# Mathematics Sentence Examples

You will be glad to hear that I enjoy

**Mathematics**now.With this was included

**mathematics**, astronomy and astrology, and even the magic arts.Of more general interest, however, are his labours in pure

**mathematics**, which appear for the most part in Crelle's Journal from 1828 to 1858.He divides geography into The Spherical Part, or that for the study of which

**mathematics**alone is required, and The Topical Part, or the description of the physical relations of parts of the earth's surface, preferring this division to that favoured by the ancient geographers - into general and special.His knowledge of the higher

**mathematics**was acquired by his own unaided efforts after he had left the college.AdvertisementEach problem was something unique; the elements of transition from one to another were wanting; and the next step which

**mathematics**had to make was to find some method of reducing, for instance, all curves to a common notation.After taking his degree he wavered between classics and

**mathematics**, but finally chose the latter.The former was professor of

**mathematics**at Bologna, and published, among other works, a treatise on the infinitesimal calculus.At Leipzig, GÃ¶ttingen and Halle he studied for four years, ultimately devoting himself to

**mathematics**and astronomy.Not until the age of seventeen did he attack the higher

**mathematics**, and his progress was much retarded by the want of efficient help. When about sixteen years of age he became assistant-master in a private school at Doncaster, and he maintained himself to the end of his life in one grade or other of the scholastic profession.AdvertisementScarcely any member of the Arabian circle of the sciences, including theology, philology,

**mathematics**, astronomy, physics and music, was left untouched by the treatises of Avicenna, many of which probably varied little, except in being commissioned by a different patron and having a different form or extent.Higher education is represented by the provincial university, which teaches science and

**mathematics**, holds examinations, distributes scholarships, and grants degrees in all subjects.As I have said before, I had no aptitude for

**mathematics**; the different points were not explained to me as fully as I wished.He began life as a clerk, but, obtaining an appointment to a cadetship at West Point in 1825, he graduated there in 1829, and acted as assistant professor of

**mathematics**1829-1832.He was then called to the bar, but in 1836 became professor of

**mathematics**and natural philosophy at Cincinnati College.AdvertisementHis taste for

**mathematics**early developed itself; and he acquired Latin that he might study Newton's Principia.He was offered, but declined, the professorship of

**mathematics**and astronomy at Harvard.Roger Bacon, his pupil, speaks highly of his attainments in theology and

**mathematics**.He was then appointed to the ordinary chair of

**mathematics**successively at Basel (1863), Tubingen (1865) and Leipzig (1868).In

**mathematics**he was twenty-fourth wrangler, Isaac Todhunter being senior.AdvertisementThough he never became either a scholar or a mathematician, he did enough accurate work to be placed in the honorary fourth class both in classics and in

**mathematics**.This view involves the denial of force as a cause, and the assertion that all we know about force is that the acceleration of one mass depends on that of another, as in

**mathematics**a function depends on a variable; and that even Newton's third law of motion is merely a description of the fact that two material points determine in one another, without reciprocally causing, opposite accelerations.This being so, he finds in

**mathematics**two kinds of transcendence - real, where the transcendent, though not actual in experience, can become partly so, e.g.Neither

**mathematics**itself, nor any branch or set of branches of**mathematics**, can be regarded as an isolated science.As to the teaching of algebra, see references under Arithmetic to works on the teaching of elementary

**mathematics**.AdvertisementThe Romans, who succeeded the Greeks as the chief civilized power in Europe, failed to set store on their literary and scientific treasures;

**mathematics**was all but neglected; and beyond a few improvements in arithmetical computations, there are no material advances to be recorded.The fame of this astronomer and mathematician rests on his work, the Aryabhattiyam, the third chapter of which is devoted to

**mathematics**.It is of great interest to the historical student, for it exhibits the influence of Greek science upon Indian

**mathematics**at a period prior to Aryabhatta.Moritz Cantor has suggested that at one time there existed two schools, one in sympathy with the Greeks, the other with the Hindus; and that, although the writings of the latter were first studied, they were rapidly discarded for the more perspicuous Grecian methods, so that, among the later Arabian writers, the Indian methods were practically forgotten and their

**mathematics**became essentially Greek in character.**Mathematics**was more or less ousted from the academic curricula by the philosophical inquiries of the schoolmen, and it was only after an interval of nearly three centuries that a worthy successor to Leonardo appeared.In it he mentions many earlier writers from whom he had learnt the science, and although it contains very little that cannot be found in Leonardo's work, yet it is especially noteworthy for the systematic employment of symbols, and the manner in which it reflects the state of

