1.
Euclid
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Euclid, sometimes called Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the father of geometry. He was active in Alexandria during the reign of Ptolemy I, in the Elements, Euclid deduced the principles of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory, Euclid is the anglicized version of the Greek name Εὐκλείδης, which means renowned, glorious. Very few original references to Euclid survive, so little is known about his life, the date, place and circumstances of both his birth and death are unknown and may only be estimated roughly relative to other people mentioned with him. He is rarely mentioned by name by other Greek mathematicians from Archimedes onward, the few historical references to Euclid were written centuries after he lived by Proclus c.450 AD and Pappus of Alexandria c.320 AD. Proclus introduces Euclid only briefly in his Commentary on the Elements, Proclus later retells a story that, when Ptolemy I asked if there was a shorter path to learning geometry than Euclids Elements, Euclid replied there is no royal road to geometry. This anecdote is questionable since it is similar to a story told about Menaechmus, a detailed biography of Euclid is given by Arabian authors, mentioning, for example, a birth town of Tyre. This biography is generally believed to be completely fictitious, however, this hypothesis is not well accepted by scholars and there is little evidence in its favor. The only reference that historians rely on of Euclid having written the Elements was from Proclus, although best known for its geometric results, the Elements also includes number theory. The geometrical system described in the Elements was long known simply as geometry, today, however, that system is often referred to as Euclidean geometry to distinguish it from other so-called non-Euclidean geometries that mathematicians discovered in the 19th century. In addition to the Elements, at least five works of Euclid have survived to the present day and they follow the same logical structure as Elements, with definitions and proved propositions. Data deals with the nature and implications of information in geometrical problems. On Divisions of Figures, which only partially in Arabic translation. It is similar to a first-century AD work by Heron of Alexandria, catoptrics, which concerns the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors. The attribution is held to be anachronistic however by J J OConnor, phaenomena, a treatise on spherical astronomy, survives in Greek, it is quite similar to On the Moving Sphere by Autolycus of Pitane, who flourished around 310 BC. Optics is the earliest surviving Greek treatise on perspective, in its definitions Euclid follows the Platonic tradition that vision is caused by discrete rays which emanate from the eye. One important definition is the fourth, Things seen under a greater angle appear greater, proposition 45 is interesting, proving that for any two unequal magnitudes, there is a point from which the two appear equal. Other works are attributed to Euclid, but have been lost
2.
Calipers
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A caliper is a device used to measure the distance between two opposite sides of an object. A caliper can be as simple as a compass with inward or outward-facing points. The tips of the caliper are adjusted to fit across the points to be measured, the caliper is then removed and it is used in many fields such as mechanical engineering, metalworking, forestry, woodworking, science and medicine. A plurale tantum sense of the word calipers coexists in natural usage with the regular noun sense of caliper, also existing colloquially but not in formal usage is referring to a vernier caliper as a vernier or a pair of verniers. In imprecise colloquial usage, some extend this even to dial calipers. In machine-shop usage, the caliper is often used in contradistinction to micrometer. In this usage, caliper implies only the factor of the vernier or dial caliper. The earliest caliper has been found in the Greek Giglio wreck near the Italian coast, the ship find dates to the 6th century BC. The wooden piece already featured a fixed and a movable jaw, although rare finds, caliper remained in use by the Greeks and Romans. A bronze caliper, dating from 9 AD, was used for minute measurements during the Chinese Xin dynasty, the caliper had an inscription stating that it was made on a gui-you day at new moon of the first month of the first year of the Shijian guo period. The calipers included a slot and pin and graduated in inches, the modern vernier caliper, reading to thousandths of an inch, was invented by American Joseph R. Brown in 1851. It was the first practical tool for exact measurements that could be sold at a price within the reach of ordinary machinists, the inside calipers are used to measure the internal size of an object. The upper caliper in the image requires manual adjustment prior to fitting, fine setting of this caliper type is performed by tapping the caliper legs lightly on a handy surface until they will almost pass over the object. A light push against the resistance of the pivot screw then spreads the legs to the correct dimension and provides the required. The lower caliper in the image has a screw that permits it to be carefully adjusted without removal of the tool from the workpiece. Outside calipers are used to measure the size of an object. The same observations and technique apply to this type of caliper, with some understanding of their limitations and usage, these instruments can provide a high degree of accuracy and repeatability. They are especially useful when measuring over very large distances, consider if the calipers are used to measure a large diameter pipe, a vernier caliper does not have the depth capacity to straddle this large diameter while at the same time reach the outermost points of the pipes diameter
3.
Academic
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Academy is a type of secondary or tertiary education institutions. The word comes from the Academy in ancient Greece, which derives from the Athenian hero, outside the city walls of Athens, the gymnasium was made famous by Plato as a center of learning. The sacred space, dedicated to the goddess of wisdom, Athena, had formerly been an olive grove, in these gardens, the philosopher Plato conversed with followers. Plato developed his sessions into a method of teaching philosophy and in 387 BC, by extension academia has come to mean the cultural accumulation of knowledge, its development and transmission across generations and its practitioners and transmitters. In the 17th century, British, Italian and French scholars used the term to describe types of institutions of higher learning, in ancient Greece, after the establishment of the original Academy, Platos colleagues and pupils developed spin-offs of his method. Arcesilaus, a Greek student of Plato established the Middle Academy, carneades, another student, established the New Academy. In 335 BC, Aristotle refined the method with his own theories, the library of Alexandria in Egypt was frequented by intellectuals from Africa, Europe and Asia studying various aspects of philosophy, language and mathematics. The University of Timbuktu was a university in Timbuktu, present-day Mali. During its zenith, the university had an attendance of around 25,000 students within a city of around 100,000 people. In China a higher education institution Shang Xiang was founded by Shun in the Youyu era before the 21st century BC, in the 8th century another kind of institution of learning emerged, named Shuyuan, which were generally privately owned. There were thousands of Shuyuan recorded in ancient times, the degrees from them varied from one to another and those advanced Shuyuan such as Bailudong Shuyuan and Yuelu Shuyuan can be classified as higher institutions of learning. Taxila or Takshashila, in ancient India, modern-day Pakistan, was an early Buddhist centre of learning and it is considered as one of the ancient universities of the world. According to scattered references which were only fixed a millennium later it may have dated back to at least the 5th century BC, some scholars date Takshashilas existence back to the 6th century BC. The school consisted of several monasteries without large dormitories or lecture halls where the instruction was most likely still provided on an individualistic basis. Takshashila is described in detail in later Jātaka tales, written in Sri Lanka around the 5th century AD. It became a centre of learning at least several centuries BC. Takshashila is perhaps best known because of its association with Chanakya, the famous treatise Arthashastra by Chanakya, is said to have been composed in Takshashila itself. Chanakya, the Maurya Emperor Chandragupta and the Ayurvedic healer Charaka studied at Taxila, generally, a student entered Takshashila at the age of sixteen
4.
Doctoral degree
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There are a variety of doctoral degrees, with the most common being the Doctor of Philosophy, which is awarded in many different fields, ranging from the humanities to the scientific disciplines. The term doctor derives from the Latin docere meaning to teach, the doctorate appeared in medieval Europe as a license to teach Latin at a university. Its roots can be traced to the church in which the term doctor referred to the Apostles, church fathers. The right to grant a licentia docendi was originally reserved to the Catholic church, the Third Council of the Lateran of 1179 guaranteed the access—at that time largely free of charge—of all able applicants. This right remained a bone of contention between the authorities and universities that were slowly distancing themselves from the Church. The right was granted by the pope to the University of Paris in 1213 where it became a universal license to teach, according to Keith Allan Noble, the first doctoral degree was awarded in medieval Paris around 1150. The so-called professional, vocational, or technical curriculum of the Middle Ages included only theology, law, the doctorate of philosophy developed in Germany in the 17th century. The term philosophy does not refer solely to the field or academic discipline of philosophy, but is used in a sense in accordance with its original Greek meaning. In most of Europe, all fields were traditionally known as philosophy, the doctorate of philosophy adheres to this historic convention, even though the degrees are not always for the study of philosophy. D. University doctoral training was a form of apprenticeship to a guild, the traditional term of study before new teachers were admitted to the guild of Masters of Arts was seven years, matching the apprenticeship term for other occupations. Originally the terms master and doctor were synonymous, but over time the doctorate came to be regarded as a higher qualification than the masters degree, University degrees, including doctorates, were originally restricted to men. The use and meaning of the doctorate has changed over time, for instance, until the early 20th century few academic staff or professors in English-speaking universities held doctorates, except for very senior scholars and those in holy orders. After that time the German practice of requiring lecturers to have completed a research doctorate spread, universities shift to research-oriented education increased the doctorates importance. Today, a doctorate or its equivalent is generally a prerequisite for an academic career. Professional doctorates developed in the United States from the 19th century onward, the first professional doctorate to be offered in the United States was the M. D. The MD became the standard first degree in medicine during the 19th century, the MD, as the standard qualifying degree in medicine, gave that profession the ability to set and raise standards for entry into professional practice. The modern research degree, in the shape of the German-style Ph. D. was first awarded in the U. S. in 1861, in the UK, research doctorates initially took the form of higher doctorates, introduced from 1882 onwards. The PhD spread to the UK from the US via Canada, following the MD, the next professional doctorate, the Juris Doctor, was established by Chicago University in 1902
5.
Master's degree
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A masters degree normally requires previous study at the bachelors level, either as a separate degree or as part of an integrated course. The original meaning of the degree was thus that someone who had been admitted to the rank of master in one university should be admitted to the same rank in other universities. This gradually became formalised as the licentia docendi, initially, the Bachelor of Arts was awarded for the study of the trivium and the Master of Arts for the study of the quadrivium. The nineteenth century saw an expansion in the variety of masters degrees offered. By 1861 this had been adopted throughout Scotland as well as by Cambridge and Durham in England, when the Philadelphia College of Surgeons was established in 1870, it too conferred the Master of Surgery, the same as that in Europe. In the United States, the first masters degrees were awarded at Harvard University soon after its foundation, at Harvard the 1700 regulations required that candidates for the masters degree had to pass a public examination, but by 1835 this was awarded Oxbridge-style 3 years after the BA. In Scotland, Edinburgh maintained separate BA and MA degrees until the mid nineteenth century, in Scotland all the statutes of the Universities which enforced conditions on the grant of degrees were a dead letter. Probably the most important masters degree introduced in the 19th century was the Master of Science, at the University of Michigan this was introduced in two forms in 1858, in course, first awarded in 1859, and on examination, first awarded in 1862. The in course MS was last awarded in 1876, in Britain, however, the degree took a while longer to arrive. The same two degrees, again omitting the masters, were awarded at Edinburgh, despite the MA being the undergraduate degree for Arts in Scotland. In 1862, a Royal Commission suggested that Durham should award masters degrees in theology and science and this scheme would appear to have then been quietly dropped, with Oxford going on to award BAs and MAs in science. The Master of Science degree was introduced in Britain in 1878 at Durham. At the Victoria University both the MA and MSc followed the lead of Durhams MA in requiring an examination for those with an ordinary bachelors degree. The Bologna declaration in 1999 started the Bologna Process, leading to the creation of the European Higher Education Area, as the process continued, descriptors were introduced for all three levels in 2004, and ECTS credit guidelines were developed. This led to questions as to the status of the masters degrees. In 1903, the London Daily News criticised the practice of Oxford and Cambridge, calling their MAs the most stupendous of academic frauds, in 1900, Dartmouth College introduced the Master of Commercial Science, first awarded in 1902. This was the first masters degree in business, the forerunner of the modern MBA, the idea quickly crossed the Atlantic, with Manchester establishing a Faculty of Commerce, awarding Bachelor and Master of Commerce degrees, in 1903. Over the first half of the century the masters degrees for honours graduates vanished as honours degrees became the standard undergraduate qualification in the UK
6.
