed a new band called Knot Feeder with Andy Curl and ex-Tabula Rasa members Rob Spagiare and Andrew Grossmann.
  
  
  
  wn.com/Mike_Banfield
• Polvo
  Polvo is an American indie noise rock band from Chapel Hill, North Carolina. The band, formed in 1990, is fronted by guitarists/vocalists Ash Bowie and Dave Brylawski. Brian Quast plays drums, and Steve Popson plays bass guitar. Eddie Watkins was the band's original drummer, but did not rejoin the band upon its reunion in 2008.
  Polvo is widely considered to be standard bearer of a genre which came to be known as math rock, although in interviews the band disavowed that categorization. Their sound was defined by complex and dissonant guitar harmonies and driving rhythm, complementing cryptic, often surrealist lyrics. Their sound was so unpredictable and angular that the band's guitarists were often accused of failing to play with correctly tuned guitars. Polvo's songs and artwork frequently featured Asian/"exotic" themes and references. The band's name means "octopus" in Portuguese and "powder" or "dust" in Spanish; in Spain it also is a slang word for sex.
  
  wn.com/Polvo
• 
  Shellac (band)
  Shellac (sometimes referred to as Shellac of North America) is an American group composed of Steve Albini (guitar and vocals), Bob Weston (bass guitar and vocals) and Todd Trainer (drums and vocals). Although they have been classified as post-hardcore they describe themselves as a "minimalist rock trio."
  Shellac formed in Chicago, Illinois, in 1992 as an informal collaboration between guitarist Steve Albini and drummer Todd Trainer. Former Naked Raygun bassist Camilo Gonzalez sat in on early rehearsals and played on one song on Shellac's first single before permanent bassist Bob Weston, formerly of Boston's Volcano Suns, joined.
  Shellac has a distinctive, minimalist sound based on unusual and urgent time signatures, repetitive heavy rhythms, an angular guitar sound, and both Albini's and Weston's surreal, bitingly sarcastic lyrics. Songs typically do not have traditional verse/chorus/verse structure and the arrangements are sparse, to the point where some describe them as "amelodic". Shellac's signature sound is often associated with their enthusiasm for vintage Travis Bean guitars, a rare brand of aluminium-based instruments, and the Interfax "Harmonic Percolator" distortion pedal. Albini is also known to use copper plectrums and unique guitar straps that fit around the waist rather than over the shoulder. The band prefers the intimacy of smaller clubs and live appearances are sporadic.
  
  wn.com/Shellac_(band)
• 
  Shudder to Think
  Shudder to Think is an American indie rock group. Formed in 1986, they released three albums on the Washington, D.C.-based label Dischord Records and were a post-hardcore band, although they drew upon a wide range of stylistic influences, including pop.
  The band's first lineup was Craig Wedren (vocals and guitar), Chris Matthews (guitar), Stuart Hill (bass) and Mike Russell (drums). In this incarnation, the band released two singles and one album (Curse, Spells, Voodoo, Mooses, 1989) before being signed by the Dischord label. Three albums were then released (Ten-Spot, 1990, Funeral at the Movies, 1991, and Get Your Goat, 1992), before the band gained greater exposure by touring with Fugazi and the Smashing Pumpkins; with their May 7, 1992 show in Albig, Germany being released by Tobby Holzinger as Your Choice Live Series Vol.21.
  Swiz ex-bassist Nathan Larson (guitars) and ex-Jawbox drummer Adam Wade replaced Matthews and Russell in 1992 (while the specific dates for the line up change are unknown, it's certain that Nathan Larson was gigging with the band prior to the release of Get Your Goat; the 1992 Live at Dobbs DVD bootleg has Craig Wedren quoting that Get Your Goat is 'out in May' and Nathan Larson is clearly the guitarist at that time). The band subsequently signed to Epic, with whom Pony Express Record was released in 1994. The album's angular, mathematical post-modernism earned it a devoted cult following. The video for "Hit Liquor" appeared on "Candy Sale", a season five episode of Beavis and Butt-head, where the song came under extremely strong criticism.
  
