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

• 1 + 2 + 4 + 8 + ...
• 2 (number)
• 3 (number)
• Absolute value
• Adele ring
• Algebraic closure
• Algebraic extension
• Algebraic number
• Almost all
• Arithmetic
• Arithmetical number
• Axiom of choice
• Balanced ternary
• Basis (topology)
• Brightness
• C-minimal theory
• Calculus
• Cantor set
• Cardinal number
• Carry (arithmetic)
• Cauchy sequence
• Chromaticity
• Colorfulness
• Commutative ring
• Compact space
• Complete space
• Complex number
• Composite number
• Computable number
• Coprime
• Countable set
• Countably infinite
• Cyclotomic field
• Dedekind domain
• Derivative
• Divisor
• Dual number
• Endomorphism ring
• Equivalence class
• Eric Hehner
• Eric W. Weisstein
• Euclidean metric
• Euler's theorem
• Exponentiation
• Factorial
• Field (mathematics)
• Field of fractions
• Fractional ideal
• Galois extension
• Galois group
• Global field
• Hausdorff space
• Helmut Hasse
• Hensel's lemma
• Hue
• Hypercomplex number
• Hyperreal number
• Idele group
• If and only if
• Integer
• Integral domain
• Inverse limit
• Irrational number
• Kurt Hensel
• Limit of a sequence
• Local field
• Locally compact
• Mahler's theorem
• Mathematics
• MathWorld
• Mersenne prime
• Metric (mathematics)
• Metric space
• Modular arithmetic
• Natural number
• Nigel Horspool
• Number field
• Number system
• Number theory
• Numerical digit
• Octonion
• Ordered field
• Ordinal number
• Ostrowski's theorem
• P-adic analysis
• P-adic number
• P-adic order
• P-adic topology
• Partial sum
• PlanetMath
• Pontryagin dual
• Power series
• Prime ideal
• Prime number
• Prosolvable
• Prüfer group
• Quaternion
• Quote notation
• Radix
• Rational number
• Rational numbers
• Real number
• Relative topology
• Residue field
• Ring of periods
• Sedenion
• Series (mathematics)
• Solvable group
• Subring
• Supernatural numbers
• Superreal number
• Surreal number
• Talk P-adic number
• Tate module
• Topological space
• Topology (structure)
• Torsion (algebra)
• Two's complement
• Ultrametric space
• Uncountable set
• Uncountably infinite
• WP references
• WP Verifiability
• Zero divisor
• 
  

• 
  Austin, Texas
  Austin (/ˈɒstɨn/ or /ˈɔːstɨn/) is the capital of the U.S. state of Texas and the seat of Travis County. Located in Central Texas on the eastern edge of the American Southwest, it is the fourth-largest city in Texas and the 14th most populous city in the United States. It was the third-fastest-growing large city in the nation from 2000 to 2006. Austin has a population of 790,390 (2010 U.S. Census). The city is the cultural and economic center of the Austin–Round Rock–San Marcos metropolitan area, which had an estimated population 1,783,519 (2011 U.S. Census), making it the 34th-largest metropolitan statistical area in the United States.
  In the 1830s, pioneers began to the settle the area in central Austin along the Colorado River. After Republic of Texas Vice President Mirabeau B. Lamar visited the area during a buffalo-hunting expedition between 1837 and 1838, he proposed that the republic's capital then located in Houston, Texas, be relocated to the area situated on the north bank of the Colorado River near the present-day Ann W. Richards Congress Avenue Bridge. In 1839, the site was officially chosen as the republic's new capital (the republic's seventh and final location) and was incorporated under the name, Waterloo. Shortly thereafter, the name was changed to Austin in honor of Stephen F. Austin, the "Father of Texas" and the republic's first secretary of state.
  
  wn.com/Austin,_Texas
• 
  Autlán, Jalisco
  Autlán de Navarro is a city and its surrounding municipality of the same name in the Costa Sur region of the southwestern part of the state of Jalisco in Mexico. At the Mexican census of 2005, the city had a population of 53,269 inhabitants. The municipality has a surface area of 962.9 km² (371.78 sq mi). The mayor is Fernando Morán Guzmán (2010-2012).
  The name comes from the Nahuatl language, Aotli (water way, water channel or water ditch) and Tlan (place of or near) and means "next to the water ditch."
  