Statistician
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A statistician is someone who works with theoretical or applied statistics. The profession exists in both the private and public sectors and it is common to combine statistical knowledge with expertise in other subjects, and statisticians may work as employees or as statistical consultants. According to the United States Bureau of Labor Statistics, as of 2014,26,970 jobs were classified as statistician in the United States, of these people, approximately 30 percent worked for governments. Statisticians are included with the professions in various national and international occupational classifications, in the United States most employment in the field requires either a masters degree in statistics or a related field or a PhD. List of statisticians Statistician entry, Occupational Outlook Handbook, U. S
7.
Actuary
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An actuary is a business professional who deals with the measurement and management of risk and uncertainty. The name of the profession is actuarial science. These risks can affect both sides of the sheet, and require asset management, liability management, and valuation skills. Actuaries provide assessments of financial security systems, with a focus on their complexity, their mathematics, Actuaries of the 21st century require analytical skills, business knowledge, and an understanding of human behavior and information systems to design and manage programs that control risk. The actual steps needed to become an actuary are usually country-specific, however, almost all processes share a rigorous schooling or examination structure, the profession has consistently been ranked as one of the most desirable. In various studies, being an actuary was ranked number one or two times since 2010. Actuaries use skills primarily in mathematics, particularly calculus-based probability and mathematical statistics, but also economics, computer science, finance, and business. Actuaries assemble and analyze data to estimate the probability and likely cost of the occurrence of an event such as death, sickness, injury, disability, most traditional actuarial disciplines fall into two main categories, life and non-life. Life actuaries, which include health and pension actuaries, primarily deal with mortality risk, morbidity risk, products prominent in their work include life insurance, annuities, pensions, short and long term disability insurance, health insurance, health savings accounts, and long-term care insurance. Non-life actuaries, also known as property and casualty or general insurance actuaries, Actuaries are also called upon for their expertise in enterprise risk management. This can involve dynamic financial analysis, stress testing, the formulation of corporate policy. Actuaries are also involved in areas of the financial services industry. On both the life and casualty sides, the function of actuaries is to calculate premiums. On the casualty side, this often involves quantifying the probability of a loss event, called the frequency. The amount of time that occurs before the event is important. On the life side, the analysis often involves quantifying how much a potential sum of money or a liability will be worth at different points in the future. Forecasting interest yields and currency movements also plays a role in determining future costs, Actuaries do not always attempt to predict aggregate future events. Often, their work may relate to determining the cost of financial liabilities that have occurred, called retrospective reinsurance
8.
Mathematics
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Mathematics is the study of topics such as quantity, structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope, Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof, when mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry, rigorous arguments first appeared in Greek mathematics, most notably in Euclids Elements. Galileo Galilei said, The universe cannot be read until we have learned the language and it is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth, carl Friedrich Gauss referred to mathematics as the Queen of the Sciences. Benjamin Peirce called mathematics the science that draws necessary conclusions, David Hilbert said of mathematics, We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules, rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise. Albert Einstein stated that as far as the laws of mathematics refer to reality, they are not certain, Mathematics is essential in many fields, including natural science, engineering, medicine, finance and the social sciences. Applied mathematics has led to entirely new mathematical disciplines, such as statistics, Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, the history of mathematics can be seen as an ever-increasing series of abstractions. The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns, in Babylonian mathematics elementary arithmetic first appears in the archaeological record. Numeracy pre-dated writing and numeral systems have many and diverse. Between 600 and 300 BC the Ancient Greeks began a study of mathematics in its own right with Greek mathematics. Mathematics has since been extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today, the overwhelming majority of works in this ocean contain new mathematical theorems and their proofs. The word máthēma is derived from μανθάνω, while the modern Greek equivalent is μαθαίνω, in Greece, the word for mathematics came to have the narrower and more technical meaning mathematical study even in Classical times
9.
Mathematical problem
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A mathematical problem is a problem that is amenable to being represented, analyzed, and possibly solved, with the methods of mathematics. This can be a problem, such as computing the orbits of the planets in the solar system, or a problem of a more abstract nature. It can also be a problem referring to the nature of mathematics itself, informal real-world mathematical problems are questions related to a concrete setting, such as Adam has five apples and gives John three. Such questions are more difficult to solve than regular mathematical exercises like 5 −3. Known as word problems, they are used in education to teach students to connect real-world situations to the abstract language of mathematics. In general, to use mathematics for solving a real-world problem and this involves abstraction from the details of the problem, and the modeller has to be careful not to lose essential aspects in translating the original problem into a mathematical one. After the problem has been solved in the world of mathematics, abstract mathematical problems arise in all fields of mathematics. While mathematicians usually study them for their own sake, by doing so results may be obtained that find application outside the realm of mathematics, theoretical physics has historically been, and remains, a rich source of inspiration. Also provably unsolvable are so-called undecidable problems, such as the problem for Turing machines. Some well-known difficult abstract problems that have been solved relatively recently are the four-colour theorem, Fermats Last Theorem, and the Poincaré conjecture. Mathematics educators using problem solving for evaluation have an issue phrased by Alan H. Schoenfeld, How can one compare test scores from year to year, the same issue was faced by Sylvestre Lacroix almost two centuries earlier. It is necessary to vary the questions that students might communicate with each other, though they may fail the exam, they might pass later. Thus distribution of questions, the variety of topics, or the answers, risks losing the opportunity to compare, with precision, such degradation of problems into exercises is characteristic of mathematics in history. For example, describing the preparations for the Cambridge Mathematical Tripos in the 19th century, many families of the then standard problems had originally taxed the abilities of the greatest mathematicians of the 18th century. List of unsolved problems in mathematics Problem solving Mathematical game List of mathematical concepts named after places Collection of Math Word Problems
10.
Number
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A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1,2,3, a notational symbol that represents a number is called a numeral. In addition to their use in counting and measuring, numerals are used for labels, for ordering. In common usage, number may refer to a symbol, a word, calculations with numbers are done with arithmetical operations, the most familiar being addition, subtraction, multiplication, division, and exponentiation. Their study or usage is called arithmetic, the same term may also refer to number theory, the study of the properties of numbers. Besides their practical uses, numbers have cultural significance throughout the world, for example, in Western society the number 13 is regarded as unlucky, and a million may signify a lot. Though it is now regarded as pseudoscience, numerology, the belief in a significance of numbers, permeated ancient. Numerology heavily influenced the development of Greek mathematics, stimulating the investigation of problems in number theory which are still of interest today. During the 19th century, mathematicians began to develop many different abstractions which share certain properties of numbers, among the first were the hypercomplex numbers, which consist of various extensions or modifications of the complex number system. Numbers should be distinguished from numerals, the used to represent numbers. Boyer showed that Egyptians created the first ciphered numeral system, Greeks followed by mapping their counting numbers onto Ionian and Doric alphabets. The number five can be represented by digit 5 or by the Roman numeral Ⅴ, notations used to represent numbers are discussed in the article numeral systems. The Roman numerals require extra symbols for larger numbers, different types of numbers have many different uses. Numbers can be classified into sets, called number systems, such as the natural numbers, the same number can be written in many different ways. For different methods of expressing numbers with symbols, such as the Roman numerals, each of these number systems may be considered as a proper subset of the next one. This is expressed, symbolically, by writing N ⊂ Z ⊂ Q ⊂ R ⊂ C, the most familiar numbers are the natural numbers,1,2,3, and so on. Traditionally, the sequence of numbers started with 1 However, in the 19th century, set theorists. Today, different mathematicians use the term to both sets, including 0 or not
11.
Space
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Space is the boundless three-dimensional extent in which objects and events have relative position and direction. Physical space is conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. The concept of space is considered to be of importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework. Many of these classical philosophical questions were discussed in the Renaissance and then reformulated in the 17th century, in Isaac Newtons view, space was absolute—in the sense that it existed permanently and independently of whether there was any matter in the space. Other natural philosophers, notably Gottfried Leibniz, thought instead that space was in fact a collection of relations between objects, given by their distance and direction from one another. In the 18th century, the philosopher and theologian George Berkeley attempted to refute the visibility of spatial depth in his Essay Towards a New Theory of Vision. Kant referred to the experience of space in his Critique of Pure Reason as being a pure a priori form of intuition. In the 19th and 20th centuries mathematicians began to examine geometries that are non-Euclidean, in space is conceived as curved. According to Albert Einsteins theory of relativity, space around gravitational fields deviates from Euclidean space. Experimental tests of general relativity have confirmed that non-Euclidean geometries provide a model for the shape of space. In the seventeenth century, the philosophy of space and time emerged as an issue in epistemology. At its heart, Gottfried Leibniz, the German philosopher-mathematician, and Isaac Newton, unoccupied regions are those that could have objects in them, and thus spatial relations with other places. For Leibniz, then, space was an abstraction from the relations between individual entities or their possible locations and therefore could not be continuous but must be discrete. Space could be thought of in a way to the relations between family members. Although people in the family are related to one another, the relations do not exist independently of the people, but since there would be no observational way of telling these universes apart then, according to the identity of indiscernibles, there would be no real difference between them. According to the principle of sufficient reason, any theory of space that implied that there could be two possible universes must therefore be wrong. Newton took space to be more than relations between objects and based his position on observation and experimentation
12.
Mathematical model
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A mathematical model is a description of a system using mathematical concepts and language. The process of developing a model is termed mathematical modeling. Mathematical models are used in the sciences and engineering disciplines. Physicists, engineers, statisticians, operations research analysts, and economists use mathematical models most extensively, a model may help to explain a system and to study the effects of different components, and to make predictions about behaviour. Mathematical models can take many forms, including systems, statistical models, differential equations. These and other types of models can overlap, with a model involving a variety of abstract structures. In general, mathematical models may include logical models, in many cases, the quality of a scientific field depends on how well the mathematical models developed on the theoretical side agree with results of repeatable experiments. Lack of agreement between theoretical mathematical models and experimental measurements often leads to important advances as better theories are developed, in the physical sciences, the traditional mathematical model contains four major elements. These are Governing equations Defining equations Constitutive equations Constraints Mathematical models are composed of relationships. Relationships can be described by operators, such as operators, functions, differential operators. Variables are abstractions of system parameters of interest, that can be quantified, a model is considered to be nonlinear otherwise. The definition of linearity and nonlinearity is dependent on context, for example, in a statistical linear model, it is assumed that a relationship is linear in the parameters, but it may be nonlinear in the predictor variables. Similarly, an equation is said to be linear if it can be written with linear differential operators. In a mathematical programming model, if the functions and constraints are represented entirely by linear equations. If one or more of the functions or constraints are represented with a nonlinear equation. Nonlinearity, even in simple systems, is often associated with phenomena such as chaos. Although there are exceptions, nonlinear systems and models tend to be difficult to study than linear ones. A common approach to nonlinear problems is linearization, but this can be if one is trying to study aspects such as irreversibility
13.
