Mathematics includes the study of such topics as quantity, structure and change. Mathematicians use patterns to formulate new conjectures; when mathematical structures are good models of real phenomena mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back; the research required to solve mathematical problems can take years or centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano, David Hilbert, others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.
Mathematics is essential in many fields, including natural science, medicine and the social sciences. Applied mathematics has led to new mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics without having any application in mind, but practical applications for what began as pure mathematics are discovered later; the history of mathematics can be seen as an ever-increasing series of abstractions. The first abstraction, shared by many animals, was that of numbers: the realization that a collection of two apples and a collection of two oranges have something in common, namely quantity of their members; as evidenced by tallies found on bone, in addition to recognizing how to count physical objects, prehistoric peoples may have recognized how to count abstract quantities, like time – days, years. Evidence for more complex mathematics does not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic and geometry for taxation and other financial calculations, for building and construction, for astronomy.
The most ancient mathematical texts from Mesopotamia and Egypt are from 2000–1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry, it is in Babylonian mathematics that elementary arithmetic first appear in the archaeological record. The Babylonians possessed a place-value system, used a sexagesimal numeral system, still in use today for measuring angles and time. Beginning in the 6th century BC with the Pythagoreans, the Ancient Greeks began a systematic study of mathematics as a subject in its own right with Greek mathematics. Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom and proof, his textbook Elements is considered the most successful and influential textbook of all time. The greatest mathematician of antiquity is held to be Archimedes of Syracuse, he developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus.
Other notable achievements of Greek mathematics are conic sections, trigonometry (Hipparchus of Nicaea, the beginnings of algebra. The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics. Other notable developments of Indian mathematics include the modern definition of sine and cosine, an early form of infinite series. During the Golden Age of Islam during the 9th and 10th centuries, mathematics saw many important innovations building on Greek mathematics; the most notable achievement of Islamic mathematics was the development of algebra. Other notable achievements of the Islamic period are advances in spherical trigonometry and the addition of the decimal point to the Arabic numeral system. Many notable mathematicians from this period were Persian, such as Al-Khwarismi, Omar Khayyam and Sharaf al-Dīn al-Ṭūsī. During the early modern period, mathematics began to develop at an accelerating pace in Western Europe.
The development of calculus by Newton and Leibniz in the 17th century revolutionized mathematics. Leonhard Euler was the most notable mathematician of the 18th century, contributing numerous theorems and discoveries; the foremost mathematician of the 19th century was the German mathematician Carl Friedrich Gauss, who made numerous contributions to fields such as algebra, differential geometry, matrix theory, number theory, statistics. In the early 20th century, Kurt Gödel transformed mathematics by publishing his incompleteness theorems, which show that any axiomatic system, consistent will contain unprovable propositions. Mathematics has since been extended, there has been a fruitful interaction between mathematics and science, to
Federal Ministry for Economic Cooperation and Development
The Federal Ministry of Economic Cooperation and Development, abbreviated BMZ, is a cabinet-level ministry of the Federal Republic of Germany. Its main office is at the former German Chancellery in Bonn with a second major office at the Europahaus in Berlin. Founded in 1961, the Ministry works to encourage economic development within Germany and in other countries through international cooperation and partnerships, it cooperates with international organizations involved in development including the International Monetary Fund, World Bank, the United Nations. Political Party: FDP CSU SPD
Humanities are academic disciplines that study aspects of human society and culture. In the Renaissance, the term contrasted with divinity and referred to what is now called classics, the main area of secular study in universities at the time. Today, the humanities are more contrasted with natural, sometimes social, sciences as well as professional training; the humanities use methods that are critical, or speculative, have a significant historical element—as distinguished from the empirical approaches of the natural sciences, unlike the sciences, it has no central discipline. The humanities include ancient and modern languages, philosophy, human geography, politics and art. Scholars in the humanities are humanists; the term "humanist" describes the philosophical position of humanism, which some "antihumanist" scholars in the humanities reject. The Renaissance scholars and artists were called humanists; some secondary schools offer humanities classes consisting of literature, global studies and art.