  
  
  wn.com/Autlán,_Jalisco
• 
  Barcelona, Spain
  Barcelona (English /bɑrsɨˈloʊnə/, Catalan: [bərsəˈɫonə], Spanish: [barθeˈlona]) is the capital of Catalonia and the second largest city in Spain, after Madrid, with a population of 1,621,537 within its administrative limits on a land area of 101.4 km² (39 sq mi). The urban area of Barcelona extends beyond the administrative city limits with a population of between 4,200,000 and 4,500,000 within an area of 803 km² (310 sq mi), being the sixth-most populous urban area in the European Union after Paris, London, the Ruhr, Madrid and Milan. About five million people live in the Barcelona metropolitan area. It is also Europe's largest metropolis on the Mediterranean Sea. It is the main component of an administrative area of Greater Barcelona, with a population of 3,218,071 in an area of 636 km² (density 5,060 hab/km²). It is located on the Mediterranean coast between the mouths of the rivers Llobregat and Besòs and is bounded to the west by the Serra de Collserola ridge (512 m/1,680 ft).
  Founded as a Roman city, Barcelona became the capital of the County of Barcelona. After merging with the Kingdom of Aragon, Barcelona became one of the most important cities of the Crown of Aragon. Besieged several times during its history, Barcelona has a rich cultural heritage and is today an important cultural centre and a major tourist destination. Particularly renowned are the architectural works of Antoni Gaudí and Lluís Domènech i Montaner, which have been designated UNESCO World Heritage Sites. The headquarters of the Union for the Mediterranean is located in Barcelona. The city is known for hosting the 1992 Summer Olympics as well as world-class conferences and expositions, including the 1888 Exposición Universal de Barcelona, the 1929 Barcelona International Exposition (Expo 1929), the 2004 Universal Forum of Cultures, and the 2004 World Urban Forum.
  
  wn.com/Barcelona,_Spain
• 
  Boca Raton, Florida
  Boca Raton ( /ˈboʊkə rəˈtoʊn/) is a city in Palm Beach County, Florida, USA, incorporated in May 1925. In the 2000 census, the city had a total population of 74,764; the 2006 population estimated by the U.S. Census Bureau was 86,396. The Census 2010 count was down slightly, to 84,392. However, the majority of the people under the postal address of Boca Raton, about 200,000 in total, are not actually within Boca Raton's municipal boundaries. As a business center, the city's daytime population increases significantly.
  In terms of both population and land area, Boca Raton is the largest city between West Palm Beach and Pompano Beach, Broward County.
  The literal translation of "Boca Raton" is "Mouth of The Mouse" ("mouse" in Spanish is "ratón"), the Spanish word boca meaning inlet and ratón being a Spanish nautical term describing rocks that gnawed at a ship's cable. Another explanation is that it refers metaphorically to a pirate's cove. The name Boca Ratones originally appeared on eighteenth century maps associated with an inlet in the Biscayne Bay area of Miami. By the beginning of the nineteenth century, the term was mistakenly moved north to its current location on most maps and applied to the inland waterway from the closed inlet north for 8.5 miles (13.7 km), which was called the "Boca Ratones Lagoon".
  
  wn.com/Boca_Raton,_Florida
• 
  Brazil
  Brazil ⁱ/brəˈzɪl/ (Portuguese: Brasil, IPA: [bɾaˈziw]), officially the Federative Republic of Brazil (Portuguese: República Federativa do Brasil,  listen (help·info)), is the largest country in South America. It is the world's fifth largest country, both by geographical area and by population with over 192 million people. It is the only Portuguese-speaking country in the Americas and the largest lusophone country in the world.
  Bounded by the Atlantic Ocean on the east, Brazil has a coastline of 7,491 km (4,655 mi). It is bordered on the north by Venezuela, Guyana, Suriname and the French overseas region of French Guiana; on the northwest by Colombia; on the west by Bolivia and Peru; on the southwest by Argentina and Paraguay and on the south by Uruguay. Numerous archipelagos form part of Brazilian territory, such as Fernando de Noronha, Rocas Atoll, Saint Peter and Paul Rocks, and Trindade and Martim Vaz. It borders all other South American countries except Ecuador and Chile.
  Brazil was a colony of Portugal from the landing of Pedro Álvares Cabral in 1500 until 1815, when it was elevated to the rank of kingdom and the United Kingdom of Portugal, Brazil and the Algarves was formed. The colonial bond was in fact broken in 1808, when the capital of the Portuguese colonial empire was transferred from Lisbon to Rio de Janeiro, after Napoleon invaded Portugal.Independence was achieved in 1822 with the formation of the Empire of Brazil, a unitary state governed under a constitutional monarchy and a parliamentary system. The country became a presidential republic in 1889, when a military coup d'état proclaimed the Republic, although the bicameral legislature, now called Congress, dates back to the ratification of the first constitution in 1824. Its current Constitution, formulated in 1988, defines Brazil as a Federal Republic. The Federation is formed by the union of the Federal District, the 26 States, and the 5,564 Municipalities.
  
  wn.com/Brazil
• 
  California
  California (pronounced ⁱ/kælɨˈfɔrnjə/) is a state located on the West Coast of the United States. It is by far the most populous U.S. state, and the third most extensive (after Alaska and Texas). It is home to the nation's second- and sixth-largest census statistical areas (Los Angeles Metropolitan Area and San Francisco Bay Area), and eight of the nation's fifty most populated cities (Los Angeles, San Diego, San Jose, San Francisco, Fresno, Sacramento, Long Beach and Oakland). The capital city is Sacramento.
  California's diverse geography ranges from the Pacific Coast in the west, to the Sierra Nevada mountains in the east – from the Redwood–Douglas-fir forests of the northwest, to the Mojave Desert areas in the southeast. The center of the state is dominated by Central Valley, a major agricultural area. California contains both the highest and lowest points in the contiguous United States (Mount Whitney and Death Valley), and has the third-longest coastline of all states (after Alaska and Florida). Earthquakes are a common occurrence due to the state's location along the Pacific Ring of Fire: about 37,000 are recorded annually.
  
  wn.com/California
• Fillmore West
  The Fillmore West was a historic music venue in San Francisco, California made famous by concert promoter Bill Graham. Named after Graham's original "Fillmore" location at the intersection of Fillmore Street and Geary Boulevard, it stood at Market Street and South Van Ness Avenue and was formerly known as both The Carousel Ballroom and El Patio.
  After two years at the Fillmore Auditorium, because of a deteriorating neighborhood and the modest capacity of the hall, Bill Graham moved the venue in July 1968 from the original building at 1805 Geary Boulevard to the Carousel Ballroom at 10 South Van Ness Avenue, at the corner of Market Street and South Van Ness Avenue (now the location of an automobile dealership), which was renamed Fillmore West (in contrast with Graham's Fillmore East auditorium in the East Village in New York City). Many Rock & Roll acts made successful appearances in the new, larger venue.
  The Celestial Synapse was a musical event held at the Fillmore West on the evening of 19 February 1969. At least 3,000 people attended the event, hosted by the Frontiers of Science Fellowship. The performance began with a Tibetan Buddhist monk playing Tibetan gongs, and The Grateful Dead played a set.
  
  wn.com/Fillmore_West
• 
  Jalisco
  Jalisco (Spanish pronunciation: [xaˈlisko]), officially Free and Sovereign State of Jalisco (Spanish: Estado Libre y Soberano de Jalisco), is one of the 31 states which, with the Federal District, comprise the 32 Federal Entities of Mexico. It is located in Western Mexico and divided in 125 municipalities and its capital city is Guadalajara. It is one of the more important states in Mexico because of its natural resources as well as its history. Many of the characteristic traits of Mexican culture, particularly outside Mexico, are originally from Jalisco, such as mariachi, ranchera music, tequila, jaripeo, etc. Economically, it is ranked third in the country, with industries centered in the Guadalajara metropolitan area, the second largest metropolitan area in Mexico. The state is home to two significant indigenous populations, the Huichols and the Nahuas. There is also a significant foreign population, mostly retirees from the United States and Canada, living in the Lake Chapala and Puerto Vallarta areas.
  