History of mathematics
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Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. The most ancient mathematical texts available are Plimpton 322, the Rhind Mathematical Papyrus, All of these texts concern the so-called Pythagorean theorem, which seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry. Greek mathematics greatly refined the methods and expanded the subject matter of mathematics, Chinese mathematics made early contributions, including a place value system. Islamic mathematics, in turn, developed and expanded the known to these civilizations. Many Greek and Arabic texts on mathematics were then translated into Latin, from ancient times through the Middle Ages, periods of mathematical discovery were often followed by centuries of stagnation. Beginning in Renaissance Italy in the 16th century, new mathematical developments, the origins of mathematical thought lie in the concepts of number, magnitude, and form. Modern studies of cognition have shown that these concepts are not unique to humans. Such concepts would have part of everyday life in hunter-gatherer societies. The idea of the number concept evolving gradually over time is supported by the existence of languages which preserve the distinction between one, two, and many, but not of numbers larger than two. Prehistoric artifacts discovered in Africa, dated 20,000 years old or more suggest early attempts to quantify time. The Ishango bone, found near the headwaters of the Nile river, may be more than 20,000 years old, common interpretations are that the Ishango bone shows either the earliest known demonstration of sequences of prime numbers or a six-month lunar calendar. He also writes that no attempt has been made to explain why a tally of something should exhibit multiples of two, prime numbers between 10 and 20, and some numbers that are almost multiples of 10, predynastic Egyptians of the 5th millennium BC pictorially represented geometric designs. All of the above are disputed however, and the currently oldest undisputed mathematical documents are from Babylonian, Babylonian mathematics refers to any mathematics of the peoples of Mesopotamia from the days of the early Sumerians through the Hellenistic period almost to the dawn of Christianity. The majority of Babylonian mathematical work comes from two widely separated periods, The first few hundred years of the second millennium BC, and it is named Babylonian mathematics due to the central role of Babylon as a place of study. Later under the Arab Empire, Mesopotamia, especially Baghdad, once again became an important center of study for Islamic mathematics, in contrast to the sparsity of sources in Egyptian mathematics, our knowledge of Babylonian mathematics is derived from more than 400 clay tablets unearthed since the 1850s. Written in Cuneiform script, tablets were inscribed whilst the clay was moist, Some of these appear to be graded homework. The earliest evidence of written mathematics dates back to the ancient Sumerians and they developed a complex system of metrology from 3000 BC. From around 2500 BC onwards, the Sumerians wrote multiplication tables on clay tablets and dealt with geometrical exercises, the earliest traces of the Babylonian numerals also date back to this period
14.
Thales of Miletus
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Thales of Miletus was a pre-Socratic Greek/Phoenician philosopher, mathematician and astronomer from Miletus in Asia Minor. He was one of the Seven Sages of Greece, Thales is recognized for breaking from the use of mythology to explain the world and the universe, and instead explaining natural objects and phenomena by theories and hypothesis, i. e. science. Aristotle reported Thales hypothesis that the principle of nature and the nature of matter was a single material substance. In mathematics, Thales used geometry to calculate the heights of pyramids and he is the first known individual to use deductive reasoning applied to geometry, by deriving four corollaries to Thales theorem. He is the first known individual to whom a mathematical discovery has been attributed, the ancient source, Apollodorus of Athens, writing during the 2nd century BCE, thought Thales was born about the year 625 BCE. The dates of Thales life are not exactly known, but are roughly established by a few events mentioned in the sources. According to Herodotus Thales predicted the eclipse of May 28,585 BC. Diogenes Laërtius quotes the chronicle of Apollodorus of Athens as saying that Thales died at the age of 78 during the 58th Olympiad and attributes his death to heat stroke while watching the games. Plutarch had earlier told this version, Solon visited Thales and asked him why he remained single, nevertheless, several years later, anxious for family, he adopted his nephew Cybisthus. Thales involved himself in many activities, taking the role of an innovator, some say that he left no writings, others say that he wrote On the Solstice and On the Equinox. Diogenes Laërtius quotes two letters from Thales, one to Pherecydes of Syros, offering to review his book on religion, Thales identifies the Milesians as Athenian colonists. He was aware of the existence of the lodestone, and was the first to be connected to knowledge of this in history, according to Aristotle, Thales thought lodestones had souls, because iron is attracted to them. According to Hieronymus, historically quoted by Diogenes Laertius, Thales found the height of pyramids by comparison between the lengths of the shadows cast by a person and by the pyramids, several anecdotes suggest Thales was not just a philosopher, but also a businessman. A story, with different versions, recounts how Thales achieved riches from an olive harvest by prediction of the weather, in one version, he bought all the olive presses in Miletus after predicting the weather and a good harvest for a particular year. Thales’ political life had mainly to do with the involvement of the Ionians in the defense of Anatolia against the power of the Persians. In neighbouring Lydia, a king had come to power, Croesus and he had conquered most of the states of coastal Anatolia, including the cities of the Ionians. The story is told in Herodotus, the war endured for five years, but in the sixth an eclipse of the Sun spontaneously halted a battle in progress. It seems that Thales had predicted this solar eclipse, the Seven Sages were most likely already in existence, as Croesus was also heavily influenced by Solon of Athens, another sage
15.
Thales' Theorem
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In geometry, Thales theorem states that if A, B and C are points on a circle where the line AC is a diameter of the circle, then the angle ∠ABC is a right angle. Thales theorem is a case of the inscribed angle theorem. It is generally attributed to Thales of Miletus, who is said to have offered an ox as a sacrifice of thanksgiving for the discovery, attribution did tend to occur at a later time. Reference to Thales was made by Proclus, and by Diogenes Laertius documenting Pamphilas statement that Thales Indian and Babylonian mathematicians knew this for special cases before Thales proved it. It is believed that Thales learned that an angle inscribed in a semicircle is a right angle during his travels to Babylon, dantes Paradiso refers to Thales theorem in the course of a speech. The following facts are used, the sum of the angles in a triangle is equal to 180° and the base angles of an isosceles triangle are equal. Since OA = OB = OC, ∆OBA and ∆OBC are isosceles triangles, Let α = ∠BAO and β = ∠OBC. The three internal angles of the triangle are α, and β. Since the sum of the angles of a triangle is equal to 180°, the theorem may also be proven using trigonometry, Let O =, A =, and C =. Then B is a point on the unit circle and we will show that ∆ABC forms a right angle by proving that AB and BC are perpendicular — that is, the product of their slopes is equal to –1. Let A B C be a triangle in a circle where A B is a diameter in that circle. Then construct a new triangle A B D by mirroring triangle A B C over the line A B, since lines A C and B D are parallel, likewise for A D and C B, the quadrilateral A C B D is a parallelogram. Since lines A B and C D are both diameters of the circle and therefore are equal length, the parallelogram must be a rectangle, all angles in a rectangle are right angles. For any triangle whatsoever, there is one circle containing all three vertices of the triangle. This circle is called the circumcircle of the triangle, one way of formulating Thales theorem is, if the center of a triangles circumcircle lies on the triangle then the triangle is right, and the center of its circumcircle lies on its hypotenuse. The converse of Thales theorem is then, the center of the circumcircle of a triangle lies on its hypotenuse. Let there be a right angle ∠ABC, r a line parallel to BC passing by A and s a line parallel to AB passing by C, Let D be the point of intersection of lines r and s The quadrilateral ABCD forms a parallelogram by construction. Since in a parallelogram adjacent angles are supplementary and ∠ABC is an angle then angles ∠BAD, ∠BCD
16.
Pythagoras of Samos
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Pythagoras of Samos was an Ionian Greek philosopher, mathematician, and the putative founder of the movement called Pythagoreanism. Most of the information about Pythagoras was written centuries after he lived. He was born on the island of Samos, and travelled, visiting Egypt and Greece, around 530 BC, he moved to Croton, in Magna Graecia, and there established some kind of school or guild. In 520 BC, he returned to Samos, Pythagoras made influential contributions to philosophy and religion in the late 6th century BC. He is often revered as a mathematician and scientist and is best known for the Pythagorean theorem which bears his name. Many of the accomplishments credited to Pythagoras may actually have been accomplishments of his colleagues, some accounts mention that the philosophy associated with Pythagoras was related to mathematics and that numbers were important. It was said that he was the first man to himself a philosopher, or lover of wisdom, and Pythagorean ideas exercised a marked influence on Plato. Burkert states that Aristoxenus and Dicaearchus are the most important accounts, Aristotle had written a separate work On the Pythagoreans, which is no longer extant. However, the Protrepticus possibly contains parts of On the Pythagoreans and his disciples Dicaearchus, Aristoxenus, and Heraclides Ponticus had written on the same subject. These writers, late as they are, were among the best sources from whom Porphyry and Iamblichus drew, while adding some legendary accounts. Herodotus, Isocrates, and other writers agree that Pythagoras was the son of Mnesarchus and born on the Greek island of Samos. His father is said to have been a gem-engraver or a wealthy merchant, a late source gives his mothers name as Pythais. As to the date of his birth, Aristoxenus stated that Pythagoras left Samos in the reign of Polycrates, at the age of 40, around 530 BC he arrived in the Greek colony of Croton in what was then Magna Graecia. There he founded his own school the members of which he engaged to a disciplined. He furthermore aquired some political influence, on Greeks and non-Greeks of the region, following a conflict with the neighbouring colony of Sybaris, internal discord drove most of the Pythagoreans out of Croton. Pythagoras left the city before the outbreak of civil unrest and moved to Metapontum, after his death, his house was transformed into a sanctuary of Demeter, out of veneration for the philosopher, by the local population. In ancient sources there was disagreement and inconsistency about the late life of Pythagoras. His tomb was shown at Metapontum in the time of Cicero, according to Walter Burkert, Most obvious is the contradiction between Aristoxenus and Dicaearchus, regarding the catastrophe that overwhelmed the Pythagorean society
17.
Pythagoreans
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Later revivals of Pythagorean doctrines led to what is now called Neopythagoreanism or Neoplatonism. Pythagorean ideas exercised an influence on Aristotle, and Plato. According to tradition, pythagoreanism developed at some point into two schools of thought, the mathēmatikoi and the akousmatikoi. There is the inner and outer circle John Burnet noted Lastly, we have one admitted instance of a philosophic guild, that of the Pythagoreans. And it will be found that the hypothesis, if it is to be called by that name, of a regular organisation of scientific activity will alone explain all the facts. The development of doctrine in the hands of Thales, Anaximander, according to Iamblichus in The life of Pythagoras, by Thomas Taylor There were also two forms of philosophy, for the two genera of those that pursued it, the Acusmatici and the Mathematici. The latter are acknowledged to be Pythagoreans by the rest but the Mathematici do not admit that the Acusmatici derived their instructions from Pythagoras, memory was the most valued faculty. All these auditions were of three kinds, some signifying what a thing is, others what it especially is, others what ought or ought not to be done. By musical sounds alone unaccompanied with words they healed the passions of the soul and certain diseases, enchanting in reality and it is probable that from hence this name epode, i. e. enchantment, came to be generally used. Each of these he corrected through the rule of virtue, attempering them through appropriate melodies, therefore its function is none of what are called ‘parts of virtue’, for it is better than all of them and the end produced is always better than the knowledge that produces it. Nor is every virtue of the soul in that way a function, nor is success, for if it is to be productive, different ones will produce different things, as the skill of building produces a house. However, intelligence is a part of virtue and of success, according to historians like Thomas Gale, Thomas Taler, or Cantor, Archytas became the head of the school, about a century after the murder of Pythagoras. According to August Böckh, who cites Nicomachus, Philolaus was the successor of Pythagoras, and according to Cicero, Philolaus was teacher of Archytas of Tarentum. According to the historians from the Stanford Encyclopedia of Philosophy, Philolaus and Eurytus are identified by Aristoxenus as teachers of the last generation of Pythagoreans, a Echecrates is mentioned by Aristoxenus as a student of Philolaus and Eurytus. The mathēmatikoi were supposed to have extended and developed the more mathematical, the mathēmatikoi did think that the akousmatikoi were Pythagorean, but felt that their own group was more representative of Pythagoras. Commentary from Sir William Smith, Dictionary of Greek and Roman Biography, Aristotle states the fundamental maxim of the Pythagoreans in various forms. According to Philolaus, number is the dominant and self-produced bond of the continuance of things. But number has two forms, the even and the odd, and a third, resulting from the mixture of the two, the even-odd and this third species is one itself, for it is both even and odd
18.