Human disciplines like history and cultural anthropology study subject matters that the manipulative experimental method does not apply to—and instead use the comparative method and comparative research. Anthropology is a science of the totality of human existence; the discipline deals with the integration of different aspects of the social sciences and human biology. In the twentieth century, academic disciplines have been institutionally divided into three broad domains; the natural sciences seek to derive general laws through verifiable experiments. The humanities study local traditions, through their history, literature and arts, with an emphasis on understanding particular individuals, events, or eras; the social sciences have attempted to develop scientific methods to understand social phenomena in a generalizable way, though with methods distinct from those of the natural sciences. The anthropological social sciences develop nuanced descriptions rather than the general laws derived in physics or chemistry, or they may explain individual cases through more general principles, as in many fields of psychology.
Anthropology does not fit into one of these categories, different branches of anthropology draw on one or more of these domains. Within the United States, anthropology is divided into four sub-fields: archaeology, physical or biological anthropology, anthropological linguistics, cultural anthropology, it is an area, offered at most undergraduate institutions. The word anthropos is from the Greek for "human being" or "person". Eric Wolf described sociocultural anthropology as "the most scientific of the humanities, the most humanistic of the sciences"; the goal of anthropology is to provide a holistic account of human nature. This means that, though anthropologists specialize in only one sub-field, they always keep in mind the biological, linguistic and cultural aspects of any problem. Since anthropology arose as a science in Western societies that were complex and industrial, a major trend within anthropology has been a methodological drive to study peoples in societies with more simple social organization, sometimes called "primitive" in anthropological literature, but without any connotation of "inferior".
Today, anthropologists use terms such as "less complex" societies, or refer to specific modes of subsistence or production, such as "pastoralist" or "forager" or "horticulturalist", to discuss humans living in non-industrial, non-Western cultures, such people or folk remaining of great interest within anthropology. The quest for holism leads most anthropologists to study a people in detail, using biogenetic and linguistic data alongside direct observation of contemporary customs. In the 1990s and 2000s, calls for clarification of what constitutes a culture, of how an observer knows where his or her own culture ends and another begins, other crucial topics in writing anthropology were heard, it is possible to view all human cultures as part of one large. These dynamic relationships, between what can be observed on the ground, as opposed to what can be observed by compiling many local observations remain fundamental in any kind of anthropology, whether cultural, linguistic or archaeological.
Archaeology is the study of human activity through the analysis of material culture. The archaeological record consists of artifacts, biofacts or ecofacts, cultural landscapes. Archaeology can be considered a branch of the humanities, it has various goals, which range from understanding culture history to reconstructing past lifeways to documenting and explaining changes in human societies through time. Archaeology is thought of as a branch of anthropology in the United States, while in Europe, it is viewed as a discipline in its own right, or grouped under other related disciplines such as history. Classics, in the Western academic tradition, refers to the studies of the cultures of classical antiquity, namely Ancient Greek and Latin and the Ancient Greek and Roman cultures. Classical studies is considered one of the cornerstones of the humanities; the influence of classical ideas on many humanities disciplines, such as philosophy and literature, remains strong. History is systematically collected information about the past.
When used as the name of a field of study, history refers to the study and interpretation of the record of humans, societies and any to
Système universitaire de documentation
The système universitaire de documentation or SUDOC is a system used by the libraries of French universities and higher education establishments to identify and manage the documents in their possession. The catalog, which contains more than 10 million references, allows students and researcher to search for bibliographical and location information in over 3,400 documentation centers, it is maintained by the Bibliographic Agency for Higher Education. Official website
Alexander von Humboldt
Friedrich Wilhelm Heinrich Alexander von Humboldt was a Prussian polymath, naturalist and influential proponent of Romantic philosophy and science. He was the younger brother of the Prussian minister and linguist Wilhelm von Humboldt. Humboldt's quantitative work on botanical geography laid the foundation for the field of biogeography. Humboldt's advocacy of long-term systematic geophysical measurement laid the foundation for modern geomagnetic and meteorological monitoring. Between 1799 and 1804, Humboldt travelled extensively in the Americas and describing them for the first time from a modern scientific point of view, his description of the journey was written up and published in an enormous set of volumes over 21 years. Humboldt was one of the first people to propose that the lands bordering the Atlantic Ocean were once joined. Humboldt resurrected the use of the word cosmos from the ancient Greek and assigned it to his multivolume treatise, Kosmos, in which he sought to unify diverse branches of scientific knowledge and culture.