  wn.com/Jalisco
• 
  Lima, Peru
  Lima is the capital and the largest city of Peru. It is located in the valleys of the Chillón, Rímac and Lurín rivers, in the central part of the country, on a desert coast overlooking the Pacific Ocean. Together with the seaport of Callao, it forms a contiguous urban area known as the Lima Metropolitan Area. With a population approaching 9 million, Lima is the fifth largest city in Latin America, behind Mexico City, São Paulo, Buenos Aires and Rio de Janeiro. Lima is home to one of the largest financial hubs in Latin America. It has been defined as a beta world city by GaWC international ranking.
  Lima was founded by Spanish conquistador Francisco Pizarro on January 18, 1535, as la Ciudad de los Reyes, or "the City of Kings". It became the capital and most important city in the Spanish Viceroyalty of Peru. Following the Peruvian War of Independence, it became the capital of the Republic of Peru. Today, around one-third of the Peruvian population lives in the metropolitan area.
  Lima is home to one of the oldest higher learning institutions in the New World. The National University of San Marcos, founded on May 12, 1551 during Spanish colonial regime, is the oldest continuously functioning university in the Americas.
  
  wn.com/Lima,_Peru
• 
  Mexico
  Mexico (ⁱ/ˈmɛksɨkoʊ/; Spanish: México, IPA: [ˈmexiko] ( listen)), officially the United Mexican States (Spanish:  Estados Unidos Mexicanos (help·info)), is a federal constitutional republic in North America. It is bordered on the north by the United States of America; on the south and west by the Pacific Ocean; on the southeast by Guatemala, Belize, and the Caribbean Sea; and on the east by the Gulf of Mexico. Covering almost two million square kilometres (over 760,000 sq mi), Mexico is the fifth largest country in the Americas by total area and the thirteenth largest independent nation in the world. With an estimated population of over 113 million, it is the eleventh most populous country and the most populous Spanish-speaking country. Mexico is a federation comprising thirty-one states and a Federal District, the capital city.
  In Pre-Columbian Mexico many cultures matured into advanced civilizations such as the Olmec, the Toltec, the Teotihuacan, the Zapotec, the Maya and the Aztec before the first contact with Europeans. In 1521, Spain conquered and colonized the territory from its base in México-Tenochtitlan, which was administered as the Viceroyalty of New Spain. This territory would eventually become Mexico as the colony's independence was recognized in 1821. The post-independence period was characterized by economic instability, the Mexican-American War and territorial cession to the United States, a civil war, two empires and a domestic dictatorship. The latter led to the Mexican Revolution in 1910, which culminated with the promulgation of the 1917 Constitution and the emergence of the country's current political system. Elections held in July 2000 marked the first time that an opposition party won the presidency from the Institutional Revolutionary Party.
  
  wn.com/Mexico
• 
  México
  Mexico (ⁱ/ˈmɛksɨkoʊ/; Spanish: México, IPA: [ˈmexiko] ( listen)), officially the United Mexican States (Spanish:  Estados Unidos Mexicanos (help·info)), is a federal constitutional republic in North America. It is bordered on the north by the United States of America; on the south and west by the Pacific Ocean; on the southeast by Guatemala, Belize, and the Caribbean Sea; and on the east by the Gulf of Mexico. Covering almost two million square kilometres (over 760,000 sq mi), Mexico is the fifth largest country in the Americas by total area and the thirteenth largest independent nation in the world. With an estimated population of over 113 million, it is the eleventh most populous country and the most populous Spanish-speaking country. Mexico is a federation comprising thirty-one states and a Federal District, the capital city.
  In Pre-Columbian Mexico many cultures matured into advanced civilizations such as the Olmec, the Toltec, the Teotihuacan, the Zapotec, the Maya and the Aztec before the first contact with Europeans. In 1521, Spain conquered and colonized the territory from its base in México-Tenochtitlan, which was administered as the Viceroyalty of New Spain. This territory would eventually become Mexico as the colony's independence was recognized in 1821. The post-independence period was characterized by economic instability, the Mexican-American War and territorial cession to the United States, a civil war, two empires and a domestic dictatorship. The latter led to the Mexican Revolution in 1910, which culminated with the promulgation of the 1917 Constitution and the emergence of the country's current political system. Elections held in July 2000 marked the first time that an opposition party won the presidency from the Institutional Revolutionary Party.
  
