"the speed of light in a vacuum. Algebra gives methods for writing formulas and solving equations that are much clearer and easier than the older method of writing everything out in words. The word ""algebra"" is also used in certain specialized ways. A special kind of mathematical object in abstract algebra is called an ""algebra"", and the word is used, for example, in the phrases linear algebra and algebraic topology. A mathematician who does research in algebra is called an algebraist. The word ""algebra"" comes from the Arabic ("""" lit. ""the reunion of broken parts"") from the title of the"
"Algebra Algebra (from Arabic """"al-jabr"""", literally meaning ""reunion of broken parts"") is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. It includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra; the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to"
"the course of solving a problem, but is specifically called on to define an infinite class of problems."" History of algebra As a branch of mathematics, algebra emerged at the end of the 16th century in Europe, with the work of François Viète. Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects. However, until the 19th century, algebra consisted essentially of the theory of equations. For example, the fundamental theorem of algebra belongs to the theory of equations and is not, nowadays, considered as belonging to algebra (in fact, every proof"
"the equation), he has been described as the father or founder of algebra. The term ""algebra"" itself comes from the title of his book (specifically the word ""al-jabr"" meaning ""completion"" or ""rejoining""). His name gave rise to the terms ""Algorism"" and ""algorithm"". His name is also the origin of (Spanish) ""guarismo"" and of (Portuguese) ""algarismo"", both meaning digit. In the 12th century, Latin translations of his textbook on arithmetic (""Algorithmo de Numero Indorum"") which codified the various Indian numerals, introduced the decimal positional number system to the Western world. ""The Compendious Book on Calculation by Completion and Balancing"", translated into"
"book ""Ilm al-jabr wa'l-muḳābala"" by the Persian mathematician and astronomer al-Khwarizmi. The word entered the English language during the fifteenth century, from either Spanish, Italian, or Medieval Latin. It originally referred to the surgical procedure of setting broken or dislocated bones. The mathematical meaning was first recorded in the sixteenth century. The word ""algebra"" has several related meanings in mathematics, as a single word or with qualifiers. Algebra began with computations similar to those of arithmetic, with letters standing for numbers. This allowed proofs of properties that are true no matter which numbers are involved. For example, in the quadratic"
"History of algebra As a branch of mathematics, algebra emerged at the end of the 16th century in Europe, with the work of François Viète. Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects. However, until the 19th century, algebra consisted essentially of the theory of equations. For example, the fundamental theorem of algebra belongs to the theory of equations and is not, nowadays, considered as belonging to algebra (in fact, every proof must use the completeness of the real numbers, which is not an algebraic property). This article describes the"
") is a mathematical book written approximately 820 CE. The book was written with the encouragement of Caliph al-Ma'mun as a popular work on calculation and is replete with examples and applications to a wide range of problems in trade, surveying and legal inheritance. The term ""algebra"" is derived from the name of one of the basic operations with equations (, meaning ""restoration"", referring to adding a number to both sides of the equation to consolidate or cancel terms) described in this book. The book was translated in Latin as ""Liber algebrae et almucabala"" by Robert of Chester (Segovia, 1145)"
"independent discipline. The word ""algebra"" is derived from the name of one of the basic operations with equations described in this book, following its Latin translation by Robert of Chester. Since the book does not give any citations to previous authors, it is not clearly known what earlier works were used by al-Khwarizmi, and modern mathematical historians put forth opinions based on the textual analysis of the book and the overall body of knowledge of the contemporary Muslim world. There are indications of connections with Indian mathematics, as he had written a book entitled ""The Book of Bringing Together and"
"his landmark text, ""Kitab al-Jabr wa-l-Muqabala"", from which the term ""algebra"" is derived. He is thus considered to be the father of algebra by some, although the Greek mathematician Diophantus has also been given this title. The terms algorism and algorithm are derived from the name of al-Khwarizmi, who was also responsible for introducing the Arabic numerals and Hindu-Arabic numeral system beyond the Indian subcontinent. Arab scientist Ibn al-Haytham (Alhazen) developed an early scientific method in his ""Book of Optics"" (1021). The most important development of the scientific method was the use of experiments to distinguish between competing scientific theories"