This important work motivated a holistic perception of the universe as one interacting entity. He was the first person to describe the phenomenon and cause of human-induced climate change, in 1800 and again in 1831, based on observations generated during his travels. Alexander von Humboldt was born in Berlin in Prussia on 14 September 1769, he was baptized with the Duke of Brunswick serving as godfather. Humboldt's father, Alexander Georg von Humboldt, belonged to a prominent Pomeranian family, although not one of the titled gentry, a major in the Prussian Army, who had served with the Duke of Brunswick. At age 42, Alexander Georg was rewarded for his services in the Seven Years' War with the post of royal chamberlain, he profited from the contract to lease state lotteries and tobacco sales. He first married the daughter of Prussian General Adjutant Schweder. In 1766, Alexander Georg married Maria Elisabeth Colomb, a well-educated woman and widow of Baron Hollwede, with whom she had a son. Alexander Georg and Maria Elisabeth had three children, a daughter, who died young, two sons and Alexander.
Her first-born son and Alexander's half-brother, was something of a ne'er do well, not mentioned in the family history. Alexander Georg died in 1779, leaving the brothers Humboldt in the care of their distant mother, she did have high ambitions for Alexander and his older brother Wilhelm, hiring excellent tutors, who were Enlightenment thinkers, including Kantian physician Marcus Herz and botanist Karl Ludwig Willdenow, who became one of the most important botanists in Germany. Humboldt's mother expected them to become civil servants of the Prussian state; the money Baron Holwede left to Alexander's mother became, after her death, instrumental in funding Alexander's explorations, contributing more than 70% of his private income. Due to his youthful penchant for collecting and labeling plants and insects, Alexander received the playful title of "the little apothecary". Marked for a political career, Alexander studied finance for six months in 1787 at the University of Frankfurt, which his mother might have chosen less for its academic excellence than its closeness to their home in Berlin.
On 25 April 1789, he matriculated at Göttingen known for the lectures of C. G. Heyne and anatomist J. F. Blumenbach, his brother Wilhelm was a student at Göttingen, but they did not interact much, since their intellectual interests were quite different. His vast and varied interests were by this time developed. At Gottingen, he met Georg Forster, a naturalist, with Captain James Cook on his second voyage. Humboldt traveled with Forster in Europe; the two traveled to England, Humboldt's first sea voyage, the Netherlands, France. In England, he met Sir Joseph Banks, president of the Royal Society, who had traveled with Captain Cook; the scientific friendship between Banks and Humboldt lasted until Banks's death in 1820, the two shared botanical specimens for study. Banks mobilized his scientific contacts in years to aid Humboldt's work. Humboldt's scientific excursion up the Rhine resulted in his 1790 treatise Mineralogische Beobachtungen über einige Basalte am Rhein. Humboldt's passion for travel was of long standing.
Humboldt's talents were devoted to the purpose of preparing himself as a scientific explorer. With this emphasis, he studied commerce and foreign languages at Hamburg, geology at Technische Universität Bergakademie Freiberg in 1791 under A. G. Werner, leader of the Neptunist school of geology. C. Loder. X. von Zach and J. G. Köhler. At Freiberg, he met a number of men who were to prove important to him in his career, including Spaniard Manuel del Rio, who became director of the School of Mines the crown established in Mexico. During this period, his brother Wilhelm married. Humboldt graduated from the Freiberg School of Mines in 1792 and was appointed to a Prussian government position in the Department of Mines as an inspector in Bayreuth and the Fichtel mountains. Humboldt was excellent at his job, with production of gold ore in his first year outstripping the previous eight years. During his period as a mine inspector, Humbo
Integrated Authority File
The Integrated Authority File or GND is an international authority file for the organisation of personal names, subject headings and corporate bodies from catalogues. It is used for documentation in libraries and also by archives and museums; the GND is managed by the German National Library in cooperation with various regional library networks in German-speaking Europe and other partners. The GND falls under the Creative Commons Zero licence; the GND specification provides a hierarchy of high-level entities and sub-classes, useful in library classification, an approach to unambiguous identification of single elements. It comprises an ontology intended for knowledge representation in the semantic web, available in the RDF format; the Integrated Authority File became operational in April 2012 and integrates the content of the following authority files, which have since been discontinued: Name Authority File Corporate Bodies Authority File Subject Headings Authority File Uniform Title File of the Deutsches Musikarchiv At the time of its introduction on 5 April 2012, the GND held 9,493,860 files, including 2,650,000 personalised names.
