Alfonso IV was the king of Aragon from 1327 to 1336, son of James II. He was well-intentioned but weak. His reign was marked by a serious revolt in Sardinia, which led to war with Genoa, and by the establishment of diplomatic relations with the Moorish kingdoms of North Africa. The failure of the

Alfonso VI was the king of Leon (1065–70) and king of reunited Castile and Leon (1072–1109), who by 1077 had proclaimed himself “emperor of all Spain” (imperator totius Hispaniae). His oppression of his Muslim vassals led to the invasion of Spain by an Almoravid army from North Africa (1086). His

Alfonso II was the king of Asturias from 791 to 842, the son of Fruela I. He had to face frequent and determined attacks by the armies of the emirate of Córdoba and was often defeated, but his doggedness saved Asturias from extinction. He built a new capital, Oviedo, on a strategic site in the

Alfonso I was the king of Asturias from 739 to 757, probably the son-in-law of the first Asturian king, Pelayo. The rebellion of the Berber garrisons in Islāmic Spain (741) and the civil strife there that followed gave him the opportunity to incorporate Galicia into his kingdom. He also campaigned

Alfonso VII was the king of Leon and Castile from 1126 to 1157, son of Raymond of Burgundy and the grandson of Alfonso VI, whose imperial title he assumed. Though his reign saw the apogee of the imperial idea in medieval Spain and though he won notable victories against the Moors, he remains a

Alfonso III was the king of Aragon from 1285 to 1291, son of Peter III. A weak king, he was involved in an unsuccessful constitutional struggle with the Aragonese nobles. In 1287 he was compelled to grant the so-called “Privilegio de la Unión,” which handed over a number of important royal

Alfonso XI was the king of Castile and Leon from 1312, who succeeded his father, Ferdinand IV, when he was only a year old. His minority was marked by violent strife between factions of nobles, but when he came of age, in 1325, he restored order with unprecedented vigour. He gave new powers to the

Alfonso III was the king of Aragon from 1285 to 1291, son of Peter III. A weak king, he was involved in an unsuccessful constitutional struggle with the Aragonese nobles. In 1287 he was compelled to grant the so-called “Privilegio de la Unión,” which handed over a number of important royal

Alfonso V was the king of Aragon (1416–58) and king of Naples (as Alfonso I, 1442–58), whose military campaigns in Italy and elsewhere in the central Mediterranean made him one of the most famous men of his day. After conquering Naples, he transferred his court there. Alfonso was born and brought

Alfonso III was the king of Asturias from 866 to 910, son of Ordoño I. Winning a contested succession, he moved his capital forward from Oviedo to the recently restored Roman city of León. Under him, Porto (Oporto) was occupied in 868, and Castile took shape around Burgos, drawing on his Basque

Alfonso IV was the king of Leon and Asturias from c. 926 to c. 932, the son of Ordoño II and the successor of his uncle Fruela II. He became a monk, abdicated, and then thought better of it and tried to recover his throne. His short reign was, in consequence, one of political chaos, ending about

Alfonso V was the king of Leon from 999 to 1028, son of Bermudo II. He came to the throne because the devastating campaigns of Almanzor (see Manṣūr, Abū ʿĀmir al-) had forced his father to accept Almanzor’s de facto suzerainty over Leon. The Leonese were forced to take part in the Moorish campaign

Alfonso X was the king of Castile and Leon from 1252 to 1284. Alfonso’s father, Ferdinand III, conquered Andalusia and imposed tribute on the remaining Muslim states in Spain—Murcia and Granada. His mother, Beatrice, was granddaughter of the Holy Roman emperor Frederick I. Alfonso, already known as

Alfonso I was the king of Aragon and of Navarre from 1104 to 1134. Alfonso was the son of Sancho V Ramírez. He was persuaded by Alfonso VI of Leon and Castile to marry the latter’s heiress, Urraca, widow of Raymond of Burgundy. In consequence, when Alfonso VI died (1109) the four Christian kingdoms

Alfonso I was the king of Asturias from 739 to 757, probably the son-in-law of the first Asturian king, Pelayo. The rebellion of the Berber garrisons in Islāmic Spain (741) and the civil strife there that followed gave him the opportunity to incorporate Galicia into his kingdom. He also campaigned

Alfonso I was the duke of Ferrara from 1505, a noted Renaissance prince of the House of Este, an engineer and patron of the arts. Alfonso succeeded to the duchy at the death of his father, Ercole I. He employed the poet Ludovico Ariosto and the painters Titian and Giovanni Bellini, and made

