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Zech
Julius August Christoph Zech (24 February 1821 Stuttgart, Germany − 13 July 1864 Berg) was a German astronomer and mathematician. In 1849, Zech published a table of logarithms; as a result, Zech logarithms for finite field In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtr ...s are named after him. References * External linksJ. Zechbiography on mathforum. 19th-century German astronomers 19th-century German mathematicians 1821 births 1864 deaths Scientists from Stuttgart {{Germany-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stuttgart
Stuttgart (; Swabian: ; ) is the capital and largest city of the German state of Baden-Württemberg. It is located on the Neckar river in a fertile valley known as the ''Stuttgarter Kessel'' (Stuttgart Cauldron) and lies an hour from the Swabian Jura and the Black Forest. Stuttgart has a population of 635,911, making it the sixth largest city in Germany. 2.8 million people live in the city's administrative region and 5.3 million people in its metropolitan area, making it the fourth largest metropolitan area in Germany. The city and metropolitan area are consistently ranked among the top 20 European metropolitan areas by GDP; Mercer listed Stuttgart as 21st on its 2015 list of cities by quality of living; innovation agency 2thinknow ranked the city 24th globally out of 442 cities in its Innovation Cities Index; and the Globalization and World Cities Research Network ranked the city as a Beta-status global city in their 2020 survey. Stuttgart was one of the host cities ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Julius Zech
Julius August Christoph Zech (24 February 1821 Stuttgart, Germany − 13 July 1864 Berg) was a German astronomer and mathematician. In 1849, Zech published a table of logarithms; as a result, Zech logarithms for finite field In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtr ...s are named after him. References * External linksJ. Zechbiography on mathforum. 19th-century German astronomers 19th-century German mathematicians 1821 births 1864 deaths Scientists from Stuttgart {{Germany-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Astronomer
An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, natural satellite, moons, comets and galaxy, galaxies – in either observational astronomy, observational (by analyzing the data) or theoretical astronomy. Examples of topics or fields astronomers study include planetary science, Sun, solar astronomy, the Star formation, origin or stellar evolution, evolution of stars, or the galaxy formation and evolution, formation of galaxies. A related but distinct subject is physical cosmology, which studies the Universe as a whole. Types Astronomers usually fall under either of two main types: observational astronomy, observational and theoretical astronomy, theoretical. Observational astronomers make direct observations of Astronomical object, celestial objects and analyze the data. In contrast, theoretical astronomers create and investigate C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logarithms
In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number to the base is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 of is , or . The logarithm of to ''base'' is denoted as , or without parentheses, , or even without the explicit base, , when no confusion is possible, or when the base does not matter such as in big O notation. The logarithm base is called the decimal or common logarithm and is commonly used in science and engineering. The natural logarithm has the number as its base; its use is widespread in mathematics and physics, because of its very simple derivative. The binary logarithm uses base and is frequently used in computer science. Logarithms were introduced by John Napier in 1614 as a means of simplifying calculations. They were rapidly adopted by navigators, scientists, engineers, surveyors and others to perform high-accur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zech's Logarithm
Zech logarithms are used to implement addition in finite fields when elements are represented as powers of a generator \alpha. Zech logarithms are named after Julius Zech, and are also called Jacobi logarithms, after Carl G. J. Jacobi who used them for number theoretic investigations. Definition Given a primitive element \alpha of a finite field, the Zech logarithm relative to the base \alpha is defined by the equation :\alpha^ = 1 + \alpha^n, which is often rewritten as :Z_\alpha(n) = \log_\alpha(1 + \alpha^n). The choice of base \alpha is usually dropped from the notation when it is clear from the context. To be more precise, Z_\alpha is a function on the integers modulo the multiplicative order of \alpha, and takes values in the same set. In order to describe every element, it is convenient to formally add a new symbol -\infty, along with the definitions :\alpha^ = 0 :n + (-\infty) = -\infty :Z_\alpha(-\infty) = 0 :Z_\alpha(e) = -\infty where e is an integer satisfying \al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Field