Hypatia
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Hypatia, often called Hypatia of Alexandria, was a Greek mathematician, astronomer, and philosopher in Egypt, then a part of the Eastern Roman Empire. She was the head of the Neoplatonic school at Alexandria, where she taught philosophy, the mathematician and philosopher Hypatia of Alexandria was the only daughter of the mathematician Theon of Alexandria. Around 400, she became head of the Neoplatonist School in Alexandria, where she imparted the knowledge of Plato and Aristotle to students, including pagans, Christians, however, not all Christians were as hostile towards her, some Christians even used Hypatia as symbolic of Virtue. Having succeeded to the school of Plato and Plotinus, she explained the principles of philosophy to her auditors, many of whom came from a distance to receive her instructions. On account of the self-possession and ease of manner which she had acquired in consequence of the cultivation of her mind, neither did she feel abashed in going to an assembly of men. For all men on account of her dignity and virtue admired her the more. Hypatia corresponded with former pupil Synesius, who was tutored by her in the school of Platonism and later became bishop of Ptolemais in 410. Together with the references by the pagan philosopher Damascius, these are the extant records left by Hypatias pupils at the Platonist school of Alexandria. Hypatia was murdered during an episode of city-wide anger stemming from a feud between Orestes, the prefect of Alexandria, and Cyril, the Bishop of Alexandria and her death is symbolic for some historians. On the other hand, Christian Wildberg notes that Hellenistic philosophy continued to flourish in the 5th and 6th centuries, of the many accounts of Hypatias death, the most complete is the one written around 415 by Socrates Scholasticus and included in the Historia Ecclesiastica. According to this account, in 415 a feud began over Jewish dancing exhibitions in Alexandria, Orestes, the Roman governor of Alexandria, and Cyril, the Bishop of Alexandria, engaged in a bitter feud in which Hypatia eventually became a main point of contention. Orestes published an edict that outlined new regulations for such gatherings, the edict angered Christians as well as Jews. At one such gathering, Hierax, a devout Christian follower of Cyril, read the edict, many people felt that Hierax was attempting to incite the crowd into sedition. Orestes reacted swiftly and violently out of what Scholasticus suspected was jealousy the growing power of the bishops… encroached on the jurisdiction of the authorities and he ordered Hierax to be seized and tortured publicly in the theater. Hearing of Hieraxs severe and public punishment, Cyril threatened to retaliate against the Jews of Alexandria with the utmost severities if the harassment of Christians did not cease immediately. In response to Cyrils threat, the Jews of Alexandria grew even more furious, Socrates of Constantinoples account says that the Jews had plotted to flush out the Christians at night by running through the streets claiming that the Church of Alexander was on fire. The feud between Cyril and Orestes intensified because of things, and both men wrote to the emperor regarding the situation. Eventually, Cyril attempted to out to Orestes through several peace overtures
19.
Al-Khawarizmi
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Muḥammad ibn Mūsā al-Khwārizmī, formerly Latinized as Algoritmi, was a Persian mathematician, astronomer, and geographer during the Abbasid Caliphate, a scholar in the House of Wisdom in Baghdad. In the 12th century, Latin translations of his work on the Indian numerals introduced the decimal number system to the Western world. Al-Khwārizmīs The Compendious Book on Calculation by Completion and Balancing presented the first systematic solution of linear and he is often considered one of the fathers of algebra. He revised Ptolemys Geography and wrote on astronomy and astrology, some words reflect the importance of al-Khwārizmīs contributions to mathematics. Algebra is derived from al-jabr, one of the two operations he used to solve quadratic equations, algorism and algorithm stem from Algoritmi, the Latin form of his name. His name is also the origin of guarismo and of algarismo, few details of al-Khwārizmīs life are known with certainty. He was born in a Persian family and Ibn al-Nadim gives his birthplace as Khwarezm in Greater Khorasan, muhammad ibn Jarir al-Tabari gives his name as Muḥammad ibn Musá al-Khwārizmiyy al-Majūsiyy al-Quṭrubbaliyy. The epithet al-Qutrubbulli could indicate he might instead have come from Qutrubbul and this would not be worth mentioning if a series of errors concerning the personality of al-Khwārizmī, occasionally even the origins of his knowledge, had not been made. Recently, G. J. Toomer. with naive confidence constructed an entire fantasy on the error which cannot be denied the merit of amusing the reader. Regarding al-Khwārizmīs religion, Toomer writes, Another epithet given to him by al-Ṭabarī, al-Majūsī, Ibn al-Nadīms Kitāb al-Fihrist includes a short biography on al-Khwārizmī together with a list of the books he wrote. Al-Khwārizmī accomplished most of his work in the period between 813 and 833, douglas Morton Dunlop suggests that it may have been possible that Muḥammad ibn Mūsā al-Khwārizmī was in fact the same person as Muḥammad ibn Mūsā ibn Shākir, the eldest of the three Banū Mūsā. Al-Khwārizmīs contributions to mathematics, geography, astronomy, and cartography established the basis for innovation in algebra, on the Calculation with Hindu Numerals written about 825, was principally responsible for spreading the Hindu–Arabic numeral system throughout the Middle East and Europe. It was translated into Latin as Algoritmi de numero Indorum, al-Khwārizmī, rendered as Algoritmi, led to the term algorithm. Some of his work was based on Persian and Babylonian astronomy, Indian numbers, al-Khwārizmī systematized and corrected Ptolemys data for Africa and the Middle East. Another major book was Kitab surat al-ard, presenting the coordinates of places based on those in the Geography of Ptolemy but with improved values for the Mediterranean Sea, Asia and he also wrote on mechanical devices like the astrolabe and sundial. He assisted a project to determine the circumference of the Earth and in making a map for al-Mamun. When, in the 12th century, his works spread to Europe through Latin translations, the Compendious Book on Calculation by Completion and Balancing is a mathematical book written approximately 830 CE. The term algebra is derived from the name of one of the operations with equations described in this book
20.
Optics
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Optics is the branch of physics which involves the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviolet, and infrared light, because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties. Most optical phenomena can be accounted for using the classical description of light. Complete electromagnetic descriptions of light are, however, often difficult to apply in practice, practical optics is usually done using simplified models. The most common of these, geometric optics, treats light as a collection of rays that travel in straight lines, physical optics is a more comprehensive model of light, which includes wave effects such as diffraction and interference that cannot be accounted for in geometric optics. Historically, the model of light was developed first, followed by the wave model of light. Progress in electromagnetic theory in the 19th century led to the discovery that waves were in fact electromagnetic radiation. Some phenomena depend on the fact that light has both wave-like and particle-like properties, explanation of these effects requires quantum mechanics. When considering lights particle-like properties, the light is modelled as a collection of particles called photons, quantum optics deals with the application of quantum mechanics to optical systems. Optical science is relevant to and studied in many related disciplines including astronomy, various engineering fields, photography, practical applications of optics are found in a variety of technologies and everyday objects, including mirrors, lenses, telescopes, microscopes, lasers, and fibre optics. Optics began with the development of lenses by the ancient Egyptians and Mesopotamians, the earliest known lenses, made from polished crystal, often quartz, date from as early as 700 BC for Assyrian lenses such as the Layard/Nimrud lens. The ancient Romans and Greeks filled glass spheres with water to make lenses, the word optics comes from the ancient Greek word ὀπτική, meaning appearance, look. Greek philosophy on optics broke down into two opposing theories on how vision worked, the theory and the emission theory. The intro-mission approach saw vision as coming from objects casting off copies of themselves that were captured by the eye, plato first articulated the emission theory, the idea that visual perception is accomplished by rays emitted by the eyes. He also commented on the parity reversal of mirrors in Timaeus, some hundred years later, Euclid wrote a treatise entitled Optics where he linked vision to geometry, creating geometrical optics. Ptolemy, in his treatise Optics, held a theory of vision, the rays from the eye formed a cone, the vertex being within the eye. The rays were sensitive, and conveyed back to the observer’s intellect about the distance. He summarised much of Euclid and went on to describe a way to measure the angle of refraction, during the Middle Ages, Greek ideas about optics were resurrected and extended by writers in the Muslim world
21.
Astronomy
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Astronomy is a natural science that studies celestial objects and phenomena. It applies mathematics, physics, and chemistry, in an effort to explain the origin of those objects and phenomena and their evolution. Objects of interest include planets, moons, stars, galaxies, and comets, while the phenomena include supernovae explosions, gamma ray bursts, more generally, all astronomical phenomena that originate outside Earths atmosphere are within the purview of astronomy. A related but distinct subject, physical cosmology, is concerned with the study of the Universe as a whole, Astronomy is the oldest of the natural sciences. The early civilizations in recorded history, such as the Babylonians, Greeks, Indians, Egyptians, Nubians, Iranians, Chinese, during the 20th century, the field of professional astronomy split into observational and theoretical branches. Observational astronomy is focused on acquiring data from observations of astronomical objects, theoretical astronomy is oriented toward the development of computer or analytical models to describe astronomical objects and phenomena. The two fields complement each other, with theoretical astronomy seeking to explain the results and observations being used to confirm theoretical results. Astronomy is one of the few sciences where amateurs can play an active role, especially in the discovery. Amateur astronomers have made and contributed to many important astronomical discoveries, Astronomy means law of the stars. Astronomy should not be confused with astrology, the system which claims that human affairs are correlated with the positions of celestial objects. Although the two share a common origin, they are now entirely distinct. Generally, either the term astronomy or astrophysics may be used to refer to this subject, however, since most modern astronomical research deals with subjects related to physics, modern astronomy could actually be called astrophysics. Few fields, such as astrometry, are purely astronomy rather than also astrophysics, some titles of the leading scientific journals in this field includeThe Astronomical Journal, The Astrophysical Journal and Astronomy and Astrophysics. In early times, astronomy only comprised the observation and predictions of the motions of objects visible to the naked eye, in some locations, early cultures assembled massive artifacts that possibly had some astronomical purpose. Before tools such as the telescope were invented, early study of the stars was conducted using the naked eye, most of early astronomy actually consisted of mapping the positions of the stars and planets, a science now referred to as astrometry. From these observations, early ideas about the motions of the planets were formed, and the nature of the Sun, Moon, the Earth was believed to be the center of the Universe with the Sun, the Moon and the stars rotating around it. This is known as the model of the Universe, or the Ptolemaic system. The Babylonians discovered that lunar eclipses recurred in a cycle known as a saros
22.