Alfonso I was the duke of Ferrara from 1505, a noted Renaissance prince of the House of Este, an engineer and patron of the arts. Alfonso succeeded to the duchy at the death of his father, Ercole I. He employed the poet Ludovico Ariosto and the painters Titian and Giovanni Bellini, and made

Alfonso II was the count of Barcelona from 1162 and king of Aragon from 1164. The son of Ramón Berenguer IV, Alfonso succeeded his father as count of Barcelona and his mother as ruler of Aragon, thus associating the two countries under the house of Barcelona—a union that was destined to be

Torquato Tasso: Early life and works.: …court of Duke Alfonso II d’Este at Ferrara, where he enjoyed the patronage of the duke’s sisters, Lucrezia and Leonora, for whom he wrote some of his finest lyrical poems. In 1569 his father died; the following year Lucrezia left Ferrara, and Tasso followed the cardinal to Paris, where he…

Alfonso II was the king of Asturias from 791 to 842, the son of Fruela I. He had to face frequent and determined attacks by the armies of the emirate of Córdoba and was often defeated, but his doggedness saved Asturias from extinction. He built a new capital, Oviedo, on a strategic site in the

Torquato Tasso: Early life and works.: …court of Duke Alfonso II d’Este at Ferrara, where he enjoyed the patronage of the duke’s sisters, Lucrezia and Leonora, for whom he wrote some of his finest lyrical poems. In 1569 his father died; the following year Lucrezia left Ferrara, and Tasso followed the cardinal to Paris, where he…

Alfonso III was the king of Aragon from 1285 to 1291, son of Peter III. A weak king, he was involved in an unsuccessful constitutional struggle with the Aragonese nobles. In 1287 he was compelled to grant the so-called “Privilegio de la Unión,” which handed over a number of important royal

Alfonso III was the king of Asturias from 866 to 910, son of Ordoño I. Winning a contested succession, he moved his capital forward from Oviedo to the recently restored Roman city of León. Under him, Porto (Oporto) was occupied in 868, and Castile took shape around Burgos, drawing on his Basque

Alfonso IV was the king of Aragon from 1327 to 1336, son of James II. He was well-intentioned but weak. His reign was marked by a serious revolt in Sardinia, which led to war with Genoa, and by the establishment of diplomatic relations with the Moorish kingdoms of North Africa. The failure of the

Alfonso IV was the king of Leon and Asturias from c. 926 to c. 932, the son of Ordoño II and the successor of his uncle Fruela II. He became a monk, abdicated, and then thought better of it and tried to recover his throne. His short reign was, in consequence, one of political chaos, ending about

Alfonso IX was the king of Leon from 1188 to 1230, son of Ferdinand II of Leon, and cousin of Alfonso VIII of Castile (next to whom he is numbered as a junior member of the family). A forceful personality, Alfonso IX was determined to recover Leonese territory lost to Castile; and, despite the fact

Gertrudis Gómez de Avellaneda: …on historic models; her play Alfonso Munio (1844; rev. ed., Munio Alfonso, 1869), based on the life of Alfonso X, and Saúl (1849), a biblical drama, achieved popular success. Her novels, such as Sab (1841), an antislavery work, are now almost completely forgotten. Twice widowed and with many lovers, she…

Alfonso I was the king of Aragon and of Navarre from 1104 to 1134. Alfonso was the son of Sancho V Ramírez. He was persuaded by Alfonso VI of Leon and Castile to marry the latter’s heiress, Urraca, widow of Raymond of Burgundy. In consequence, when Alfonso VI died (1109) the four Christian kingdoms

Alfonso VI was the king of Leon (1065–70) and king of reunited Castile and Leon (1072–1109), who by 1077 had proclaimed himself “emperor of all Spain” (imperator totius Hispaniae). His oppression of his Muslim vassals led to the invasion of Spain by an Almoravid army from North Africa (1086). His

Alfonso III was the king of Aragon from 1285 to 1291, son of Peter III. A weak king, he was involved in an unsuccessful constitutional struggle with the Aragonese nobles. In 1287 he was compelled to grant the so-called “Privilegio de la Unión,” which handed over a number of important royal

Alfonso I was the king of Asturias from 739 to 757, probably the son-in-law of the first Asturian king, Pelayo. The rebellion of the Berber garrisons in Islāmic Spain (741) and the civil strife there that followed gave him the opportunity to incorporate Galicia into his kingdom. He also campaigned

Alfonso II was the king of Asturias from 791 to 842, the son of Fruela I. He had to face frequent and determined attacks by the armies of the emirate of Córdoba and was often defeated, but his doggedness saved Asturias from extinction. He built a new capital, Oviedo, on a strategic site in the

Alfonso VII was the king of Leon and Castile from 1126 to 1157, son of Raymond of Burgundy and the grandson of Alfonso VI, whose imperial title he assumed. Though his reign saw the apogee of the imperial idea in medieval Spain and though he won notable victories against the Moors, he remains a

Alfonso III was the king of Asturias from 866 to 910, son of Ordoño I. Winning a contested succession, he moved his capital forward from Oviedo to the recently restored Roman city of León. Under him, Porto (Oporto) was occupied in 868, and Castile took shape around Burgos, drawing on his Basque

Alfonso XI was the king of Castile and Leon from 1312, who succeeded his father, Ferdinand IV, when he was only a year old. His minority was marked by violent strife between factions of nobles, but when he came of age, in 1325, he restored order with unprecedented vigour. He gave new powers to the

Alfonso IV was the king of Aragon from 1327 to 1336, son of James II. He was well-intentioned but weak. His reign was marked by a serious revolt in Sardinia, which led to war with Genoa, and by the establishment of diplomatic relations with the Moorish kingdoms of North Africa. The failure of the

Alfonso X was the king of Castile and Leon from 1252 to 1284. Alfonso’s father, Ferdinand III, conquered Andalusia and imposed tribute on the remaining Muslim states in Spain—Murcia and Granada. His mother, Beatrice, was granddaughter of the Holy Roman emperor Frederick I. Alfonso, already known as

Alfonso III was the king of Aragon from 1285 to 1291, son of Peter III. A weak king, he was involved in an unsuccessful constitutional struggle with the Aragonese nobles. In 1287 he was compelled to grant the so-called “Privilegio de la Unión,” which handed over a number of important royal

Alfonso V was the king of Aragon (1416–58) and king of Naples (as Alfonso I, 1442–58), whose military campaigns in Italy and elsewhere in the central Mediterranean made him one of the most famous men of his day. After conquering Naples, he transferred his court there. Alfonso was born and brought

Alfonso IV was the king of Leon and Asturias from c. 926 to c. 932, the son of Ordoño II and the successor of his uncle Fruela II. He became a monk, abdicated, and then thought better of it and tried to recover his throne. His short reign was, in consequence, one of political chaos, ending about

Alfonso V was the king of Leon from 999 to 1028, son of Bermudo II. He came to the throne because the devastating campaigns of Almanzor (see Manṣūr, Abū ʿĀmir al-) had forced his father to accept Almanzor’s de facto suzerainty over Leon. The Leonese were forced to take part in the Moorish campaign

Alfonso X was the king of Castile and Leon from 1252 to 1284. Alfonso’s father, Ferdinand III, conquered Andalusia and imposed tribute on the remaining Muslim states in Spain—Murcia and Granada. His mother, Beatrice, was granddaughter of the Holy Roman emperor Frederick I. Alfonso, already known as

Alfonso V was the king of Leon from 999 to 1028, son of Bermudo II. He came to the throne because the devastating campaigns of Almanzor (see Manṣūr, Abū ʿĀmir al-) had forced his father to accept Almanzor’s de facto suzerainty over Leon. The Leonese were forced to take part in the Moorish campaign

Alfonso V was the king of Aragon (1416–58) and king of Naples (as Alfonso I, 1442–58), whose military campaigns in Italy and elsewhere in the central Mediterranean made him one of the most famous men of his day. After conquering Naples, he transferred his court there. Alfonso was born and brought

Alfonso VI was the king of Leon (1065–70) and king of reunited Castile and Leon (1072–1109), who by 1077 had proclaimed himself “emperor of all Spain” (imperator totius Hispaniae). His oppression of his Muslim vassals led to the invasion of Spain by an Almoravid army from North Africa (1086). His

Alfonso VII was the king of Leon and Castile from 1126 to 1157, son of Raymond of Burgundy and the grandson of Alfonso VI, whose imperial title he assumed. Though his reign saw the apogee of the imperial idea in medieval Spain and though he won notable victories against the Moors, he remains a

Alfonso VIII was the king of Castile from 1158, son of Sancho III, whom he succeeded when three years old. Before Alfonso came of age, his reign was troubled by internal strife and the intervention of the kingdom of Navarre in Castilian affairs. Throughout his reign he maintained a close alliance