"""algebra"", and zanahoria ""carrot"". It is thought that the bilingualism of the Mozarabs facilitated the transfer of vocabulary from Arabic to Castilian. The neighboring Romance languages—Portuguese/Galician, Catalan, French, and Occitan—contributed greatly to the Spanish lexicon throughout the Middle Ages and into the modern era. Borrowing from Italian occurred most frequently in the 16th and 17th centuries, due largely to the influence of the Italian Renaissance. With the development of the Spanish Empire in the New World came lexical borrowing from indigenous languages of the Americas, especially vocabulary dealing with flora, fauna, and cultural concepts unique to the Americas. Borrowing from"
"name of which is derived from the Arabic word meaning completion or ""reunion of broken parts"", flourished during the Islamic golden age. Muhammad ibn Musa al-Khwarizmi, a scholar in the House of Wisdom in Baghdad, is along with the Greek mathematician Diophantus, known as the father of algebra. In his book ""The Compendious Book on Calculation by Completion and Balancing"", Al-Khwarizmi deals with ways to solve for the positive roots of first and second degree (linear and quadratic) polynomial equations. He also introduces the method of reduction, and unlike Diophantus, gives general solutions for the equations he deals with. Al-Khwarizmi's"
"with the word ""algebra"" in the name. Many mathematical structures are called algebras: Elementary algebra is the most basic form of algebra. It is taught to students who are presumed to have no knowledge of mathematics beyond the basic principles of arithmetic. In arithmetic, only numbers and their arithmetical operations (such as +, −, ×, ÷) occur. In algebra, numbers are often represented by symbols called variables (such as ""a"", ""n"", ""x"", ""y"" or ""z""). This is useful because: A polynomial is an expression that is the sum of a finite number of non-zero terms, each term consisting of the"
"proof of the intromission theory of light. Algebra was also pioneered by Persian Scientist Muhammad ibn Mūsā al-Khwārizmī during this time in his landmark text, Kitab al-Jabr wa-l-Muqabala, from which the term algebra is derived. He is thus considered to be the father of algebra. The terms algorism and algorithm are also derived from the name of al-Khwarizmi, who was responsible for introducing the Arabic numerals and Hindu-Arabic numeral system beyond the Indian Subcontinent. Medicine was advanced particularly during the Abbasids' reign in Central Asia. During the ninth century, Baghdad contained over 800 doctors, and great discoveries in the understanding"
"word algebra means both a subject within mathematics as well as an object studied in the subject of algebra.) An algebra consists of a choice of two rings and an operation which takes an element from each ring and returns an element of the second ring. This operation makes the second ring into a module over the first. Often the first ring is a field. Words such as ""element"" and ""combining operation"" are very general, and can be applied to many real-world and abstract situations. Any set of things that obeys all the rules for one (or two) operation(s) is,"
"Words such as 'algebra','algorism (algorithm)', 'alcohol', 'azimuth', 'sugar', 'coffee' and many others were incorporated into Portuguese and are everyday words: Many words from the Islamic period were borrowings from Spanish and Mozarabic dialects from the South. Because Portugal expelled the Moors 300 years earlier than Spain, the Arabic influence in Portuguese was relatively small and left no loanwords in the Portuguese lexicon related to human feelings or emotions. Arabic-derived words are easily identifiable in toponymic names of towns and villages, increasing as you travel south Alfama, Alcácer do Sal, Alcoutim, Aljustrel, Algarve and in words relating to geography, agriculture, architecture,"
"could be attributed to Islamic authors"". The words algorithm, deriving from Al-Khwarizmi's Latinized name Algorismi, and algebra, deriving from the title of his AD 820 book ""Hisab al-jabr w’al-muqabala, Kitab al-Jabr wa-l-Muqabala"" are themselves Arabic loanwords. This and other Arabic astronomical and mathematical works, such as those by al-Battani and Muhammad al-Fazari's ""Great Sindhind"" (based on the ""Surya Siddhanta"" and the works of Brahmagupta). were translated into Latin during the 12th century. Al-Khazini's ""Zij as-Sanjari"" (1115–1116) was translated into Greek by Gregory Choniades in the 13th century and was studied in the Byzantine Empire. The astronomical modifications to the Ptolemaic"