  wn.com/México
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  Nicaragua
  Nicaragua (ⁱ/ˌnɪkəˈrɑːɡwə/ nik-ə-RAH-gwə), officially the Republic of Nicaragua (Spanish: República de Nicaragua [reˈpuβlika ðe nikaˈɾaɣwa] ( listen)), is the largest country in the Central American isthmus, bordered by Honduras to the north and Costa Rica to the south. The country is situated between 11 and 14 degrees north of the Equator in the Northern Hemisphere, which places it entirely within the tropics. The Pacific Ocean lies to the west, and the Caribbean Sea to the east. The country's physical geography divides it into three major zones: Pacific lowlands; wet, cooler central highlands; and the Caribbean lowlands. On the Pacific side of the country are the two largest fresh water lakes in Central America—Lake Managua and Lake Nicaragua. Surrounding these lakes and extending to their northwest along the rift valley of the Gulf of Fonseca are fertile lowland plains, with soil highly enriched by ash from nearby volcanoes of the central highlands. Nicaragua's abundance of biologically significant and unique ecosystems contribute to Mesoamerica's designation as a biodiversity hotspot.
  
  wn.com/Nicaragua
• 
  Nigeria
  Nigeria ⁱ/naɪˈdʒɪəriə/, officially the Federal Republic of Nigeria, is a federal constitutional republic comprising 36 states and its Federal Capital Territory, Abuja. The country is located in West Africa and shares land borders with the Republic of Benin in the west, Chad and Cameroon in the east, and Niger in the north. Its coast in the south lies on the Gulf of Guinea on the Atlantic Ocean. The three largest and most influential ethnic groups in Nigeria are the Hausa, Igbo and Yoruba.
  In terms of religion Nigeria is roughly split half and half between Muslims in the North and Christians in the South; a very small minority practice traditional religion. Since 2002 there have been a spate of clashes, particularly in the North of the country, between government forces and the Islamists Boko Haram, militant jihadists who seek to establish sharia law.
  The people of Nigeria have an extensive history. Archaeological evidence shows that human habitation of the area dates back to at least 9000 BCE. The area around the Benue and Cross River is thought to be the original homeland of the Bantu migrants who spread across most of central and southern Africa in waves between the 1st millennium BC and the 2nd millennium.
  
  wn.com/Nigeria
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  San Francisco
  San Francisco (/ˌsæn frənˈsɪskoʊ/), officially the City and County of San Francisco, is the financial, cultural, and transportation center of the San Francisco Bay Area, a region of 7.6 million people which includes San Jose and Oakland. The only consolidated city-county in California, it encompasses a land area of about 46.9 square miles (121 km²) on the northern end of the San Francisco Peninsula, giving it a density of about 17,179 people per square mile (6,632 people per km²). It is the most densely settled large city (population greater than 200,000) in the state of California and the second-most densely populated large city in the United States after New York City. San Francisco is the fourth most populous city in California and the 13th most populous city in the United States, with a population of 805,235 as of the 2010 Census. The San Francisco-Oakland-Fremont metropolitan area has a population of 4,335,391.
  In 1776, colonists from Spain established a fort at the Golden Gate and a mission named for Francis of Assisi a few miles away. The California Gold Rush of 1849 propelled the city into a period of rapid growth, increasing the population in one year from 1,000 to 25,000, and thus transforming it into the largest city on the West Coast at the time. After three-quarters of the city was destroyed by the 1906 earthquake and fire, San Francisco was quickly rebuilt, hosting the Panama-Pacific International Exposition nine years later. During World War II, San Francisco was the port of embarkation for service members shipping out to the Pacific Theater. After the war, the confluence of returning servicemen, massive immigration, liberalizing attitudes, and other factors led to the Summer of Love and the gay rights movement, cementing San Francisco as a center of liberal activism in the United States.
  