Ibn al-Haytham
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Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham, also known by the Latinization Alhazen or Alhacen, was an Arab Muslim scientist, mathematician, astronomer, and philosopher. Ibn al-Haytham made significant contributions to the principles of optics, astronomy, mathematics and he was the first to explain that vision occurs when light bounces on an object and then is directed to ones eyes. He spent most of his close to the court of the Fatimid Caliphate in Cairo and earned his living authoring various treatises. In medieval Europe, Ibn al-Haytham was honored as Ptolemaeus Secundus or simply called The Physicist and he is also sometimes called al-Baṣrī after his birthplace Basra in Iraq, or al-Miṣrī. Ibn al-Haytham was born c.965 in Basra, which was part of the Buyid emirate. Alhazen arrived in Cairo under the reign of Fatimid Caliph al-Hakim, Alhazen continued to live in Cairo, in the neighborhood of the famous University of al-Azhar, until his death in 1040. Legend has it that after deciding the scheme was impractical and fearing the caliphs anger, during this time, he wrote his influential Book of Optics and continued to write further treatises on astronomy, geometry, number theory, optics and natural philosophy. Among his students were Sorkhab, a Persian from Semnan who was his student for three years, and Abu al-Wafa Mubashir ibn Fatek, an Egyptian prince who learned mathematics from Alhazen. Alhazen made significant contributions to optics, number theory, geometry, astronomy, Alhazens work on optics is credited with contributing a new emphasis on experiment. In al-Andalus, it was used by the prince of the Banu Hud dynasty of Zaragossa and author of an important mathematical text. A Latin translation of the Kitab al-Manazir was made probably in the twelfth or early thirteenth century. His research in catoptrics centred on spherical and parabolic mirrors and spherical aberration and he made the observation that the ratio between the angle of incidence and refraction does not remain constant, and investigated the magnifying power of a lens. His work on catoptrics also contains the known as Alhazens problem. Alhazen wrote as many as 200 books, although only 55 have survived, some of his treatises on optics survived only through Latin translation. During the Middle Ages his books on cosmology were translated into Latin, Hebrew, the crater Alhazen on the Moon is named in his honour, as was the asteroid 59239 Alhazen. In honour of Alhazen, the Aga Khan University named its Ophthalmology endowed chair as The Ibn-e-Haitham Associate Professor, Alhazen, by the name Ibn al-Haytham, is featured on the obverse of the Iraqi 10, 000-dinar banknote issued in 2003, and on 10-dinar notes from 1982. The 2015 International Year of Light celebrated the 1000th anniversary of the works on optics by Ibn Al-Haytham, Alhazens most famous work is his seven-volume treatise on optics Kitab al-Manazir, written from 1011 to 1021. Optics was translated into Latin by a scholar at the end of the 12th century or the beginning of the 13th century
23.
Renaissance
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The Renaissance was a period in European history, from the 14th to the 17th century, regarded as the cultural bridge between the Middle Ages and modern history. It started as a movement in Italy in the Late Medieval period and later spread to the rest of Europe. This new thinking became manifest in art, architecture, politics, science, Early examples were the development of perspective in oil painting and the recycled knowledge of how to make concrete. Although the invention of movable type sped the dissemination of ideas from the later 15th century. In politics, the Renaissance contributed to the development of the customs and conventions of diplomacy, the Renaissance began in Florence, in the 14th century. Other major centres were northern Italian city-states such as Venice, Genoa, Milan, Bologna, the word Renaissance, literally meaning Rebirth in French, first appeared in English in the 1830s. The word also occurs in Jules Michelets 1855 work, Histoire de France, the word Renaissance has also been extended to other historical and cultural movements, such as the Carolingian Renaissance and the Renaissance of the 12th century. The Renaissance was a movement that profoundly affected European intellectual life in the early modern period. Renaissance scholars employed the humanist method in study, and searched for realism, however, a subtle shift took place in the way that intellectuals approached religion that was reflected in many other areas of cultural life. In addition, many Greek Christian works, including the Greek New Testament, were back from Byzantium to Western Europe. Political philosophers, most famously Niccolò Machiavelli, sought to describe life as it really was. Others see more competition between artists and polymaths such as Brunelleschi, Ghiberti, Donatello, and Masaccio for artistic commissions as sparking the creativity of the Renaissance. Yet it remains much debated why the Renaissance began in Italy, accordingly, several theories have been put forward to explain its origins. During the Renaissance, money and art went hand in hand, Artists depended entirely on patrons while the patrons needed money to foster artistic talent. Wealth was brought to Italy in the 14th, 15th, and 16th centuries by expanding trade into Asia, silver mining in Tyrol increased the flow of money. Luxuries from the Eastern world, brought home during the Crusades, increased the prosperity of Genoa, unlike with Latin texts, which had been preserved and studied in Western Europe since late antiquity, the study of ancient Greek texts was very limited in medieval Western Europe. One of the greatest achievements of Renaissance scholars was to bring this entire class of Greek cultural works back into Western Europe for the first time since late antiquity, Arab logicians had inherited Greek ideas after they had invaded and conquered Egypt and the Levant. Their translations and commentaries on these ideas worked their way through the Arab West into Spain and Sicily and this work of translation from Islamic culture, though largely unplanned and disorganized, constituted one of the greatest transmissions of ideas in history
24.
Luca Pacioli
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Fra Luca Bartolomeo de Pacioli was an Italian mathematician, Franciscan friar, collaborator with Leonardo da Vinci, and a seminal contributor to the field now known as accounting. He is referred to as The Father of Accounting and Bookkeeping in Europe and he was also called Luca di Borgo after his birthplace, Borgo Sansepolcro, Tuscany. Luca Pacioli was born between 1446 and 1448 in Sansepolcro where he received an abbaco education and this was education in the vernacular rather than Latin and focused on the knowledge required of merchants. His father was Bartolomeo Pacioli, however Luca Pacioli was said to have lived with the Befolci family as a child in his birth town Sansepolcro. He moved to Venice around 1464, where he continued his own education while working as a tutor to the three sons of a merchant and it was during this period that he wrote his first book, a treatise on arithmetic for the boys he was tutoring. Between 1472 and 1475, he became a Franciscan friar, in 1475, he started teaching in Perugia, first as a private teacher, from 1477 holding the first chair in mathematics. He wrote a textbook in the vernacular for his students. He continued to work as a tutor of mathematics and was, in fact. In 1494, his first book to be printed, Summa de arithmetica, proportioni et proportionalita, was published in Venice. In 1497, he accepted an invitation from Duke Ludovico Sforza to work in Milan, there he met, taught mathematics to, collaborated and lived with Leonardo da Vinci. In 1499, Pacioli and Leonardo were forced to flee Milan when Louis XII of France seized the city and their paths appear to have finally separated around 1506. Pacioli died at about the age of 70 in 1517, most likely in Sansepolcro where it is thought that he had spent much of his final years, the manuscript was written between December 1477 and 29 April 1478. It contains 16 sections on merchant arithmetic, such as barter, exchange, profit, mixing metals, one part of 25 pages is missing from the chapter on algebra. A modern transcription has been published by Calzoni and Cavazzoni along with a translation of the chapter on partitioning problems. Proportioni et proportionalita, a textbook for use in the schools of Northern Italy and it was a synthesis of the mathematical knowledge of his time and contained the first printed work on algebra written in the vernacular. It is also notable for including the first published description of the method that Venetian merchants used during the Italian Renaissance. The system he published included most of the cycle as we know it today. He described the use of journals and ledgers, and warned that a person should not go to sleep at night until the debits equaled the credits
25.
Accounting
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Accounting or accountancy is the measurement, processing and communication of financial information about economic entities such as businesses and corporations. The modern field was established by the Italian mathematician Luca Pacioli in 1494, practitioners of accounting are known as accountants. The terms accounting and financial reporting are often used as synonyms, Accounting can be divided into several fields including financial accounting, management accounting, external auditing, and tax accounting. Accounting information systems are designed to support accounting functions and related activities, Accounting is facilitated by accounting organizations such as standard-setters, accounting firms and professional bodies. Financial statements are audited by accounting firms, and are prepared in accordance with generally accepted accounting principles. GAAP is set by various standard-setting organizations such as the Financial Accounting Standards Board in the United States, as of 2012, all major economies have plans to converge towards or adopt the International Financial Reporting Standards. The history of accounting is thousands of old and can be traced to ancient civilizations. By the time of the Emperor Augustus, the Roman government had access to detailed financial information, double-entry bookkeeping developed in medieval Europe, and accounting split into financial accounting and management accounting with the development of joint-stock companies. The first work on a double-entry bookkeeping system was published in Italy, both the words accounting and accountancy were in use in Great Britain by the mid-1800s, and are derived from the words accompting and accountantship used in the 18th century. In Middle English the verb to account had the form accounten, which was derived from the Old French word aconter, which is in turn related to the Vulgar Latin word computare, meaning to reckon. The base of computare is putare, which meant to prune, to purify, to correct an account, hence, to count or calculate. The word accountant is derived from the French word compter, which is derived from the Italian. Accountancy refers to the occupation or profession of an accountant, particularly in British English, Accounting has several subfields or subject areas, including financial accounting, management accounting, auditing, taxation and accounting information systems. Financial accounting focuses on the reporting of a financial information to external users of the information, such as investors. It calculates and records business transactions and prepares financial statements for the users in accordance with generally accepted accounting principles. GAAP, in turn, arises from the agreement between accounting theory and practice, and change over time to meet the needs of decision-makers. This branch of accounting is also studied as part of the exams for qualifying as an actuary. It is interesting to note that two professionals, accountants and actuaries, have created a culture of being archrivals
26.
Gerolamo Cardano
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He wrote more than 200 works on science. He made significant contributions to hypocycloids, published in De proportionibus, the generating circles of these hypocycloids were later named Cardano circles or cardanic circles and were used for the construction of the first high-speed printing presses. Today, he is known for his achievements in algebra. He was born in Pavia, Lombardy, the child of Fazio Cardano, a mathematically gifted jurist, lawyer. In his autobiography, Cardano wrote that his mother, Chiara Micheri, had taken various abortive medicines to terminate the pregnancy, he was taken by violent means from my mother and she was in labour for three days. Shortly before his birth, his mother had to move from Milan to Pavia to escape the Plague and his eccentric and confrontational style did not earn him many friends and he had a difficult time finding work after his studies had ended. In 1525, Cardano repeatedly applied to the College of Physicians in Milan and he suffered from impotence throughout the early part of his life, but recovered and married Lucia Banderini in 1531. Before her death in 1546, she bore him three children, Giovanni Battista, Chiara and Aldo, Cardano was the first mathematician to make systematic use of numbers less than zero. He published with attribution the solution of Scipione del Ferro to the cubic equation and the solution of his student Lodovico Ferrari to the quartic equation in his 1545 book Ars Magna. The solution to one case of the cubic equation a x 3 + b x + c =0, had been communicated to him by Niccolò Fontana Tartaglia in the form of a poem. In Opus novum de proportionibus he introduced the binomial coefficients and the binomial theorem, Cardano was notoriously short of money and kept himself solvent by being an accomplished gambler and chess player. He used the game of throwing dice to understand the concepts of probability. He demonstrated the efficacy of defining odds as the ratio of favourable to unfavourable outcomes and he was also aware of the multiplication rule for independent events but was not certain about what values should be multiplied. Cardano made several contributions to hydrodynamics and held that perpetual motion is impossible and he published two encyclopedias of natural science which contain a wide variety of inventions, facts, and occult superstitions. He also introduced the Cardan grille, a tool, in 1550. Someone also assigned to Cardano the credit for the invention of the so-called Cardanos Rings, also called Chinese Rings and he was familiar with a report by Rudolph Agricola about a deaf mute who had learned to write. Two of Cardanos children—Giovanni and Aldo Battista—came to ignoble ends, Giovanni Battista, Cardanos eldest and favorite son, was tried and beheaded in 1560 for poisoning his wife, after he discovered that their three children were not his. Aldo Battista was a gambler, who stole money from his father and was disinherited by him in 1569, Cardano was arrested by the Inquisition in 1570 for unknown reasons, and forced to spend several months in prison and abjure his professorship
27.