There are seven main types of GND entities: LIBRIS Virtual International Authority File Information pages about the GND from the German National Library Search via OGND Bereitstellung des ersten GND-Grundbestandes DNB, 19 April 2012 From Authority Control to Linked Authority Data Presentation given by Reinhold Heuvelmann to the ALA MARC Formats Interest Group, June 2012
Natural science is a branch of science concerned with the description and understanding of natural phenomena, based on empirical evidence from observation and experimentation. Mechanisms such as peer review and repeatability of findings are used to try to ensure the validity of scientific advances. Natural science can be divided into two main branches: physical science. Physical science is subdivided into branches, including physics, chemistry and earth science; these branches of natural science may be further divided into more specialized branches. In Western society's analytic tradition, the empirical sciences and natural sciences use tools from formal sciences, such as mathematics and logic, converting information about nature into measurements which can be explained as clear statements of the "laws of nature"; the social sciences use such methods, but rely more on qualitative research, so that they are sometimes called "soft science", whereas natural sciences, insofar as they emphasize quantifiable data produced and confirmed through the scientific method, are sometimes called "hard science".
Modern natural science succeeded more classical approaches to natural philosophy traced to ancient Greece. Galileo, Descartes and Newton debated the benefits of using approaches which were more mathematical and more experimental in a methodical way. Still, philosophical perspectives and presuppositions overlooked, remain necessary in natural science. Systematic data collection, including discovery science, succeeded natural history, which emerged in the 16th century by describing and classifying plants, minerals, so on. Today, "natural history" suggests observational descriptions aimed at popular audiences. Philosophers of science have suggested a number of criteria, including Karl Popper's controversial falsifiability criterion, to help them differentiate scientific endeavors from non-scientific ones. Validity and quality control, such as peer review and repeatability of findings, are amongst the most respected criteria in the present-day global scientific community; this field encompasses a set of disciplines.
The scale of study can range from sub-component biophysics up to complex ecologies. Biology is concerned with the characteristics and behaviors of organisms, as well as how species were formed and their interactions with each other and the environment; the biological fields of botany and medicine date back to early periods of civilization, while microbiology was introduced in the 17th century with the invention of the microscope. However, it was not until the 19th century. Once scientists discovered commonalities between all living things, it was decided they were best studied as a whole; some key developments in biology were the discovery of genetics. Modern biology is divided into subdisciplines by the type of organism and by the scale being studied. Molecular biology is the study of the fundamental chemistry of life, while cellular biology is the examination of the cell. At a higher level and physiology look at the internal structures, their functions, of an organism, while ecology looks at how various organisms interrelate.
Constituting the scientific study of matter at the atomic and molecular scale, chemistry deals with collections of atoms, such as gases, molecules and metals. The composition, statistical properties and reactions of these materials are studied. Chemistry involves understanding the properties and interactions of individual atoms and molecules for use in larger-scale applications. Most chemical processes can be studied directly in a laboratory, using a series of techniques for manipulating materials, as well as an understanding of the underlying processes. Chemistry is called "the central science" because of its role in connecting the other natural sciences. Early experiments in chemistry had their roots in the system of Alchemy, a set of beliefs combining mysticism with physical experiments; the science of chemistry began to develop with the work of Robert Boyle, the discoverer of gas, Antoine Lavoisier, who developed the theory of the Conservation of mass. The discovery of the chemical elements and atomic theory began to systematize this science, researchers developed a fundamental understanding of states of matter, chemical bonds and chemical reactions.
The success of this science led to a complementary chemical industry that now plays a significant role in the world economy. Physics embodies the study of the fundamental constituents of the universe, the forces and interactions they exert on one another, the results produced by these interactions. In general, physics is regarded as the fundamental science, because all other natural sciences use and obey the principles and laws set down by the field. Physics relies on mathematics as the logical framework for formulation and quantification of principles; the study of the principles of the universe has a long history and derives from direct observation and experimentation. The formulation of theories about the governing laws of the universe has been central to the study of physics from early on, with philosophy yielding to systematic, quantitative experimental testing and observation as the source of verification. Key historical developments in physics include Isaac Newton's theory of universal g