  wn.com/San_Francisco
• 
  Skopje
  Skopje (Macedonian: Скопје, [ˈskɔpjɛ] ( listen)) is the capital and largest city of the Republic of Macedonia with about a third of the total population. It is the country's political, cultural, economic, and academic centre. It was known in the Roman period under the name Scupi.
  The territory of Skopje has been inhabited since at least 4000 BC; remains of Neolithic settlements have been found within the old Kale Fortress that overlooks the modern city centre. On the eve of the 1st century AD, the settlement was seized by the Romans and became a military camp. When the Roman Empire was divided into eastern and western halves in 395 AD, Scupi came under Byzantine rule from Constantinople. During much of the early medieval period, the town was contested between the Byzantines and the Bulgarian Empire, whose capital it was between 972 and 992. From 1282 the town was part of the Serbian realm and its capital city since 1346. In 1392 the city was conquered by the Ottoman Turks who called the town Üsküp. The town stayed under Ottoman control over 500 years, serving as the capital of pashasanjak of Üsküb and later the Vilayet of Kosovo. At that time the city was famous for its oriental architecture. In 1912 the city was conquered by the Kingdom of Serbia during the Balkan Wars and after the First World War the city became part of the newly formed Kingdom of Serbs, Croats and Slovenes (Kingdom of Yugoslavia). In the Second World War the city was conquered by the Bulgarian Army, which was part of Axis powers. In 1944 it became the capital city of Democratic Macedonia (later Socialist Republic of Macedonia), which was a federal state, part of Democratic Federal Yugoslavia (later Socialist Federal Republic of Yugoslavia). The city developed rapidly after World War II, but this trend was interrupted in 1963 when it was hit by a disastrous earthquake. In 1991 it became the capital city of independent Macedonia.
  
  wn.com/Skopje
• 
  Tempe, Arizona
  Tempe ( /tɛmˈpiː/, US dict: tem-ˈpē;Oidbaḍ in Pima), also known as Hayden's Ferry during the territorial times of Arizona, is a city in Maricopa County, Arizona, USA, with the Census Bureau reporting a 2010 population of 161,719. The city is named after the Vale of Tempe in Greece. Tempe is located in the East Valley section of metropolitan Phoenix; it is bordered by Phoenix and Guadalupe on the west, Scottsdale on the north, Chandler on the south, and Mesa on the east. Tempe is the location of US Airways Group's corporate headquarters, and of Arizona State University's oldest and largest "Tempe" campus.
  The Hohokam initially lived in this area and built canals to support their agriculture. They abandoned their settlements during the 15th century, with a few individuals and families remaining nearby.
  Fort McDowell was established approximately 25 miles northeast of present downtown Tempe on the upper Salt River in 1865 allowing for new towns to be built further down the Salt River. US military service members and Hispanic workers were hired to grow food and animal feed to supply the fort, and less than a year later, had set up small camps near the river that were the first permanent communities in the Valley after the fall of the Hohokam. (Phoenix was settled shortly afterward, by 1867-68.) The two settlements were 'Hayden's Ferry', named after a ferry service operated by Charles T. Hayden, and 'San Pablo', and were located west and east of Hayden Butte respectively. The ferry became the key river crossing in the area. The Tempe Irrigating Canal Company was soon established by William Kirkland and James McKinney to provide water for alfalfa, wheat, barley, oats, and cotton.
  
  wn.com/Tempe,_Arizona
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  Tijuana
  Tijuana (/tiːəˈwɑːnə/ tee-ə-WAH-nə or /tiːˈwɑːnə/; Spanish: [tiˈxwana]) is the largest city on the Baja California Peninsula and center of the Tijuana metropolitan area, part of the international San Diego–Tijuana metropolitan area. An industrial and financial center of Mexico, Tijuana exerts a strong influence on economics, education, culture, art, and politics. As the city has become a leading center in the country, so has the surrounding metropolitan area, a major industrial and paramount metropolis in northwestern Mexico. Currently one of the fastest growing cities in Mexico, Tijuana maintains global city status.
  On the Gold Coast of Baja California, Tijuana is the municipal seat, cultural, and commercial center of Tijuana Municipality. A dominant manufacturing center of the North American continent, the city maintains facilities of numerous multinational conglomerate companies. The 2000's saw Tijuana become the medical device manufacturing capital of North America. Also a growing cultural center, Tijuana has been recognized as one of most important new cultural meccas. The city is the most visited border city in the globe; sharing an approximate 24-kilometre-long border (15 mi) with its sister city San Diego, over fifty million people annually cross the border between these two cities. This metropolitan crossing makes the San Ysidro Port of Entry the busiest land-border crossing in the world. It is estimated that the two border crossing stations between the cities proper of San Diego and Tijuana account for 300,000 daily border crossings alone.
  
