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Mathematical Notation
Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations and any other mathematical objects, and assembling them into expressions and formulas. Mathematical notation is widely used in mathematics, science, and engineering for representing complex concepts and properties in a concise, unambiguous and accurate way. For example, Albert Einstein's equation E=mc^2 is the quantitative representation in mathematical notation of the mass–energy equivalence. Mathematical notation was first introduced by François Viète at the end of the 16th century, and largely expanded during the 17th and 18th century by René Descartes, Isaac Newton, Gottfried Wilhelm Leibniz, and overall Leonhard Euler. Symbols The use of many symbols is the basis of mathematical notation. They play a similar role as words in natural languages. They may play different roles in mathematical notation similarly as verbs, adjective and nouns play different ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Glossary Of Mathematical Symbols
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for expressing all mathematics. The most basic symbols are the decimal digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), and the letters of the Latin alphabet. The decimal digits are used for representing numbers through the Hindu–Arabic numeral system. Historically, upper-case letters were used for representing points in geometry, and lower-case letters were used for variables and constants. Letters are used for representing many other sorts of mathematical objects. As the number of these sorts has remarkably increased in modern mathematics, the Greek alphabet and some Hebrew letters are also used. In mathematical formulas, the standard typeface is it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Gottfried Wilhelm Leibniz
Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mathematics. He wrote works on philosophy, theology, ethics, politics, law, history and philology. Leibniz also made major contributions to physics and technology, and anticipated notions that surfaced much later in probability theory, biology, medicine, geology, psychology, linguistics and computer science. In addition, he contributed to the field of library science: while serving as overseer of the Wolfenbüttel library in Germany, he devised a cataloging system that would have served as a guide for many of Europe's largest libraries. Leibniz's contributions to this vast array of subjects were scattered in various learned journals, in tens of thousands of letters and in unpublished manuscripts. He wrote in several languages, primaril ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Function (mathematics)
In mathematics, a function from a set to a set assigns to each element of exactly one element of .; the words map, mapping, transformation, correspondence, and operator are often used synonymously. The set is called the domain of the function and the set is called the codomain of the function.Codomain ''Encyclopedia of Mathematics'Codomain. ''Encyclopedia of Mathematics''/ref> The earliest known approach to the notion of function can be traced back to works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a ''function'' of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Derivative
In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the "instantaneous rate of change", the ratio of the instantaneous change in the dependent variable to that of the independent variable. Derivatives can be generalized to functions of several real variables. In this generalization, the deriv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Fourier Transform
A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, which will output a function depending on temporal frequency or spatial frequency respectively. That process is also called ''analysis''. An example application would be decomposing the waveform of a musical chord into terms of the intensity of its constituent pitches. The term ''Fourier transform'' refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of space or time. The Fourier transform of a function is a complex-valued function representing the complex sinusoids that comprise the original function. For each frequency, the magnitude ( absolute value) of the complex value represents the amplitude of a constituent complex sinusoid wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Superscript
A subscript or superscript is a character (such as a number or letter) that is set slightly below or above the normal line of type, respectively. It is usually smaller than the rest of the text. Subscripts appear at or below the baseline, while superscripts are above. Subscripts and superscripts are perhaps most often used in formulas, mathematical expressions, and specifications of chemical compounds and isotopes, but have many other uses as well. In professional typography, subscript and superscript characters are not simply ordinary characters reduced in size; to keep them visually consistent with the rest of the font, typeface designers make them slightly heavier (i.e. medium or bold typography) than a reduced-size character would be. The vertical distance that sub- or superscripted text is moved from the original baseline varies by typeface and by use. In typesetting, such types are traditionally called "superior" and "inferior" letters, figures, etc., or just "superior ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Diacritic
A diacritic (also diacritical mark, diacritical point, diacritical sign, or accent) is a glyph added to a letter or to a basic glyph. The term derives from the Ancient Greek (, "distinguishing"), from (, "to distinguish"). The word ''diacritic'' is a noun, though it is sometimes used in an attributive sense, whereas ''diacritical'' is only an adjective. Some diacritics, such as the acute ( ◌́ ) and grave ( ◌̀ ), are often called ''accents''. Diacritics may appear above or below a letter or in some other position such as within the letter or between two letters. The main use of diacritics in Latin script is to change the sound-values of the letters to which they are added. Historically, English has used the diaeresis diacritic to indicate the correct pronunciation of ambiguous words, such as "coöperate", without which the letter sequence could be misinterpreted to be pronounced . Other examples are the acute and grave accents, which can ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Sine Function
In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that of the hypotenuse. For an angle \theta, the sine and cosine functions are denoted simply as \sin \theta and \cos \theta. More generally, the definitions of sine and cosine can be extended to any real value in terms of the lengths of certain line segments in a unit circle. More modern definitions express the sine and cosine as infinite series, or as the solutions of certain differential equations, allowing their extension to arbitrary positive and negative values and even to complex numbers. The sine and cosine functions are commonly used to model periodic phenomena such as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Hebrew Alphabet
The Hebrew alphabet ( he, אָלֶף־בֵּית עִבְרִי, ), known variously by scholars as the Ktav Ashuri, Jewish script, square script and block script, is an abjad script used in the writing of the Hebrew language and other Jewish languages, most notably Yiddish, Ladino, Judeo-Arabic, and Judeo-Persian. It is also used informally in Israel to write Levantine Arabic, especially among Druze. It is an offshoot of the Imperial Aramaic alphabet, which flourished during the Achaemenid Empire and which itself derives from the Phoenician alphabet. Historically, two separate abjad scripts have been used to write Hebrew. The original, old Hebrew script, known as the paleo-Hebrew alphabet, has been largely preserved in a variant form as the Samaritan alphabet. The present "Jewish script" or "square script", on the contrary, is a stylized form of the Aramaic alphabet and was technically known by Jewish sages as Ktav Ashuri, Ashurit (lit. "Assyrian script"), since its o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Greek Alphabet
The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BCE. It is derived from the earlier Phoenician alphabet, and was the earliest known alphabetic script to have distinct letters for vowels as well as consonants. In Archaic and early Classical times, the Greek alphabet existed in many local variants, but, by the end of the 4th century BCE, the Euclidean alphabet, with 24 letters, ordered from alpha to omega, had become standard and it is this version that is still used for Greek writing today. The uppercase and lowercase forms of the 24 letters are: : , , , , , , , , , , , , , , , , , /ς, , , , , , . The Greek alphabet is the ancestor of the Latin and Cyrillic scripts. Like Latin and Cyrillic, Greek originally had only a single form of each letter; it developed the letter case distinction between uppercase and lowercase in parallel with Latin during the modern era. Sound values and conventional transcriptions for some ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Latin Alphabet
The Latin alphabet or Roman alphabet is the collection of letters originally used by the ancient Romans to write the Latin language. Largely unaltered with the exception of extensions (such as diacritics), it used to write English and the other modern European languages. With modifications, it is also used for other alphabets, such as the Vietnamese alphabet. Its modern repertoire is standardised as the ISO basic Latin alphabet. Etymology The term ''Latin alphabet'' may refer to either the alphabet used to write Latin (as described in this article) or other alphabets based on the Latin script, which is the basic set of letters common to the various alphabets descended from the classical Latin alphabet, such as the English alphabet. These Latin-script alphabets may discard letters, like the Rotokas alphabet, or add new letters, like the Danish and Norwegian alphabets. Letter shapes have evolved over the centuries, including the development in Medieval Latin of lower ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |