24 résultats pour "mathematical"
- Mathematical Symbols I INTRODUCTION Mathematical Symbols Mathematics employs many symbols to describe numerical operations and relationships.
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Game Theory
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INTRODUCTION
Game Theory, mathematical analysis of any situation involving a conflict of interest, with the intent of indicating the optimal choices that, under given conditions, will
lead to a desired outcome.
C Zero-Sum Games A game is said to be a zero-sum game if the total amount of payoffs at the end of the game is zero. Thus, in a zero-sum game the total amount won is exactly equal tothe amount lost. In economic contexts, zero-sum games are equivalent to saying that no production or destruction of goods takes place within the “game economy” inquestion. Von Neumann and Oskar Morgenstern showed in 1944 that any n-person non-zero-sum game can be reduced to an n + 1 zero-sum game, and that such n...
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Algebra
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INTRODUCTION
Algebra, branch of mathematics in which symbols (usually letters) represent unknown numbers in mathematical equations.
B Order of Operations and Grouping Algebra relies on an established sequence for performing arithmetic operations. This ensures that everyone who executes a string of operations arrives at the sameanswer. Multiplication is performed first, then division, followed by addition, then subtraction. For example: 1 + 2 · 3 equals 7 because 2 and 3 are multiplied first and then added to 1. Exponents and roots have even higher priority than multiplication: 3 · 2 2 = 3 · 4 = 12 Grouping symbols override...
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Arithmetic
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INTRODUCTION
Arithmetic, branch of mathematics that arises from counting, the most basic mathematical operation.
Subtract the units: 6 - 3 = 3. Then subtract the tens column: 6 – 2 = 4. The results of these two single-digit subtractions, written side by side, provide the answer: Subtraction is a bit more complicated if we need to subtract a larger digit from a smaller one. For example, when subtracting 47 from 92, the units value (7) of 47 isgreater than the units value (2) of 92. We can handle this situation using a procedure called borrowing, which is like carrying in reverse. Ten units can be borrowe...
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Puzzle.
Visual puzzles involve searching a picture to find hidden or disguised figures or answering a question about some part of a visual illusion. For instance, the popular 19th- century prints of American lithographic company Currier & Ives featured hidden people, animals, and other objects. A 16th-century painting from Bukhara, Uzbekistan,of a camel includes hidden figures of 17 people, 10 rabbits, a monkey, and a dragon (Metropolitan Museum of Art, New York City). B Mathematical Puzzles and Logic...
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Physical Chemistry - chemistry.
by the system in the form of the flow of electrical currents, formation of surfaces and changes in surface tension, changes in volume or pressure, and formation ordisappearance of chemical species. B Chemical Kinetics This field studies the rates of chemical processes as a function of the concentration of the reacting species, of the products of the reaction, of catalysts and inhibitors, ofvarious solvent media, of temperature, and of all other variables that can affect the reaction rate. It is...
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Condorcet, Marie-Jean-Antoine-Nicolas Caritat de
years he also came under the influence of Euler, Fontaine, the Bernouillis and, above all, of the distinguished mathematician and academician, Jean Le Rond D'Alembert , who became his patron. He was elected Perpetual Secretary of the Academy of Sciences in 1773, and in 1782 became a member of the French Academy. An enthusiastic supporter and theorist of the Revolution, he played an important role in the drafting of the Déclaration des droits in 1789. Suspected later of being a Girondin, he w...
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Math is Fun
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."[15] Albert Einstein (1879–1955) stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."[16] French mathematician Claire Vois...
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Isaac NewtonIINTRODUCTIONIsaac Newton (1642-1727), English physicist, mathematician, and natural philosopher, considered one of the most important scientists of all time.
B Calculus (Newton’s “Fluxional Method”) In 1669 Newton gave his Trinity mathematics professor Isaac Barrow an important manuscript, which is generally known by its shortened Latin title, De Analysi . This work contained many of Newton’s conclusions about calculus (what Newton called his “fluxional method”). Although the paper was not immediately published, Barrowmade its results known to several of the leading mathematicians of Britain and Europe. This paper established Newton as one of the...
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Isaac Newton.
B Calculus (Newton’s “Fluxional Method”) In 1669 Newton gave his Trinity mathematics professor Isaac Barrow an important manuscript, which is generally known by its shortened Latin title, De Analysi . This work contained many of Newton’s conclusions about calculus (what Newton called his “fluxional method”). Although the paper was not immediately published, Barrowmade its results known to several of the leading mathematicians of Britain and Europe. This paper established Newton as one of the t...
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Statistics
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INTRODUCTION
Statistics, branch of mathematics that deals with the collection, organization, and analysis of numerical data and with such problems as experiment design and decision
making.
frequency, column (d), is the ratio of the frequency of an interval to the total count; the relative frequency is multiplied by 100 to obtain the percent relative frequency.The cumulative frequency, column (e), represents the number of students receiving grades equal to or less than the range in each succeeding interval; thus, thenumber of students with grades of 30 or less is obtained by adding the frequencies in column (c) for the first three intervals, which total 53. The cumulative relativef...
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Map - Geography.
Often only southeast slopes are hachured or shaded, giving somewhat the effect of a bird's-eye view of the area illuminated by light from the northwest. Shadings orcarefully drawn hachures, neither of which give elevations, are more easily interpreted than contour lines and are sometimes used in conjunction with them for greaterclarity. IV MAP PROJECTIONS For the representation of the entire surface of the earth without any kind of distortion, a map must have a spherical surface; a map of this...
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Physics
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INTRODUCTION
Physics, major science, dealing with the fundamental constituents of the universe, the forces they exert on one another, and the results produced by these forces.