  wn.com/Tijuana
• 
  Woodstock
  Woodstock Music & Art Fair (informally, Woodstock or The Woodstock Festival) was a music festival, billed as "An Aquarian Exposition: 3 Days of Peace & Music". It was held at Max Yasgur's 600-acre (2.4 km²; 240 ha, 0.94 mi²) dairy farm in the Catskills near the hamlet of White Lake in the town of Bethel, New York, from August 15 to August 18, 1969. Bethel, in Sullivan County, is 43 miles (69 km) southwest of the town of Woodstock, New York, in adjoining Ulster County.
  During the sometimes rainy weekend, thirty-two acts performed outdoors in front of 500,000 concert-goers. It is widely regarded as a pivotal moment in popular music history. Rolling Stone called it one of the 50 Moments That Changed the History of Rock and Roll.
  The event was captured in the 1970 documentary movie Woodstock, an accompanying soundtrack album, and Joni Mitchell's song "Woodstock" which commemorated the event and became a major hit for Crosby, Stills, Nash & Young.
  Woodstock was initiated through the efforts of Michael Lang, John Roberts, Joel Rosenman, and Artie Kornfeld. It was Roberts and Rosenman who had the finances. Lang had experience as a promoter and had already organized the largest festival on the East Coast at the time, the Miami Pop Festival, which had an estimated 100,000 people attend the two day event. Roberts and Rosenman placed the following advertisement in The New York Times and The Wall Street Journal under the name of Challenge International, Ltd.: "Young men with unlimited capital looking for interesting, legitimate investment opportunities and business propositions".
  
  wn.com/Woodstock
• 
  Woodstock Festival
  Woodstock Music & Art Fair (informally, Woodstock or The Woodstock Festival) was a music festival, billed as "An Aquarian Exposition: 3 Days of Peace & Music". It was held at Max Yasgur's 600-acre (2.4 km²; 240 ha, 0.94 mi²) dairy farm in the Catskills near the hamlet of White Lake in the town of Bethel, New York, from August 15 to August 18, 1969. Bethel, in Sullivan County, is 43 miles (69 km) southwest of the town of Woodstock, New York, in adjoining Ulster County.
  During the sometimes rainy weekend, thirty-two acts performed outdoors in front of 500,000 concert-goers. It is widely regarded as a pivotal moment in popular music history. Rolling Stone called it one of the 50 Moments That Changed the History of Rock and Roll.
  The event was captured in the 1970 documentary movie Woodstock, an accompanying soundtrack album, and Joni Mitchell's song "Woodstock" which commemorated the event and became a major hit for Crosby, Stills, Nash & Young.
  Woodstock was initiated through the efforts of Michael Lang, John Roberts, Joel Rosenman, and Artie Kornfeld. It was Roberts and Rosenman who had the finances. Lang had experience as a promoter and had already organized the largest festival on the East Coast at the time, the Miami Pop Festival, which had an estimated 100,000 people attend the two day event. Roberts and Rosenman placed the following advertisement in The New York Times and The Wall Street Journal under the name of Challenge International, Ltd.: "Young men with unlimited capital looking for interesting, legitimate investment opportunities and business propositions".
  
  wn.com/Woodstock_Festival

• Eric Hehner
  
  Eric C. R. Hehner, called Rick, is a Canadian computer scientist.
  Eric Hehner was born on 16 September 1947 in Ottawa. He studied mathematics and physics at Carleton University, obtaining his first degree in 1969. He gained a PhD in computer science from the University of Toronto in 1974. He then joined the faculty there, becoming a full professor in 1983. He became the Bell University Chair in Software Engineering in 2001.
  Hehner's main research area is formal methods, particularly for programming. In 1979, Hehner invented a method of representing rational numbers with current University of Victoria professor Nigel Horspool called quote notation, which allows for easier arithmetic and produces no roundoff error in arithmetic calculations implementing a generalization of radix notation. Hehner has also influenced many other computer science researchers with his ideas, including Tony Hoare, especially with his concept of predicative programming.
  