Alfonso X was the king of Castile and Leon from 1252 to 1284. Alfonso’s father, Ferdinand III, conquered Andalusia and imposed tribute on the remaining Muslim states in Spain—Murcia and Granada. His mother, Beatrice, was granddaughter of the Holy Roman emperor Frederick I. Alfonso, already known as

Alfonso XI was the king of Castile and Leon from 1312, who succeeded his father, Ferdinand IV, when he was only a year old. His minority was marked by violent strife between factions of nobles, but when he came of age, in 1325, he restored order with unprecedented vigour. He gave new powers to the

Alfonso XII was a Spanish king whose short reign (1874–85) gave rise to hopes for a stable constitutional monarchy in Spain. The eldest surviving son of Queen Isabella II and, presumably, her consort, the duque de Cádiz, Alfonso accompanied his mother into exile following her deposition by the

Alfonso XIII was a Spanish king (1902–31) who by authorizing a military dictatorship hastened his own deposition by advocates of the Second Republic. The posthumous son of Alfonso XII, Alfonso XIII was immediately proclaimed king under the regency of his mother, María Cristina. Although lively and

fado: In the 1970s José Alfonso pioneered a fado-based fusion music in which he combined fado with rock music, as well as with various folk music traditions, most notably nueva canción (“new song”), a type of political protest music that was popular throughout Latin America at the time.

West Memphis Three: Paradise Lost and prison release: …maneuver is known as an Alford plea. They were released after each was sentenced to time served and received a 10-year suspended sentence. These developments were chronicled in Paradise Lost 3: Purgatory (2011). While other suspects were discussed on the Internet and in such media projects as the documentary West…

West Memphis Three: Paradise Lost and prison release: …maneuver is known as an Alford plea. They were released after each was sentenced to time served and received a 10-year suspended sentence. These developments were chronicled in Paradise Lost 3: Purgatory (2011). While other suspects were discussed on the Internet and in such media projects as the documentary West…

To Kill a Mockingbird: Cast:

Dorothy Wordsworth: …an English prose writer whose Alfoxden Journal 1798 and Grasmere Journals 1800–03 are remarkable for the imaginative power of their description of nature. Her journals also shed significant light on her brother, the Romantic poet William Wordsworth, whose own work was profoundly influenced by her writing.

Alfred was the king of Wessex (871–899), a Saxon kingdom in southwestern England. He prevented England from falling to the Danes and promoted learning and literacy. Compilation of the Anglo-Saxon Chronicle began during his reign, circa 890. When he was born, it must have seemed unlikely that Alfred

Alfred A. Knopf: …of the prestigious publishing house Alfred A. Knopf, Inc.

Berlin Zoo: A notable feature is the Alfred Brehm Animal House, one of the largest zoo buildings in the world. This structure houses a huge aviary containing hundreds of species of birds. The aviary is flanked by cages of wild cats and by terrariums of lizards and snakes, and the whole is…

For swimmers competing in the 1896 Athens Olympics, the events required more than a show of strength and speed; they also tested the swimmers’ abilities to withstand the elements. Rather than being held in a swimming pool, the races took place in the Bay of Zea near Piraeus. Unseasonably cold

Robert Altman: Early years: Bonanza, and Alfred Hitchcock Presents, among many other programs.

Five years after his Psycho forever changed perspectives on taking a shower, the legendary film director and “master of suspense” Alfred Hitchcock shared his knowledge in the 14th edition of the Encyclopædia Britannica. His discussion of film production was first published in 1965 as part of a

Robert Altman: Early years: Bonanza, and Alfred Hitchcock Presents, among many other programs.

Theatre of Cruelty: …and Robert Aron founded the Théâtre Alfred Jarry in 1926; they presented four programs, including August Strindberg’s A Dream Play and Vitrac’s Victor, before disbanding in 1929. Between 1931 and 1936 Artaud formulated a theory for what he called a Theatre of Cruelty in a series of essays published in…

Alfred Jewel, elaborate gold ornament consisting of an enameled plaque with a figure held in place on one side by an engraved design and on the other by a gold fret of Old English words. The inscription reads, “Aelfred mec heht gewyrcan” (“Alfred ordered me to be made”). The Alfred Jewel (now in

Oklahoma City: History: …bomb destroyed part of the Alfred P. Murrah Federal Building in the downtown area, killing 168 people and injuring more than 500. Timothy J. McVeigh was found guilty of the bombing in 1997 and was executed in 2001. The Oklahoma City National Memorial, established in 1997, encompasses an outdoor memorial,…

Census of Marine Life: Origins and oversight: …report was forwarded to the Alfred P. Sloan Foundation, an American nonprofit that provided research grants. In 1997 the foundation proceeded to commission a series of workshops to determine the feasibility of such a survey.