  wn.com/Shudder_to_Think
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  Slint
  Slint was an American rock band consisting of Brian McMahan (guitar and vocals), David Pajo (guitar), Britt Walford (drums), Todd Brashear (bass on Spiderland) and Ethan Buckler (bass on Tweez). They formed in Louisville, Kentucky, United States in 1986 and disbanded following the recording of their second album, Spiderland, in 1991.
  The band reformed to play a number of live shows in 2005 and 2007, though they released no new material.
  Walford and McMahan began performing music together at an early age, forming Languid and Flaccid with Ned Oldham (later of The Anomoanoan) while still in middle school. Walford and McMahan later played together in the seminal Louisville punk band Squirrel Bait, though Walford left the band following their first recording session. Prior to Slint, Pajo and Walford (and, briefly, McMahan) were also in the band Maurice with future members of Kinghorse. Walford, Pajo, and Buckler played their first show together in 1985 under the name Small Tight Dirty Tufts of Hair; BEADS.
  
  wn.com/Slint
• 
  Steve Albini
  Steven Frank Albini (pronounced /ælˈbiːni/) (born July 22, 1962) is an American singer, songwriter, guitarist, audio engineer, and music journalist. He was a member of Big Black, Rapeman, and Flour, and is currently a member of Shellac. He is the founder, owner, and engineer of Electrical Audio, a recording studio complex located in Chicago, and has worked with musical acts such as Sparklehorse, Nirvana, The Stooges, Pixies, Jawbreaker, Manic Street Preachers, Cheap Trick, PJ Harvey, The Jesus Lizard, Bush, Electrelane, and Scrawl, among others.
  In his youth, Albini's family moved often, before settling in Missoula, Montana in 1974. The activities of bored teenagers in rural Missoula provided much inspiration for later Albini-penned songs. While recovering from a broken leg, Albini began playing bass guitar. According to Thrill Jockey's Looking for a Thrill, Albini was exposed to punk rock by a schoolmate and subsequently bought every Ramones recording available.
  He took bass lessons in high school for one week and started playing in bands. He played with drummer Joey Cregg, son of former Mayor Bill Cregg, in the punk band Just Ducky, which quickly disbanded. While growing up in Montana, he became a fan of bands such as The Stooges, the Ramones, Television, Suicide, Wire, The Fall, The Velvet Underground, Throbbing Gristle, Kraftwerk, The Birthday Party, Pere Ubu, Public Image Ltd., Rudimentary Peni and Killing Joke.
  
  wn.com/Steve_Albini
• 
  Steve Reich
  Stephen Michael "Steve" Reich ( /ˈraɪʃ/; born October 3, 1936) is an American composer who is one of the pioneering composers of minimal music along with La Monte Young, Terry Riley, and Philip Glass.
  His innovations include using tape loops to create phasing patterns (examples are his early compositions, "It's Gonna Rain" and "Come Out"), and the use of simple, audible processes to explore musical concepts (for instance, "Pendulum Music" and "Four Organs"). These compositions, marked by their use of repetitive figures, slow harmonic rhythm and canons, have significantly influenced contemporary music, especially in the US. Reich's work took on a darker character in the 1980s with the introduction of historical themes as well as themes from his Jewish heritage, notably the Grammy Award-winning Different Trains.
  Reich's style of composition influenced many other composers and musical groups. Reich has been described, in The Guardian by music critic Andrew Clements, as one of "a handful of living composers who can legitimately claim to have altered the direction of musical history", and the critic Kyle Gann has said Reich "may...be considered, by general acclamation, America's greatest living composer."
  
  wn.com/Steve_Reich
• The For Carnation
  The For Carnation are a post-rock band from Louisville, Kentucky who formed in 1994. The band was formed by Brian McMahan, who is the only constant group member. McMahan's previous band Slint hinted at the distinctive sound and sombre aesthetic he would create in The For Carnation. To date they have released an EP and two albums: Fight Songs (Matador Records, 1995), Marshmallows (Matador, 1996), and The For Carnation (Touch and Go Records, 2000). Fight Songs and Marshmallows were compiled into one record, Promised Works, and released by Runt in 1997. Promised Works was re-released by Touch and Go Records in 2007. The band has included Doug McCombs and Johnny "Machine" Herndon of Tortoise, Todd Cook (Shipping News) as well as Britt Walford and David Pajo of Slint.
  They returned in December 2009 to play a show at the "Ten Years Of ATP" All Tomorrow's Parties music festival in England.
  A new track 'There's Something on Your Mind' appeared as a free download on Last FM in November 2009.
  
  
  
  wn.com/The_For_Carnation

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