  
  
  
  
  wn.com/Eric_Hehner
• Eric W. Weisstein
  Eric Wolfgang Weisstein (born March 18, 1969, in Bloomington, Indiana) is an encyclopedist who created and maintains MathWorld and Eric Weisstein's World of Science (ScienceWorld). He currently works for Wolfram Research, Inc.
  Weisstein holds a Ph.D. in planetary astronomy which he obtained from the California Institute of Technology's (Caltech) Division of Geological and Planetary Sciences in 1996 as well as an M.S. in planetary astronomy in 1993 also from Caltech. Weisstein graduated Cum Laude from Cornell University with a B.A. in physics and a minor in astronomy in 1990. During his summers away from Cornell, Weisstein participated in research at the Arecibo Observatory, a radio telescope facility in Puerto Rico operated by Cornell. As a graduate student, Weisstein also participated in research at Goddard Space Flight Center in Greenbelt, MD. During his time at Goddard, Weisstein participated in the development of hurricane visualization software. In 1996 Weisstein published his doctoral thesis titled Millimeter/Submillimeter Fourier Transform Spectroscopy of Jovian Planet Atmospheres which was completed under faculty advisor Dewey Muhleman and in association with Eugene Serabyn, who is now a member of the Caltech Jet Propulsion Laboratory (JPL).
  
  wn.com/Eric_W._Weisstein
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  Helmut Hasse
  Helmut Hasse (German pronunciation: [ˈhasə]; 25 August 1898 – 26 December 1979) was a German mathematician working in algebraic number theory, known for fundamental contributions to class field theory, the application of p-adic numbers to local classfield theory and diophantine geometry (Hasse principle), and to local zeta functions.
  He was born in Kassel, and died in Ahrensburg.
  After serving in the navy in World War I, he studied at the University of Göttingen, and then at Marburg under Kurt Hensel, writing a dissertation in 1921 containing the Hasse–Minkowski theorem, as it is now called, on quadratic forms over number fields. He then held positions at Kiel, Halle and Marburg. He was Hermann Weyl's replacement at Göttingen in 1934; politically he was a right-wing nationalist, and applied for membership in the Nazi Party in 1937 but this was denied to him because he had Jewish ancestors. After war work he returned to Göttingen briefly in 1945 but was excluded by the British authorities. After brief appointments in Berlin from 1948 he settled permanently as professor in Hamburg.
  
  wn.com/Helmut_Hasse
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  Kurt Hensel
  Kurt Wilhelm Sebastian Hensel (29 December 1861 – 1 June 1941) was a German mathematician born in Königsberg, Prussia.
  He was the son of the landowner and entrepreneur Sebastian Hensel, brother of the philosopher Paul Hensel, grandson of the composer Fanny Mendelssohn and the painter Wilhelm Hensel, and a descendant of the philosopher Moses Mendelssohn.
  He studied mathematics in Berlin and Bonn, under mathematicians like Leopold Kronecker and Karl Weierstrass.
  Later in his life he was a professor at the University of Marburg until 1930. He was also an editor of the mathematical Crelle's Journal.
  He is well known for his introduction of p-adic numbers. First described by him in 1897, they became increasingly important in number theory and other fields during the twentieth century.
  
  wn.com/Kurt_Hensel
• Nigel Horspool
  R. Nigel Horspool is a professor of computer science at the University of Victoria. He invented the Boyer–Moore–Horspool algorithm, a fast string search algorithm adapted from the Boyer–Moore string search algorithm. Horspool is co-inventor of dynamic Markov compression and is co-editor of the journal Software: Practice and Experience.
  Nigel Horspool is British by birth, but is now a citizen of Canada. After a public school education at Monmouth School, he studied at Pembroke College, Cambridge where he received a BA in Natural Science, but specializing in Theoretical Physics, in 1969. After two years employment as an assembly language programmer on a failed air traffic control system project, he went to the University of Toronto for a MSc followed by a PhD in computer science. This was followed by seven years as an Assistant Professor and then an Associate Professor at McGill University. In 1983, he made a permanent move to the University of Victoria.
  
  
  
  wn.com/Nigel_Horspool