Starting about 1665, at the age of 23, Newton enunciated the principles of mechanics, formulated the law of universal gravitation, separated white light into colors,proposed a theory for the propagation of light, and invented differential and integral calculus. Newton's contributions covered an enormous range of naturalphenomena: He was thus able to show that not only Kepler's laws of planetary motion but also Galileo's discoveries of falling bodies follow a combination of his ownsecond law of m...
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Comte, Isidore-Auguste-Marie-François-Xavier
1 Life Auguste Comte was born in Montpellier, France. He attended the École Polytechnique, from which he was expelled in 1816, for political reasons. Comte's main concern throughout his life was resolving the political, social and moral problems caused by the French Revolution. To that end, he embarked upon an encyclopedic work, which he first conceived under the inspiration of Henri de Saint-Simon , for whom he worked as secretary from 1817 to 1824. At that time, he proposed several pla...
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Geography - Geography.
Geographers have developed a standard pattern of map symbols for identifying such cultural features as homes, factories, and churches; dams, bridges, and tunnels;railways, highways, and travel routes; and mines, farms, and grazing lands. C Analyzing Geographic Information Techniques that use mathematics or statistics to analyze data are known as quantitative methods. The use of quantitative methods enables geographers to treat a largeamount of data and a large number of variables in an objectiv...
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Relativity
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INTRODUCTION
Albert Einstein
In 1905 German-born American physicist Albert Einstein published his first paper outlining the theory of relativity.
in calculating very large distances or very large aggregations of matter. As the quantum theory applies to the very small, so the relativity theory applies to the verylarge. Until 1887 no flaw had appeared in the rapidly developing body of classical physics. In that year, the Michelson-Morley experiment, named after the American physicistAlbert Michelson and the American chemist Edward Williams Morley, was performed. It was an attempt to determine the rate of the motion of the earth through t...
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History of Chemistry - chemistry.
even better distillation apparatus than the Arabs had made and to condense the more volatile products of distillation. Among the important products obtained in thisway were alcohol and the mineral acids: nitric, aqua regia (a mixture of nitric and hydrochloric), sulfuric, and hydrochloric. Many new reactions could be carried outusing these powerful reagents. Word of the Chinese discovery of nitrates and the manufacture of gunpowder also came to the West through the Arabs. The Chinese atfirst use...
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Bradwardine, Thomas
velocity is a self-contradiction, a vacuum is impossible. In De proportionibus , Bradwardine first laid out the theory of ratios familiar from the theory of musical ratios as found in Boethius . He used this understanding of operations on ratios to reinterpret Aristotle 's theory. Velocities vary, he said, as the ratio of force to resistance. When the ratio of force to resistance is ‘doubled' the velocity is doubled, when the ratio is ‘tripled' the velocity is tripled and so on, with the...
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Programming Language.
Logic languages use logic as their mathematical base. A logic program consists of sets of facts and if-then rules, which specify how one set of facts may be deducedfrom others, for example: If the statement X is true, then the statement Y is false. In the execution of such a program, an input statement can be logically deduced from other statements in the program. Many artificial intelligence programs are writtenin such languages. IV LANGUAGE STRUCTURE AND COMPONENTS Programming languages use...
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Statistics
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INTRODUCTION
Statistics, branch of mathematics that deals with the collection, organization, and analysis of numerical data and with such problems as experiment design and decision
making.
Professional pollsters typically conduct their surveys among sample populations of 1,000 people. Statistical measurementsshow that reductions in the margin of error flatten out considerably after the sample size reaches 1,000.© Microsoft Corporation. All Rights Reserved. The raw materials of statistics are sets of numbers obtained from enumerations or measurements. In collecting statistical data, adequate precautions must be taken tosecure complete and accurate information. The first problem of...
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Conceptual analysis
Kant's important idea that conceptual truths can be either analytic a priori or synthetic a priori is effectively erased by Gottlob Frege in his Foundations of Arithmetic (1884). Frege's overriding philosophical aim is to put mathematical proof on a firm footing by reducing the truths of arithmetic to analytic truths of logic. In view of this, the proper goal of an analysis is the production of non-circular, explanatory, yet meaning-preserving general definitions of fundamental concepts -...
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Babylonia - USA History.
Pharmacology, too, doubtless had made considerable progress, although the only major direct evidence of this comes from a Sumerian tablet written several centuriesbefore Hammurabi. C Legal System and Writing Law and justice were key concepts in the Babylonian way of life. Justice was administered by the courts, each of which consisted of from one to four judges. Often theelders of a town constituted a tribunal. The judges could not reverse their decisions for any reason, but appeals from their...
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History of Astronomy - astronomy.
Egypt, the Sun was directly overhead at noon. On the same date and time in Alexandria, Egypt, the Sun was about 7 degrees south of zenith. With simple geometryand knowledge of the distance between the two cities, he estimated the circumference of the Earth to be 250,000 stadia. (The stadium was a unit of length, derivedfrom the length of the racetrack in an ancient Greek stadium. We have an approximate idea of how big an ancient Greek stadium was, and based on that approximationEratosthenes was...
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Chemistry - chemistry.
parts of oxygen by weight, which is a ratio of about 1 to 8, regardless of whether the water came from the Mississippi River or the ice of Antarctica. In other words, acompound has a definite, invariable composition, always containing the same elements in the same proportions by weight; this is the law of definite proportions. Many elements combine in more than one ratio, giving different compounds. In addition to forming water, hydrogen and oxygen also form hydrogen peroxide.Hydrogen peroxide h...