Alfred was the king of Wessex (871–899), a Saxon kingdom in southwestern England. He prevented England from falling to the Danes and promoted learning and literacy. Compilation of the Anglo-Saxon Chronicle began during his reign, circa 890. When he was born, it must have seemed unlikely that Alfred

Alfred University, private, coeducational institution of higher learning in Alfred, New York, U.S. The university comprises the privately endowed Colleges of Liberal Arts and Sciences, Business, and Engineering and Professional Studies and the publicly funded New York State College of Ceramics,

Thomas Arne: …melodic style was apparent in Alfred, a Masque (notable for “Rule, Britannia”) and The Judgment of Paris, both produced at the Prince of Wales’s residence at Cliveden in 1740. Arne’s settings of Shakespeare’s songs, written for revivals of As You Like It, Twelfth Night, and The Merchant of Venice in…

Alfred, Lord Tennyson was an English poet often regarded as the chief representative of the Victorian age in poetry. He was raised to the peerage in 1884. Tennyson was the fourth of 12 children, born into an old Lincolnshire family, his father a rector. Alfred, with two of his brothers, Frederick

Ottawa Senators: …the play of right winger Daniel Alfredsson and centre Alexi Yashin, Ottawa made its first trip to the play-offs, where it lost in the opening round to the Buffalo Sabres. The following season the Senators earned the lowest seed in the Eastern Conference play-offs, in which they upset the top-seeded…

aurora: Alfvén waves—which are generated in the dayside and nightside regions of the magnetosphere and in the region of the magnetosphere called the magnetotail—push these electrons along and accelerate them up to 72.4 million km (45 million miles) per hour. They collide with oxygen and nitrogen…

Hannes Alfvén was an astrophysicist and winner, with Louis Néel of France, of the Nobel Prize for Physics in 1970 for his essential contributions in founding plasma physics—the study of plasmas (ionized gases). Alfvén was educated at Uppsala University and in 1940 joined the staff of the Royal

Hannes Alfvén was an astrophysicist and winner, with Louis Néel of France, of the Nobel Prize for Physics in 1970 for his essential contributions in founding plasma physics—the study of plasmas (ionized gases). Alfvén was educated at Uppsala University and in 1940 joined the staff of the Royal

Zhores Alferov was a Soviet physicist who, with Herbert Kroemer and Jack S. Kilby, was awarded the Nobel Prize for Physics in 2000 for their work that laid the foundation for the modern era of computers and information technology. Alferov received a doctorate in physics and mathematics from the

algae, members of a group of predominantly aquatic photosynthetic organisms of the kingdom Protista. Algae have many types of life cycles, and they range in size from microscopic Micromonas species to giant kelps that reach 60 metres (200 feet) in length. Their photosynthetic pigments are more

algae, members of a group of predominantly aquatic photosynthetic organisms of the kingdom Protista. Algae have many types of life cycles, and they range in size from microscopic Micromonas species to giant kelps that reach 60 metres (200 feet) in length. Their photosynthetic pigments are more

ostariophysan: Annotated classification: Family Gyrinocheilidae (algae eaters) Adaptations to fast currents include fleshy, suctorial mouth and inhalant-exhalant gill openings. Algae feeders. Size to 30 cm (12 inches). Inhabits mountain streams of Southeast Asia. 1 genus, 3 species. Family Psilorhynchidae (mountain carps) Size to about 8 cm (3.3 inches). Inhabits mountain…

ocean warming: Biological effects: …changes also promote the growth algal blooms, including red tides and pathogenic vibrio bacteria, increasing the risk of humans and other animals coming into contact with them.

algae: Toxicity: Some algae can be harmful to humans. A few species produce toxins that may be concentrated in shellfish and finfish, which are thereby rendered unsafe or poisonous for human consumption. The dinoflagellates (class Dinophyceae) are the most notorious producers of toxins. Paralytic

algae: Toxicity: Some algae can be harmful to humans. A few species produce toxins that may be concentrated in shellfish and finfish, which are thereby rendered unsafe or poisonous for human consumption. The dinoflagellates (class Dinophyceae) are the most notorious producers of toxins. Paralytic

Alessandro Algardi was one of the most important Roman sculptors of the 17th century working in the Baroque style. Algardi, the son of a silk merchant from Bologna, was trained under Lodovico Carracci at the Accademia degli Incamminati, where he acquired the skills of a first-rate draftsman. After