"Elements of Algebra Elements of Algebra is an elementary mathematics textbook written by mathematician Leonhard Euler and originally published in 1770 in German. ""Elements of Algebra"" is one of the earliest books to set out algebra in the modern form we would recognize today (another early book being ""Elements of Algebra"" by Nicholas Saunderson, published in 1740), and is one of Euler's few writings, along with ""Letters to a German Princess"", that are accessible to the general public. Written in numbered paragraphs as was common practice till the 19th century, ""Elements"" begins with the definition of mathematics and builds on"
"In addition to the three stages of expressing algebraic ideas, some authors recognized four conceptual stages in the development of algebra that occurred alongside the changes in expression. These four stages were as follows: The origins of algebra can be traced to the ancient Babylonians, who developed a positional number system that greatly aided them in solving their rhetorical algebraic equations. The Babylonians were not interested in exact solutions but approximations, and so they would commonly use linear interpolation to approximate intermediate values. One of the most famous tablets is the Plimpton 322 tablet, created around 1900–1600 BC, which gives"
"algebra was introduced by George Boole in his first book ""The Mathematical Analysis of Logic"" (1847), and set forth more fully in his ""An Investigation of the Laws of Thought"" (1854). According to Huntington, the term ""Boolean algebra"" was first suggested by Sheffer in 1913, although Charles Sanders Peirce in 1880 gave the title ""A Boolian Algebra with One Constant"" to the first chapter of his ""The Simplest Mathematics"". Boolean algebra has been fundamental in the development of digital electronics, and is provided for in all modern programming languages. It is also used in set theory and statistics. Boole's algebra"
"Term algebra In universal algebra and mathematical logic, a term algebra is a freely generated algebraic structure over a given signature. For example, in a signature consisting of a single binary operation, the term algebra over a set ""X"" of variables is exactly the free magma generated by ""X"". Other synonyms for the notion include absolutely free algebra and anarchic algebra. From a category theory perspective, a term algebra is the initial object for the category of all algebras of the same signature, and this object, unique up to isomorphism, is called an initial algebra; it generates by homomorphic projection"
"algebra arise in the works of Diophantus. Greek algebra continued to be studied in the east well after the fall of the Western Empire, where it matured into modern algebra in the hands of al-Khwārizmī (see the history of algebra). The study of Diophantine Equations and Diophantine Approximations are still important areas of mathematical research today. All of the planets in the Solar System, excluding Earth and Uranus, are named after Roman deities. Although the law of the Roman Empire is not used today, modern law in many jurisdictions is based on principles of law used and developed during the"
"Mediterranean languages. Examples of such words include admiral, adobe, alchemy, alcohol, algebra, algorithm, alkaline, almanac, amber, arsenal, assassin, candy, carat, cipher, coffee, cotton, ghoul, hazard, jar, kismet, lemon, loofah, magazine, mattress, sherbet, sofa, sumac, tariff, and zenith. Other languages such as Maltese and Kinubi derive ultimately from Arabic, rather than merely borrowing vocabulary or grammatical rules. Terms borrowed range from religious terminology (like Berber ""taẓallit"", ""prayer"", from ""salat"" ( """")), academic terms (like Uyghur ""mentiq"", ""logic""), and economic items (like English ""coffee"") to placeholders (like Spanish ""fulano"", ""so-and-so""), everyday terms (like Hindustani ""lekin"", ""but"", or Spanish ""taza"" and French ""tasse"","
"commentaries on them, scholars at the Bayt al-Hikma produced important original research. For example, the noted mathematician al-Khwarizmi worked in al-Ma'mun's House of Wisdom and is famous for his contributions to the development of algebra. Muhammad ibn Musa al-Khwarizmi was born around 780 and died around 850. He was known as a mathematician and an astronomer in the House of Wisdom, and is also known for his book ""Kitab al-Jabr"" in which he develops a number of algorithms. The application of the word ""algebra"" to mathematics and the etymology of the word ""algorithm"" can be traced back to al-Khwarizmi —"
"other European languages, English contains many words derived from Arabic, often through other European languages, especially Spanish. Among them is every-day vocabulary like ""sugar"" (""sukkar""), ""cotton"" (""quṭn"") or ""magazine"" (""""). More recognizable are words like ""algebra"" (""al-jabr""), ""alcohol"" (""al-kuhūl""), ""alchemy"" (""al-kimiya""), ""alkali"", ""cypher"" and ""zenith"" (see list of English words of Arabic origin). A more indirect form of influence is the use of certain Latinate words in an unclassical sense, derived from their use in Latin translations of medieval Arabic philosophical works (e.g. those of Averroes), which entered the scholastic vocabulary and later came into normal use in modern languages."