Robert Recorde
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Robert Recorde was a Welsh physician and mathematician. He invented the sign and also introduced the pre-existing plus sign to English speakers in 1557. A member of a family of Tenby, Wales, born in 1512, Recorde entered the University of Oxford about 1525. Having adopted medicine as a profession, he went to the University of Cambridge to take the degree of M. D. in 1545 and he afterwards returned to Oxford, where he publicly taught mathematics, as he had done prior to going to Cambridge. It appears that he went to London, and acted as physician to King Edward VI and to Queen Mary. He was also controller of the Royal Mint and served as Comptroller of Mines and Monies in Ireland, after being sued for defamation by a political enemy, he was arrested for debt and died in the Kings Bench Prison, Southwark, by the middle of June 1558. The Pathway to Knowledge, containing the First Principles of Geometry, a book explaining Ptolemaic astronomy while mentioning the Copernican heliocentric model in passing. The Whetstone of Witte, whiche is the seconde parte of Arithmeteke, containing the extraction of rootes, the practise, with the rule of equation. This was the book in which the sign was introduced. With the publication of this book Recorde is credited with introducing algebra into England, a medical work, The Urinal of Physick, frequently reprinted. Sherburne states that Recorde also published Cosmographiae isagoge, and that he wrote books entitled De Arte faciendi Horologium, recordes chief contributions to the progress of algebra were in the way of systematising its notation. This article incorporates text from a now in the public domain, Chisholm, Hugh, ed. Recorde. The World of Mathematics Vol.1 Commentary on Robert Recorde Jourdain, the Nature of Mathematics Roberts, Gareth, and Fenny Smith, eds. Robert Recorde, The Life and Times of a Tudor Mathematician 232 pages Williams, Jack, Robert Recorde, Tudor Polymath, Expositor, the Mathematical Gazette Vol.60 No.411 Mar 1976 p 59-61 Roberts, Gordon, Robert Recorde, Tudor Scholar and Mathematician
28.
Robert Hooke
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Robert Hooke FRS was an English natural philosopher, architect and polymath. Allan Chapman has characterised him as Englands Leonardo, Robert Gunthers Early Science in Oxford, a history of science in Oxford during the Protectorate, Restoration and Age of Enlightenment, devotes five of its fourteen volumes to Hooke. Hooke studied at Wadham College, Oxford during the Protectorate where he became one of a tightly knit group of ardent Royalists led by John Wilkins. Here he was employed as an assistant to Thomas Willis and to Robert Boyle and he built some of the earliest Gregorian telescopes and observed the rotations of Mars and Jupiter. In 1665 he inspired the use of microscopes for scientific exploration with his book, based on his microscopic observations of fossils, Hooke was an early proponent of biological evolution. Much of Hookes scientific work was conducted in his capacity as curator of experiments of the Royal Society, much of what is known of Hookes early life comes from an autobiography that he commenced in 1696 but never completed. Richard Waller mentions it in his introduction to The Posthumous Works of Robert Hooke, the work of Waller, along with John Wards Lives of the Gresham Professors and John Aubreys Brief Lives, form the major near-contemporaneous biographical accounts of Hooke. Robert Hooke was born in 1635 in Freshwater on the Isle of Wight to John Hooke, Robert was the last of four children, two boys and two girls, and there was an age difference of seven years between him and the next youngest. Their father John was a Church of England priest, the curate of Freshwaters Church of All Saints, Robert Hooke was expected to succeed in his education and join the Church. John Hooke also was in charge of a school, and so was able to teach Robert. He was a Royalist and almost certainly a member of a group who went to pay their respects to Charles I when he escaped to the Isle of Wight, Robert, too, grew up to be a staunch monarchist. As a youth, Robert Hooke was fascinated by observation, mechanical works and he dismantled a brass clock and built a wooden replica that, by all accounts, worked well enough, and he learned to draw, making his own materials from coal, chalk and ruddle. Hooke quickly mastered Latin and Greek, made study of Hebrew. Here, too, he embarked on his study of mechanics. It appears that Hooke was one of a group of students whom Busby educated in parallel to the work of the school. Contemporary accounts say he was not much seen in the school, in 1653, Hooke secured a choristers place at Christ Church, Oxford. He was employed as an assistant to Dr Thomas Willis. There he met the natural philosopher Robert Boyle, and gained employment as his assistant from about 1655 to 1662, constructing, operating and he did not take his Master of Arts until 1662 or 1663
29.
Robert Boyle
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Robert William Boyle FRS was an Anglo-Irish natural philosopher, chemist, physicist and inventor born in Lismore, County Waterford, Ireland. Boyle is largely regarded today as the first modern chemist, and therefore one of the founders of modern chemistry, and one of the pioneers of modern experimental scientific method. He is best known for Boyles law, which describes the proportional relationship between the absolute pressure and volume of a gas, if the temperature is kept constant within a closed system. Among his works, The Sceptical Chymist is seen as a book in the field of chemistry. He was a devout and pious Anglican and is noted for his writings in theology, Boyle was born in Lismore Castle, in County Waterford, Ireland, the seventh son and fourteenth child of Richard Boyle, 1st Earl of Cork, and Catherine Fenton. Richard Boyle arrived in Dublin from England in 1588 during the Tudor plantations of Ireland and he had amassed enormous landholdings by the time Robert was born. As a child, Boyle was fostered to a local family, Boyle received private tutoring in Latin, Greek, and French and when he was eight years old, following the death of his mother, he was sent to Eton College in England. His fathers friend, Sir Henry Wotton, was then the provost of the college, during this time, his father hired a private tutor, Robert Carew, who had knowledge of Irish, to act as private tutor to his sons in Eton. After spending over three years at Eton, Robert travelled abroad with a French tutor and they visited Italy in 1641 and remained in Florence during the winter of that year studying the paradoxes of the great star-gazer Galileo Galilei, who was elderly but still living in 1641. Boyle returned to England from continental Europe in mid-1644 with a keen interest in scientific research and his father had died the previous year and had left him the manor of Stalbridge in Dorset, England and substantial estates in County Limerick in Ireland that he had acquired. They met frequently in London, often at Gresham College, having made several visits to his Irish estates beginning in 1647, Robert moved to Ireland in 1652 but became frustrated at his inability to make progress in his chemical work. In one letter, he described Ireland as a country where chemical spirits were so misunderstood. In 1654, Boyle left Ireland for Oxford to pursue his work more successfully, an inscription can be found on the wall of University College, Oxford the High Street at Oxford, marking the spot where Cross Hall stood until the early 19th century. It was here that Boyle rented rooms from the apothecary who owned the Hall. An account of Boyles work with the air pump was published in 1660 under the title New Experiments Physico-Mechanical, Touching the Spring of the Air, the person who originally formulated the hypothesis was Henry Power in 1661. Boyle in 1662 included a reference to a written by Power. In continental Europe the hypothesis is attributed to Edme Mariotte. In 1680 he was elected president of the society, but declined the honour from a scruple about oaths and they are extraordinary because all but a few of the 24 have come true
30.
Isaac Newton
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His book Philosophiæ Naturalis Principia Mathematica, first published in 1687, laid the foundations of classical mechanics. Newton also made contributions to optics, and he shares credit with Gottfried Wilhelm Leibniz for developing the infinitesimal calculus. Newtons Principia formulated the laws of motion and universal gravitation that dominated scientists view of the universe for the next three centuries. Newtons work on light was collected in his influential book Opticks. He also formulated a law of cooling, made the first theoretical calculation of the speed of sound. Newton was a fellow of Trinity College and the second Lucasian Professor of Mathematics at the University of Cambridge, politically and personally tied to the Whig party, Newton served two brief terms as Member of Parliament for the University of Cambridge, in 1689–90 and 1701–02. He was knighted by Queen Anne in 1705 and he spent the last three decades of his life in London, serving as Warden and Master of the Royal Mint and his father, also named Isaac Newton, had died three months before. Born prematurely, he was a child, his mother Hannah Ayscough reportedly said that he could have fit inside a quart mug. When Newton was three, his mother remarried and went to live with her new husband, the Reverend Barnabas Smith, leaving her son in the care of his maternal grandmother, Newtons mother had three children from her second marriage. From the age of twelve until he was seventeen, Newton was educated at The Kings School, Grantham which taught Latin and Greek. He was removed from school, and by October 1659, he was to be found at Woolsthorpe-by-Colsterworth, Henry Stokes, master at the Kings School, persuaded his mother to send him back to school so that he might complete his education. Motivated partly by a desire for revenge against a bully, he became the top-ranked student. In June 1661, he was admitted to Trinity College, Cambridge and he started as a subsizar—paying his way by performing valets duties—until he was awarded a scholarship in 1664, which guaranteed him four more years until he would get his M. A. He set down in his notebook a series of Quaestiones about mechanical philosophy as he found it, in 1665, he discovered the generalised binomial theorem and began to develop a mathematical theory that later became calculus. Soon after Newton had obtained his B. A. degree in August 1665, in April 1667, he returned to Cambridge and in October was elected as a fellow of Trinity. Fellows were required to become ordained priests, although this was not enforced in the restoration years, however, by 1675 the issue could not be avoided and by then his unconventional views stood in the way. Nevertheless, Newton managed to avoid it by means of a special permission from Charles II. A and he was elected a Fellow of the Royal Society in 1672. Newtons work has been said to distinctly advance every branch of mathematics then studied and his work on the subject usually referred to as fluxions or calculus, seen in a manuscript of October 1666, is now published among Newtons mathematical papers
31.
Lucasian Professor of Mathematics
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The Lucasian Chair of Mathematics is a mathematics professorship in the University of Cambridge, England, its holder is known as the Lucasian Professor. The post was founded in 1663 by Henry Lucas, who was Cambridge Universitys Member of Parliament from 1639–1640, the current and 19th Lucasian Professor is Michael Cates, succeeding Michael Green now retired, starting from 1 July 2015. The previous holder of the post was the theoretical physicist Michael Green who was a fellow in Clare Hall at the University of Cambridge. He was appointed in October 2009, succeeding Stephen Hawking, who retired in September 2009, in the year of his 67th birthday. Hawking and Green now hold the position of Emeritus Lucasian Professor of Mathematics, kevin Knox and Richard Noakes, From Newton to Hawking, A History of Cambridge Universitys Lucasian Professors of Mathematics ISBN 0-521-66310-5
32.