Francesco Algarotti was a cosmopolitan connoisseur of the arts and sciences who was esteemed by the philosophers of the Enlightenment for his wide knowledge and elegant presentation of advanced ideas. Algarotti was the son of well-to-do middle-class parents. He was educated in his native Venice and

Algarve, historical province of southern Portugal, bounded by the Atlantic Ocean (south and west) and the lower Guadiana River (east). Much of the interior upland region is of low productivity and is sparsely populated; the fertile coastal lowland is more densely inhabited. The Phoenicians

algae, members of a group of predominantly aquatic photosynthetic organisms of the kingdom Protista. Algae have many types of life cycles, and they range in size from microscopic Micromonas species to giant kelps that reach 60 metres (200 feet) in length. Their photosynthetic pigments are more

algebra, branch of mathematics in which arithmetical operations and formal manipulations are applied to abstract symbols rather than specific numbers. The notion that there exists such a distinct subdiscipline of mathematics, as well as the term algebra to denote it, resulted from a slow historical

Arundhati Roy: Nonfiction works: …publications are Power Politics (2001), The Algebra of Infinite Justice (2002), War Talk (2003), Public Power in the Age of Empire (2004), Field Notes on Democracy: Listening to Grasshoppers (2009), Broken Republic: Three Essays (2011), and Capitalism: A Ghost Story (2014). My Seditious Heart (2019) is a

elementary algebra, branch of mathematics that deals with the general properties of numbers and the relations between them. Algebra is fundamental not only to all further mathematics and statistics but to the natural sciences, computer science, economics, and business. Along with writing, it is a

fundamental theorem of algebra, theorem of equations proved by Carl Friedrich Gauss in 1799. It states that every polynomial equation of degree n with complex number coefficients has n roots, or solutions, in the complex numbers. The roots can have a multiplicity greater than zero. For example, x2

linear algebra, mathematical discipline that deals with vectors and matrices and, more generally, with vector spaces and linear transformations. Unlike other parts of mathematics that are frequently invigorated by new ideas and unsolved problems, linear algebra is very well understood. Its value

modern algebra, branch of mathematics concerned with the general algebraic structure of various sets (such as real numbers, complex numbers, matrices, and vector spaces), rather than rules and procedures for manipulating their individual elements. During the second half of the 19th century, various

Algebraic Versus Transcendental Objects: One important difference between the differential calculus of Pierre de Fermat and René Descartes and the full calculus of Isaac Newton and Gottfried Wilhelm Leibniz is the difference between algebraic and transcendental objects. The rules of differential calculus are complete

algebraic equation, statement of the equality of two expressions formulated by applying to a set of variables the algebraic operations, namely, addition, subtraction, multiplication, division, raising to a power, and extraction of a root. Examples are x3 + 1 and (y4x2 + 2xy – y)/(x – 1) = 12. An

elementary algebra: Algebraic expressions: Any of the quantities mentioned so far may be combined in expressions according to the usual arithmetic operations of addition, subtraction, and multiplication. Thus, ax + by and axx + bx + c are common algebraic expressions. However, exponential notation is commonly used…

Arthur Cayley: …quantic, known today as an algebraic form, is a polynomial with the same total degree for each term; for example, every term in the following polynomial has a total degree of 3: x3 + 7x2y − 5xy2 + y3. Alongside work produced by his friend James Joseph Sylvester, Cayley’s study…

elementary algebra: Algebraic expressions: Any of the quantities mentioned so far may be combined in expressions according to the usual arithmetic operations of addition, subtraction, and multiplication. Thus, ax + by and axx + bx + c are common algebraic expressions. However, exponential notation is commonly used…

algebraic geometry, study of the geometric properties of solutions to polynomial equations, including solutions in dimensions beyond three. (Solutions in two and three dimensions are first covered in plane and solid analytic geometry, respectively.) Algebraic geometry emerged from analytic geometry

mathematics: Developments in pure mathematics: …two reasons: the theory of algebraic integers forms part of it, because algebraic integers naturally form into rings; and (as Kronecker and Hilbert had argued) algebraic geometry forms another part. The rings that arise there are rings of functions definable on the curve, surface, or manifold or are definable on…

linguistics: Mathematical linguistics: …may be termed statistical and algebraic linguistics, respectively, are typically distinct. Attempts have been made to derive the grammatical rules of languages from the statistical structure of texts written in those languages, but such attempts are generally thought to have been not only unsuccessful so far in practice but also,…