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules. The most common examples of finite fields are given by the integers mod when is a prime number. The ''order'' of a finite field is its number of elements, which is either a prime number or a prime power. For every prime number and every positive integer there are fields of order p^k, all of which are isomorphic. Finite fields are fundamental in a number of areas of mathematics and computer science, including number theory, algebraic geometry, Galois theory, finite geometry, cryptography and coding theory. Properties A finite field is a finite set which is a field; this means that multiplication, addition, subtraction and division (excluding division by zero) are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
19th-century German Astronomers
The 19th (nineteenth) century began on 1 January 1801 ( MDCCCI), and ended on 31 December 1900 ( MCM). The 19th century was the ninth century of the 2nd millennium. The 19th century was characterized by vast social upheaval. Slavery was abolished in much of Europe and the Americas. The First Industrial Revolution, though it began in the late 18th century, expanding beyond its British homeland for the first time during this century, particularly remaking the economies and societies of the Low Countries, the Rhineland, Northern Italy, and the Northeastern United States. A few decades later, the Second Industrial Revolution led to ever more massive urbanization and much higher levels of productivity, profit, and prosperity, a pattern that continued into the 20th century. The Islamic gunpowder empires fell into decline and European imperialism brought much of South Asia, Southeast Asia, and almost all of Africa under colonial rule. It was also marked by the collapse of the large ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
19th-century German Mathematicians
The 19th (nineteenth) century began on 1 January 1801 ( MDCCCI), and ended on 31 December 1900 ( MCM). The 19th century was the ninth century of the 2nd millennium. The 19th century was characterized by vast social upheaval. Slavery was abolished in much of Europe and the Americas. The First Industrial Revolution, though it began in the late 18th century, expanding beyond its British homeland for the first time during this century, particularly remaking the economies and societies of the Low Countries, the Rhineland, Northern Italy, and the Northeastern United States. A few decades later, the Second Industrial Revolution led to ever more massive urbanization and much higher levels of productivity, profit, and prosperity, a pattern that continued into the 20th century. The Islamic gunpowder empires fell into decline and European imperialism brought much of South Asia, Southeast Asia, and almost all of Africa under colonial rule. It was also marked by the collapse of the large S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1821 Births
Eighteen or 18 may refer to: * 18 (number), the natural number following 17 and preceding 19 * one of the years 18 BC, AD 18, 1918, 2018 Film, television and entertainment * ''18'' (film), a 1993 Taiwanese experimental film based on the short story ''God's Dice'' * ''Eighteen'' (film), a 2005 Canadian dramatic feature film * 18 (British Board of Film Classification), a film rating in the United Kingdom, also used in Ireland by the Irish Film Classification Office * 18 (''Dragon Ball''), a character in the ''Dragon Ball'' franchise * "Eighteen", a 2006 episode of the animated television series '' 12 oz. Mouse'' Music Albums * ''18'' (Moby album), 2002 * ''18'' (Nana Kitade album), 2005 * '' 18...'', 2009 debut album by G.E.M. Songs * "18" (5 Seconds of Summer song), from their 2014 eponymous debut album * "18" (One Direction song), from their 2014 studio album ''Four'' * "18", by Anarbor from their 2013 studio album '' Burnout'' * "I'm Eighteen", by Alice Cooper commo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1864 Deaths
Events January–March * January 13 – American songwriter Stephen Foster ("Oh! Susanna", "Old Folks at Home") dies aged 37 in New York City, leaving a scrap of paper reading "Dear friends and gentle hearts". His parlor song " Beautiful Dreamer" is published in March. * January 16 – Denmark rejects an Austrian-Prussian ultimatum to repeal the Danish Constitution, which says that Schleswig-Holstein is part of Denmark. * January 21 – New Zealand Wars: The Tauranga campaign begins. * February – John Wisden publishes '' The Cricketer's Almanack for the year 1864'' in England; it will go on to become the major annual cricket reference publication. * February 1 – Danish-Prussian War (Second Schleswig War): 57,000 Austrian and Prussian troops cross the Eider River into Denmark. * February 15 – Heineken brewery founded in Netherlands. * February 17 – American Civil War: The tiny Confederate hand-propelled submarine ''H. L. Hunley'' s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
