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(Brunswick, now Germany, 1777 - Göttingen, id., 1855) Mathematician, physicist and astronomer German. Born into a poor family from a very early age, Karl Friedrich Gauss displayed a prodigious capacity for mathematics (according to legend, broke in three years his father when he was busy in the accounts of his business to tell a calculation error), to the point of being recommended to the Duke of Brunswick by their primary school teachers.
Duke gave financial assistance in high school and college, which was conducted at the University of Göttingen between 1795 and 1798. His doctoral thesis (1799) dealt with the fundamental theorem of algebra (which states that any algebraic equation has complex coefficients equally complex solutions), which Gauss proved.
In 1801 Gauss published a book aimed at a decisive influence in shaping the mathematics of the rest of the century, and particularly in the field the theory of numbers, arithmetic Disquisitions , whose numerous findings include: the first test of the quadratic reciprocity law, an algebraic solution to the problem of how to determine if a regular n-sided polygon can be constructed so geometric (unresolved since the time of Euclid), an exhaustive treatment of the theory of congruent numbers, and many results with numbers and complex functions (which would return to in 1831, describing exactly how to develop a complete theory them from their representations in the plane x, y) that marked the starting point of the modern theory of algebraic numbers. His fame as a mathematician
grew considerably this year, when he was able to predict accurately the orbital behavior of the asteroid Ceres, first sighted a few months before, for which employed the method of least squares, developed by himself in 1794 and even today the basis of modern computational tools astronomical estimate.
In 1807 he accepted the post of professor of astronomy at the Observatory of Göttingen, a post he remained all his life. Two years later, his first wife, whom he married in 1805, died giving birth to her third child later is remarried and had three more children. In those years Gauss matured his ideas on non-Euclidean geometry, ie the construction of a logically coherent dispense geometry of Euclid's postulate of parallels, but did not publish his findings, was ahead by more than thirty years later work Lobachewski and Bolyai.
Around 1820, held in the correct mathematical determination of the shape and size of the globe, Gauss developed many tools for the treatment of observational data, among which the error distribution curve that bears his name, also known by the appellation normal distribution and is one of the pillars of statistics.
Other results related to his interest in surveying are the invention of the heliotrope, and in the field of pure mathematics, its ideas on the study of the characteristics of curved surfaces, explicit in his general Disquisitiones circa curved surfaces ( 1828), laid the foundations of modern differential geometry. Also deserve your attention the phenomenon of magnetism, which culminated in the installation of the first electric telegraph (1833). Closely related to their investigations on this matter were the principles of the mathematical theory of potential he published in 1840.
Other areas of physics that Gauss studied were mechanical, acoustic, capillary and, in particular, optics, discipline on which the treaty published dioptric Research (1841), in which showed that a lens system is either always reducible to a single lens with the appropriate characteristics. It was perhaps the last major contribution of Karl Friedrich Gauss, a scientist whose depth of analysis, breadth of interest and rigor of treatment in life earned him the nickname "prince of mathematicians".

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What is mathematics?

Although mathematics is the "Queen of Sciences, there are some mathematicians do not consider it a natural science. Mainly, mathematicians define and investigate structures and abstractions for reasons purely internal to mathematics, because these structures can provide, for example, an elegant generalization, or useful tool for common calculations. In addition, many mathematicians see mathematics as an art form rather than a practical or applied science. However, the mathematical structures that researchers often do have their origin in the natural sciences, and often found applications in them, particularly in physics.
Mathematics is an art but it is a science study. Informally, one can say which is the study of "numbers and symbols." That is, research is defined abstract structures from first principles, using logic and mathematical notation. It is also the science of spatial and quantitative relations. This is the exact relationships between quantities and magnitudes, and the methods by which, according to these relations, quantities sought are deducible from other quantities known or presupposed.
not uncommon to find who describes mathematics as a simple extension of human natural languages, which uses a grammar and vocabulary defined with extreme precision, which aims at the description and exploration of conceptual and physical relationships. Recently, however, advances in the study of human language pointing in a different direction: natural languages \u200b\u200b(like English and French) and formal languages \u200b\u200b(such as mathematics and programming languages) are fundamentally different structures in nature .

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What is an algorithm?

In mathematics, computer science and related disciplines, an algorithm (Latin dixit Algorithmus and this in turn from Persian mathematician al-Khwarizmi) is a well-defined list, ordered and finite operations able to find a solution to a problem. Given an initial state and an input, through well-defined successive steps leads to a final state, obtaining a solution. The algorithms are studied in the algorithms, and its definition is formalized by the computational model of the Turing machine.

Its importance lies in showing how to implement processes and solve mathematical problems mechanically or otherwise. As mathematical functions, algorithms receive an input and transform it into an outlet, behaving like a black box. However, for an algorithm can be considered as such, must be deterministic, efficient, have a number Instruction finite and must end. By deterministic means that if you follow the same process more than once, always comes to the same result, for efficient, time-consuming and memory should be near or be the minimum.

The concept of algorithm, although similar and obviously related, not to be confused with the concept of program. While the first is the specification of a set of steps (operations, instructions, orders ,...) oriented problem solving, the second is the set of operations specified in a particular programming language and for a specific computer, capable of being executed (or compiled or interpreted). An algorithm, strictly speaking, can not run until it is implemented, either in a programming language in an electrical circuit, a mechanical device, using paper and pencil, or some other model of computation.

In everyday life algorithms are used many times to solve different problems. Some examples are found in the instructions (user manuals), which show the algorithms to use the device in question or even in a worker receives instructions from his employer. There are also examples of mathematics such as the division algorithm to calculate the ratio of two numbers, the Euclidean algorithm to compute the maximum common divisor of two positive integers, or the Gauss method for solving a linear system of equations.

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What is a mathematician? Aristotle

A mathematician is a person whose primary area of \u200b\u200bstudy and research is mathematics. In other words, a mathematician is a person who contributes new knowledge in the field of mathematics. In this way, which only apply mathematical theories are not considered mathematical, such as engineers, economists, etc.
Mathematicians are employed in private companies or as teachers in universities, institutes, research organizations, or government agencies. To give an example: in the United States the largest employer of mathematicians is the National Security Agency.
Because mathematics is useful in several areas, many mathematicians are involved in physics and computer science.

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Aristotle (384-322 BC) Greek philosopher and scientist, is one of the most outstanding philosophers of antiquity. Wrote among other trials, a summary of the doctrines of Pythagoras, of which a few excerpts have survived. These texts are based largely on the notes compiled and arranged by editors later. Among them are treatises on logic called Organon ("instrument") as they provide the means by which knowledge is to achieve positive.
In logic, developed rules to establish a chained reasoning that, if respected and if the reflection started from true premises (validity rules) does not produce false conclusions.) Reasoning, the basic links were syllogisms: propositions matched that, overall, provided a new conclusion. The most famous example, "All humans are mortal" and "All Greeks are human", it concludes that valid "All Greeks are mortal."
Science is the result of building systems increasingly complex reasoning. Distinguished between dialectic and analytic. The dialectic only tests opinions for their logical consistency. The analytic works deductively from principles resting on experience and a thorough inspection. This represents a break with the ideas of Plato, the dialectic was the only valid logical method, so effective in applied science and philosophy.