"Algebra over a field In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic structure, which consists of a set, together with operations of multiplication, addition, and scalar multiplication by elements of the underlying field, and satisfies the axioms implied by ""vector space"" and ""bilinear"". The multiplication operation in an algebra may or may not be associative, leading to the notions of associative algebras and nonassociative algebras. Given an integer ""n"", the ring of real square matrices of order ""n"" is an example"
"Mathematics alongside Arabs. In the 9th century, the Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī wrote several important books on the Hindu–Arabic numerals and on methods for solving equations. His book ""On the Calculation with Hindu Numerals"", written about 825, along with the work of Al-Kindi, were instrumental in spreading Indian mathematics and Indian numerals to the West. The word ""algorithm"" is derived from the Latinization of his name, Algoritmi, and the word ""algebra"" from the title of one of his works, ""Al-Kitāb al-mukhtaṣar fī hīsāb al-ğabr wa’l-muqābala"" (""The Compendious Book on Calculation by Completion and Balancing""). He gave an exhaustive"
"law"" for numbers. For the integers and and × is said to be ""distributive"" over +. The integers are an example of a ring. The integers have additional properties which make it an integral domain. A field is a ""ring"" with the additional property that all the elements excluding 0 form an ""abelian group"" under ×. The multiplicative (×) identity is written as 1 and the multiplicative inverse of ""a"" is written as ""a"". The rational numbers, the real numbers and the complex numbers are all examples of fields. Algebra Algebra (from Arabic """"al-jabr"""", literally meaning ""reunion of broken parts"")"
"de Lagarde, shortly after he published his edition of a 1505 Spanish/Arabic bilingual glossary in which Spanish ""cosa"" (""thing"") was paired with its Arabic equivalent, شىء (""shay""), transcribed as ""xei"". (The ""sh"" sound in Old Spanish was routinely spelled ""x"".) Evidently Lagarde was aware that Arab mathematicians, in the ""rhetorical"" stage of algebra's development, often used that word to represent the unknown quantity. He surmised that ""nothing could be more natural"" (Nichts war also natürlicher...) than for the initial of the Arabic word—romanized as the Old Spanish ""x""—to be adopted for use in algebra. A later reader reinterpreted Lagarde's conjecture"
"as follows: Thus, according to Budge and others, chemistry derives from an Egyptian word ""khemein"" or ""khēmia"", ""preparation of black powder"", ultimately derived from the name ""khem"", Egypt. A decree of Diocletian, written about 300 AD in Greek, speaks against ""the ancient writings of the Egyptians, which treat of the ""khēmia"" transmutation of gold and silver"". Arabic ""al-kīmiyaʾ"" or ""al-khīmiyaʾ"" ( or ), according to some, is thought to derive from the Koine Greek word ""khymeia"" () meaning ""the art of alloying metals, alchemy""; in the manuscripts, this word is also written ""khēmeia"" () or ""kheimeia"" (), which is the"
"Relation algebra In mathematics and abstract algebra, a relation algebra is a residuated Boolean algebra expanded with an involution called converse, a unary operation. The motivating example of a relation algebra is the algebra 2 of all binary relations on a set ""X"", that is, subsets of the cartesian square ""X"", with ""R""•""S"" interpreted as the usual composition of binary relations ""R"" and ""S"", and with the converse of ""R"" as the converse relation. Relation algebra emerged in the 19th-century work of Augustus De Morgan and Charles Peirce, which culminated in the algebraic logic of Ernst Schröder. The equational form"
"hence ""algebra"", and also by Gerard of Cremona. A unique Arabic copy is kept at Oxford and was translated in 1831 by F. Rosen. A Latin translation is kept in Cambridge. It provided an exhaustive account of solving polynomial equations up to the second degree, and discussed the fundamental methods of ""reduction"" and ""balancing"", referring to the transposition of terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation. Al-Khwārizmī's method of solving linear and quadratic equations worked by first reducing the equation to one of six standard forms"
"Etymology of chemistry In the history of science, the etymology of the word chemistry is debatable. It is agreed that the word derives from the word ""alchemy"", which is a European one, derived from ""kimiya"" () and alchemy ""al-kīmiyāʾ"" (). The Arabic term is derived from the Ancient Greek ""khēmia"" or ""khēmeia"". However, the ultimate origin of the root word, ""chem"", is uncertain. According to the ""Oxford English Dictionary"", ""al-kīmiyāʾ"" is derived from , which is derived from the ancient Egyptian name of Egypt (""khem"" or ""khm"", ""khame"", or ""khmi"", meaning ""blackness"" Therefore, alchemy is the ""Black Art"". However, it"
"divisions geometry, arithmetic, and algebra. The study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols. The science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects. Bertrand Russell wrote this famous tongue-in-cheek definition, describing the way all terms in mathematics are ultimately defined by reference to undefined terms: The subject in which we never know what we are talking about, nor whether what we are saying is true. Many other attempts to characterize mathematics have led to humor or poetic prose: A mathematician"