Friedrich Schleiermacher
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He also became influential in the evolution of Higher Criticism, and his work forms part of the foundation of the modern field of hermeneutics. Because of his effect on subsequent Christian thought, he is often called the Father of Modern Liberal Theology and is considered an early leader in liberal Christianity. The Neo-Orthodoxy movement of the century, typically seen to be spearheaded by Karl Barth, was in many ways an attempt to challenge his influence. As a theology student Schleiermacher pursued an independent course of reading and neglected the study of the Old Testament, at the same time he studied the writings of Immanuel Kant and Friedrich Heinrich Jacobi, and began to apply ideas from the Greek philosophers to a reconstruction of Kants system. Schleiermacher developed a deep-rooted skepticism as a student, and soon he rejected orthodox Christianity and he has himself read some of the skeptical literature, he says, and can assure Schleiermacher that it is not worth wasting time on. For six whole months there is no word from his son. In a moving letter of 21 January 1787, Schleiermacher admits that the doubts alluded to are his own and his father has said that faith is the regalia of the Godhead, that is, Gods royal due. Schleiermacher confessed, Faith is the regalia of the Godhead, you say, I cannot believe that he who called himself the Son of Man was the true, eternal God, I cannot believe that his death was a vicarious atonement. Two years later, in 1796, he became chaplain to the Charité Hospital in Berlin, here Schleiermacher became acquainted with art, literature, science and general culture. He was strongly influenced by German Romanticism, as represented by his friend Karl Wilhelm Friedrich von Schlegel, though his ultimate principles remained unchanged, he placed more emphasis on human emotion and the imagination. Meanwhile, he studied Spinoza and Plato, both of whom were important influences and he became more indebted to Kant, though they differed on fundamental points. He sympathised with some of Jacobis positions, and took some ideas from Fichte, the literary product of this period of rapid development was his influential book, Reden über die Religion and his new years gift to the new century, the Monologen. This established the programme of his subsequent theological system, from 1802 to 1804, Schleiermacher served as a pastor in the Pomeranian town of Stolp. He relieved Friedrich Schlegel entirely of his responsibility for the translation of Plato. The obscurity of the style and its negative tone prevented immediate success. At the foundation of the University of Berlin, in which he took a prominent part, Schleiermacher obtained a theological chair, and soon became secretary to the Prussian Academy of Sciences. The twenty-four years of his career in Berlin began with his short outline of theological study. At the same time Schleiermacher prepared his chief theological work Der christliche Glaube nach den Grundsätzen der evangelischen Kirche and he felt isolated, although his church and his lecture-room continued to be crowded
33.
Age of Enlightenment
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The Enlightenment was an intellectual movement which dominated the world of ideas in Europe during the 18th century, The Century of Philosophy. In France, the doctrines of les Lumières were individual liberty and religious tolerance in opposition to an absolute monarchy. French historians traditionally place the Enlightenment between 1715, the year that Louis XIV died, and 1789, the beginning of the French Revolution, some recent historians begin the period in the 1620s, with the start of the scientific revolution. Les philosophes of the widely circulated their ideas through meetings at scientific academies, Masonic lodges, literary salons, coffee houses. The ideas of the Enlightenment undermined the authority of the monarchy and the Church, a variety of 19th-century movements, including liberalism and neo-classicism, trace their intellectual heritage back to the Enlightenment. The Age of Enlightenment was preceded by and closely associated with the scientific revolution, earlier philosophers whose work influenced the Enlightenment included Francis Bacon, René Descartes, John Locke, and Baruch Spinoza. The major figures of the Enlightenment included Cesare Beccaria, Voltaire, Denis Diderot, Jean-Jacques Rousseau, David Hume, Adam Smith, Benjamin Franklin visited Europe repeatedly and contributed actively to the scientific and political debates there and brought the newest ideas back to Philadelphia. Thomas Jefferson closely followed European ideas and later incorporated some of the ideals of the Enlightenment into the Declaration of Independence, others like James Madison incorporated them into the Constitution in 1787. The most influential publication of the Enlightenment was the Encyclopédie, the ideas of the Enlightenment played a major role in inspiring the French Revolution, which began in 1789. After the Revolution, the Enlightenment was followed by an intellectual movement known as Romanticism. René Descartes rationalist philosophy laid the foundation for enlightenment thinking and his attempt to construct the sciences on a secure metaphysical foundation was not as successful as his method of doubt applied in philosophic areas leading to a dualistic doctrine of mind and matter. His skepticism was refined by John Lockes 1690 Essay Concerning Human Understanding and his dualism was challenged by Spinozas uncompromising assertion of the unity of matter in his Tractatus and Ethics. Both lines of thought were opposed by a conservative Counter-Enlightenment. In the mid-18th century, Paris became the center of an explosion of philosophic and scientific activity challenging traditional doctrines, the political philosopher Montesquieu introduced the idea of a separation of powers in a government, a concept which was enthusiastically adopted by the authors of the United States Constitution. Francis Hutcheson, a philosopher, described the utilitarian and consequentialist principle that virtue is that which provides, in his words. Much of what is incorporated in the method and some modern attitudes towards the relationship between science and religion were developed by his protégés David Hume and Adam Smith. Hume became a figure in the skeptical philosophical and empiricist traditions of philosophy. Immanuel Kant tried to reconcile rationalism and religious belief, individual freedom and political authority, as well as map out a view of the sphere through private
34.
University of Oxford
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The University of Oxford is a collegiate research university located in Oxford, England. It grew rapidly from 1167 when Henry II banned English students from attending the University of Paris, after disputes between students and Oxford townsfolk in 1209, some academics fled north-east to Cambridge where they established what became the University of Cambridge. The two ancient universities are frequently referred to as Oxbridge. The university is made up of a variety of institutions, including 38 constituent colleges, All the colleges are self-governing institutions within the university, each controlling its own membership and with its own internal structure and activities. Being a city university, it not have a main campus, instead, its buildings. Oxford is the home of the Rhodes Scholarship, one of the worlds oldest and most prestigious scholarships, the university operates the worlds oldest university museum, as well as the largest university press in the world and the largest academic library system in Britain. Oxford has educated many notable alumni, including 28 Nobel laureates,27 Prime Ministers of the United Kingdom, the University of Oxford has no known foundation date. Teaching at Oxford existed in form as early as 1096. It grew quickly in 1167 when English students returned from the University of Paris, the historian Gerald of Wales lectured to such scholars in 1188 and the first known foreign scholar, Emo of Friesland, arrived in 1190. The head of the university had the title of chancellor from at least 1201, the university was granted a royal charter in 1248 during the reign of King Henry III. After disputes between students and Oxford townsfolk in 1209, some academics fled from the violence to Cambridge, the students associated together on the basis of geographical origins, into two nations, representing the North and the South. In later centuries, geographical origins continued to many students affiliations when membership of a college or hall became customary in Oxford. At about the time, private benefactors established colleges as self-contained scholarly communities. Among the earliest such founders were William of Durham, who in 1249 endowed University College, thereafter, an increasing number of students lived in colleges rather than in halls and religious houses. In 1333–34, an attempt by some dissatisfied Oxford scholars to found a new university at Stamford, Lincolnshire was blocked by the universities of Oxford and Cambridge petitioning King Edward III. Thereafter, until the 1820s, no new universities were allowed to be founded in England, even in London, thus, Oxford and Cambridge had a duopoly, the new learning of the Renaissance greatly influenced Oxford from the late 15th century onwards. Among university scholars of the period were William Grocyn, who contributed to the revival of Greek language studies, and John Colet, the noted biblical scholar. With the English Reformation and the breaking of communion with the Roman Catholic Church, recusant scholars from Oxford fled to continental Europe, as a centre of learning and scholarship, Oxfords reputation declined in the Age of Enlightenment, enrolments fell and teaching was neglected
35.
University of Cambridge
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The University of Cambridge is a collegiate public research university in Cambridge, England, often regarded as one of the most prestigious universities in the world. Founded in 1209 and given royal status by King Henry III in 1231, Cambridge is the second-oldest university in the English-speaking world. The university grew out of an association of scholars who left the University of Oxford after a dispute with the townspeople, the two ancient universities share many common features and are often referred to jointly as Oxbridge. Cambridge is formed from a variety of institutions which include 31 constituent colleges, Cambridge University Press, a department of the university, is the worlds oldest publishing house and the second-largest university press in the world. The university also operates eight cultural and scientific museums, including the Fitzwilliam Museum, Cambridges libraries hold a total of around 15 million books, eight million of which are in Cambridge University Library, a legal deposit library. In the year ended 31 July 2015, the university had an income of £1.64 billion. The central university and colleges have an endowment of around £5.89 billion. The university is linked with the development of the high-tech business cluster known as Silicon Fen. It is a member of associations and forms part of the golden triangle of leading English universities and Cambridge University Health Partners. As of 2017, Cambridge is ranked the fourth best university by three ranking tables and no other institution in the world ranks in the top 10 for as many subjects. Cambridge is consistently ranked as the top university in the United Kingdom, the university has educated many notable alumni, including eminent mathematicians, scientists, politicians, lawyers, philosophers, writers, actors, and foreign Heads of State. Ninety-five Nobel laureates, fifteen British prime ministers and ten Fields medalists have been affiliated with Cambridge as students, faculty, by the late 12th century, the Cambridge region already had a scholarly and ecclesiastical reputation, due to monks from the nearby bishopric church of Ely. The University of Oxford went into suspension in protest, and most scholars moved to such as Paris, Reading. After the University of Oxford reformed several years later, enough remained in Cambridge to form the nucleus of the new university. A bull in 1233 from Pope Gregory IX gave graduates from Cambridge the right to teach everywhere in Christendom, the colleges at the University of Cambridge were originally an incidental feature of the system. No college is as old as the university itself, the colleges were endowed fellowships of scholars. There were also institutions without endowments, called hostels, the hostels were gradually absorbed by the colleges over the centuries, but they have left some indicators of their time, such as the name of Garret Hostel Lane. Hugh Balsham, Bishop of Ely, founded Peterhouse, Cambridges first college, the most recently established college is Robinson, built in the late 1970s
36.
Research
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It is used to establish or confirm facts, reaffirm the results of previous work, solve new or existing problems, support theorems, or develop new theories. A research project may also be an expansion on past work in the field, to test the validity of instruments, procedures, or experiments, research may replicate elements of prior projects or the project as a whole. The primary purposes of research are documentation, discovery, interpretation, or the research and development of methods. Approaches to research depend on epistemologies, which vary considerably both within and between humanities and sciences, there are several forms of research, scientific, humanities, artistic, economic, social, business, marketing, practitioner research, life, technological, etc. The earliest recorded use of the term was in 1577, Research has been defined in a number of different ways. Another definition of research is given by John W. Creswell and it consists of three steps, pose a question, collect data to answer the question, and present an answer to the question. Original research is research that is not exclusively based on a summary and this material is of a primary source character. The purpose of the research is to produce new knowledge. Original research can take a number of forms, depending on the discipline it pertains to, in analytical work, there are typically some new mathematical results produced, or a new way of approaching an existing problem. The degree of originality of the research is among major criteria for articles to be published in academic journals, graduate students are commonly required to perform original research as part of a dissertation. Scientific research is a way of gathering data and harnessing curiosity. This research provides scientific information and theories for the explanation of the nature, scientific research is funded by public authorities, by charitable organizations and by private groups, including many companies. Scientific research can be subdivided into different classifications according to their academic, Research in the humanities involves different methods such as for example hermeneutics and semiotics. Humanities scholars usually do not search for the correct answer to a question. Context is always important, and context can be social, historical, political, cultural, an example of research in the humanities is historical research, which is embodied in historical method. Historians use primary sources and other evidence to systematically investigate a topic, other studies aim to merely examine the occurrence of behaviours in societies and communities, without particularly looking for reasons or motivations to explain these. These studies may be qualitative or quantitative, and can use a variety of approaches, Artistic research, also seen as practice-based research, can take form when creative works are considered both the research and the object of research itself. It is the body of thought which offers an alternative to purely scientific methods in research in its search for knowledge
37.
Laboratories
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A laboratory is a facility that provides controlled conditions in which scientific or technological research, experiments, and measurement may be performed. Laboratories used for scientific research take many forms because of the requirements of specialists in the various fields of science. A physics laboratory might contain a particle accelerator or vacuum chamber, a chemist or biologist might use a wet laboratory, while a psychologists laboratory might be a room with one-way mirrors and hidden cameras in which to observe behavior. In some laboratories, such as commonly used by computer scientists. Scientists in other fields will use other types of laboratories. Engineers use laboratories as well to design, build, and test technological devices, scientific laboratories can be found as research and learning spaces in schools and universities, industry, government, or military facilities, and even aboard ships and spacecraft. Early instances of laboratories recorded in English involved alchemy and the preparation of medicines, larger or more sophisticated equipment is generally called a scientific instrument. Both laboratory equipment and scientific instruments are increasingly being designed and shared using open hardware principles, open source labs use open source scientific hardware. The title of laboratory is used for certain other facilities where the processes or equipment used are similar to those in scientific laboratories. In many labs, though, hazards are present, in laboratories where dangerous conditions might exist, safety precautions are important. Rules exist to minimize the risk, and safety equipment is used to protect the lab user from injury or to assist in responding to an emergency. This standard is referred to as the Laboratory Standard. Under this standard, a laboratory is required to produce a Chemical Hygiene Plan which addresses the specific hazards found in its location, the CHP must be reviewed annually. Many schools and businesses employ safety, health, and environmental specialists, such as a Chemical Hygiene Officer to develop, manage, and evaluate their CHP. Additionally, third party review is used to provide an objective outside view which provides a fresh look at areas. An important element of such audits is the review of regulatory compliance, training is critical to the ongoing safe operation of the laboratory facility. Educators, staff and management must be engaged in working to reduce the likelihood of accidents, injuries, efforts are made to ensure laboratory safety videos are both relevant and engaging. The dictionary definition of laboratory at Wiktionary Media related to Laboratory at Wikimedia Commons Nobel Laureates Interactive 360° Laboratories
38.
University of Berlin
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The Humboldt university model has strongly influenced other European and Western universities. In 1949, it changed its name to Humboldt-Universität in honour of both its founder Wilhelm and his brother, geographer Alexander von Humboldt. The first semester at the newly founded Berlin university occurred in 1810 with 256 students and 52 lecturers in faculties of law, medicine, theology, du Bois and European unifier Robert Schuman, as well as the influential surgeon Johann Friedrich Dieffenbach in the early half of the 1800s. The structure of German research-intensive universities, such as Humboldt, served as a model for institutions like Johns Hopkins University, Alexander von Humboldt, brother of the founder William, promoted the new learning. With the construction of research facilities in the second half of the 19th Century teaching of the natural sciences began. During this period of enlargement, Berlin University gradually expanded to other previously separate colleges in Berlin. An example would be the Charité, the Pépinière and the Collegium Medico-chirurgicum, in 1717, King Friedrich I had built a quarantine house for Plague at the city gates, which in 1727 was rechristened by the soldier king Friedrich Wilhelm, Es soll das Haus die Charité heißen. By 1829 the site became Berlin Universitys medical campus and remained so until 1927 when the more modern University Hospital was constructed, Berlin University started a natural history collection in 1810, which, by 1889 required a separate building and became the Museum für Naturkunde. The preexisting Tierarznei School, founded in 1790 and absorbed by the university, also the Landwirtschaftliche Hochschule Berlin, founded in 1881 was affiliated with the Agricultural Faculties of the University. After 1933, like all German universities, it was affected by the Nazi regime, the rector during this period was Eugen Fischer. The Law for the Restoration of the Professional Civil Service resulted in 250 Jewish professors and employees being fired during 1933/1934, students and scholars and political opponents of Nazis were ejected from the university and often deported. During this time one third of all of the staff were fired by the Nazis. The Soviet Military Administration in Germany ordered the opening of the university in January 1946, the SMAD wanted a redesigned Berlin University based on the Soviet model, however they insisted on the phrasing newly opened and not re-opened for political reasons. The University of Berlin must effectively start again in almost every way and you have before you this image of the old university. What remains of that is nought but ruins, the teaching was limited to seven departments working in reopened, war-damaged buildings, with many of the teachers dead or missing. However, by the semester of 1946, the Economic. This program existed at Berlin University until 1962, the East-West conflict in post-war Germany led to a growing communist influence in the university. This was controversial, and incited strong protests within the student body, Soviet NKVD secret police arrested a number of students in March 1947 as a response
39.
Graduate-level
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A graduate school is a school that awards advanced academic degrees with the general requirement that students must have earned a previous undergraduate degree with a high grade point average. The distinction between schools and professional schools is not absolute, as various professional schools offer graduate degrees. Also, some graduate degrees train students for a specific profession, many universities award graduate degrees, a graduate school is not necessarily a separate institution. Those attending graduate schools are called students, or often in British English as postgraduate students and, colloquially, postgraduates. Degrees awarded to students include masters degrees, doctoral degrees. Producing original research is a significant component of graduate studies in the humanities, sciences and this research typically leads to the writing and defense of a thesis or dissertation. In graduate programs that are oriented towards professional training, the degrees may consist solely of coursework, the term graduate school is primarily North American. Unlike in undergraduate programs, however, it is common for graduate students to take coursework outside their specific field of study at graduate or graduate entry level. Some institutions designate separate graduate versus undergraduate staff and denote other divisions, Graduate degrees in Brazil are called postgraduate degrees, and can be taken only after an undergraduate education has been concluded. Lato sensu graduate degrees, degrees that represent a specialization in a certain area, sometimes it can be used to describe a specialization level between a masters degree and a MBA. However, since there are no norms to regulate this, both names are used indiscriminately most of the time, stricto sensu graduate degrees, degrees for those who wish to pursue an academic career. Usually serves as qualification for those seeking a differential on the job market. Most doctoral programs in Brazil require a degree, meaning that a Lato Sensu Degree is usually insufficient to start a doctoral program. Doctors / PhD, 3–4 years for completion, usually used as a stepping stone for academic life. In Canada, the Schools and Faculties of Graduate Studies are represented by the Canadian Association of Graduate Studies or Association canadienne pour les études supérieures and its mandate is to promote, advance, and foster excellence in graduate education and university research in Canada. In addition to a conference, the association prepares briefs on issues related to graduate studies including supervision, funding. Admission to a masters program generally requires a degree in a related field, with sufficiently high grades usually ranging from B+ and higher. Some schools require samples of the writing as well as a research proposal
40.
Doctoral dissertation
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A thesis or dissertation is a document submitted in support of candidature for an academic degree or professional qualification presenting the authors research and findings. In some contexts, the thesis or a cognate is used for part of a bachelors or masters course, while dissertation is normally applied to a doctorate, while in other contexts. The term graduate thesis is used to refer to both masters theses and doctoral dissertations. The required complexity or quality of research of a thesis or dissertation can vary by country, university, or program, the word dissertation can at times be used to describe a treatise without relation to obtaining an academic degree. The term thesis is used to refer to the general claim of an essay or similar work. The term thesis comes from the Greek θέσις, meaning something put forth, Dissertation comes from the Latin dissertātiō, meaning path. A thesis may be arranged as a thesis by publication or a monograph, with or without appended papers, an ordinary monograph has a title page, an abstract, a table of contents, comprising the various chapters, and a bibliography or a references section. They differ in their structure in accordance with the different areas of study. In a thesis by publication, the chapters constitute an introductory, Dissertations normally report on a research project or study, or an extended analysis of a topic. The structure of the thesis or dissertation explains the purpose, the research literature which impinges on the topic of the study, the methods used. Degree-awarding institutions often define their own style that candidates have to follow when preparing a thesis document. Other applicable international standards include ISO2145 on section numbers, ISO690 on bibliographic references, some older house styles specify that front matter uses a separate page-number sequence from the main text, using Roman numerals. They therefore avoid the traditional separate number sequence for front matter, however, strict standards are not always required. Most Italian universities, for example, have only general requirements on the size and the page formatting. A thesis or dissertation committee is a committee that supervises a students dissertation, the committee members are doctors in their field and have the task of reading the dissertation, making suggestions for changes and improvements, and sitting in on the defense. Sometimes, at least one member of the committee must be a professor in a department that is different from that of the student, all the dissertation referees must already have achieved at least the academic degree that the candidate is trying to reach. At English-speaking Canadian universities, writings presented in fulfillment of undergraduate coursework requirements are normally called papers, a longer paper or essay presented for completion of a 4-year bachelors degree is sometimes called a major paper. High-quality research papers presented as the study of a postgraduate consecutive bachelor with Honours or Baccalaureatus Cum Honore degree are called thesis
41.
Applied mathematics
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Applied mathematics is a branch of mathematics that deals with mathematical methods that find use in science, engineering, business, computer science, and industry. Thus, applied mathematics is a combination of science and specialized knowledge. The term applied mathematics also describes the professional specialty in which work on practical problems by formulating and studying mathematical models. The activity of applied mathematics is thus connected with research in pure mathematics. Historically, applied mathematics consisted principally of applied analysis, most notably differential equations, approximation theory, quantitative finance is now taught in mathematics departments across universities and mathematical finance is considered a full branch of applied mathematics. Engineering and computer science departments have made use of applied mathematics. Today, the applied mathematics is used in a broader sense. It includes the areas noted above as well as other areas that have become increasingly important in applications. Even fields such as number theory that are part of mathematics are now important in applications. There is no consensus as to what the various branches of applied mathematics are, such categorizations are made difficult by the way mathematics and science change over time, and also by the way universities organize departments, courses, and degrees. Many mathematicians distinguish between applied mathematics, which is concerned with methods, and the applications of mathematics within science. Mathematicians such as Poincaré and Arnold deny the existence of applied mathematics, similarly, non-mathematicians blend applied mathematics and applications of mathematics. The use and development of mathematics to industrial problems is also called industrial mathematics. Historically, mathematics was most important in the sciences and engineering. Academic institutions are not consistent in the way they group and label courses, programs, at some schools, there is a single mathematics department, whereas others have separate departments for Applied Mathematics and Mathematics. It is very common for Statistics departments to be separated at schools with graduate programs, many applied mathematics programs consist of primarily cross-listed courses and jointly appointed faculty in departments representing applications. Some Ph. D. programs in applied mathematics require little or no coursework outside of mathematics, in some respects this difference reflects the distinction between application of mathematics and applied mathematics. Research universities dividing their mathematics department into pure and applied sections include MIT, brigham Young University also has an Applied and Computational Emphasis, a program that allows student to graduate with a Mathematics degree, with an emphasis in Applied Math