**mathematics**in Europe during this period.These works are the earliest printed books on

**mathematics**.The renaissance of

**mathematics**was thus effected in Italy, and it is to that country that the leading developments of the following century were due.The 17th century is a famous epoch in the progress of science, and the

**mathematics**in no way lagged behind.Notable service was also rendered by Augustus de Morgan, who applied logical analysis to the laws of

**mathematics**.He devoted his youth to the study of history, chronology,

**mathematics**, astronomy, philosophy and medicine.Other works of his, chiefly on

**mathematics**and astronomy, are still in manuscript only.Born on the 15th of February 1514, he studied at Tiguri with Oswald Mycone, and afterwards went to Wittenberg where he was appointed professor of

**mathematics**in 1537.He projected numerous other works, as is shown by a letter to Peter Ramus in 1568, which Adrian Romanus inserted in the preface to his Idea of

**Mathematics**.Borrell entrusted him to the care of a Bishop Hatto, under whose instruction Gerbert made great progress in

**mathematics**.He soon distinguished himself as a student and made rapid progress, especially in

**mathematics**.As a politician Fourier achieved uncommon success, but his fame chiefly rests on his strikingly original contributions to science and

**mathematics**.Here Jacques Davy received his education, being taught Latin and

**mathematics**by his father, and learning Greek and Hebrew and the philosophy then in vogue.As a foundation his education must be thorough in the natural and physical sciences and

**mathematics**.These miners' schools (Bergschule, ecoles des mineurs) give elementary instruction in chemistry, physics, mechanics, mineralogy, geology and

**mathematics**and drawing, as well as in such details of the art of mining as will best supplement the practical information already acquired in underground work.The invention of the mechanical air-pump is generally attributed to Otto von Guericke, consul of Magdeburg, who exhibited his instrument in 1654; it was first described in 1657 by Gaspar Schott, professor of

**mathematics**at Wurttemberg, in his NI echanica hydraulico-pneumatica, and afterwards (in 1672) by Guericke in his Experimenta nova Magdeburgica de vacus spatia.Trained for the scholastic profession, he was appointed assistant professor at the Academy of Paris in 1831, professor of

**mathematics**at Lyons in 1834, rector of the Academy of Grenoble in 1835, inspector-general of studies in 1838, rector of the Academy of Dijon and honorary inspectorgeneral in 1854, retiring in 1862.Cournot was the first who, with a competent knowledge of both subjects, endeavoured to apply

**mathematics**to the treatment of economic questions.Notwithstanding Cournot's just reputation as a writer on

**mathematics**, the Recherches made little impression.The development of astronomy implies considerable progress in

**mathematics**; it is not surprising, therefore, that the Babylonians should have invented an extremely simple method of ciphering or have discovered the convenience of the duodecimal system.The first forty-two years of his life are obscure; we learn from incidental remarks of his that he was a Sunnite, probably according to the IIanifite rite, well versed in all the branches of natural science, in medicine,

**mathematics**, astronomy and astrology, in.In natural science, geography, natural history,

**mathematics**and astronomy he took a genuine interest.In1824-1828he was professor of

**mathematics**and natural philosophy at Brown University, acting as president in 1826-1827; in1828-1831was president of Transylvania University, Lexington, Kentucky; and in1831-1837was president of the University of Alabama at Tuscaloosa, where he organized the Alabama Female Athenaeum.The study of

**mathematics**learned from Greece and India was developed by Arabian writers, who in turn became the teachers of Europe in the 16th century.The university, founded in 1338, has faculties of law, medicine,

**mathematics**and philosophy and literature, and is to this day one of the most famous in Italy.All these have faculties of letters and law, and San Marcos has in addition faculties of theology, medicine,

**mathematics**and science, philosophy and administrative and political economy.Godin, a member of the French commission for measuring an arc of the meridian near Quito, became professor of

**mathematics**at San Marcos in 1750; and the botanical expeditions sent out from Spain gave further zest to scientific research.Thence he journeyed to Bagdad, where he learned Arabic and gave himself to the study of

**mathematics**, medicine and philosophy, especially the works of Aristotle.Taylor's Methodus Incrementorum Directa et Inversa (London, 1715) added a new branch to the higher

**mathematics**, now designated the " calculus of finite differences."Grant was the best horseman of his class, and took a respectable place in

**mathematics**, but at his graduation in 1843 he only ranked twenty-first in a class of thirty-nine.To the great dissatisfaction of his parents, he resolved to return to Paris (1816), and to earn his living there by giving lessons in

**mathematics**.This and two other engagements as a teacher of

**mathematics**secured him an income of some £400 a year.They are thus the double key of The double Comte's systematization of the philosophy of all the key of sciences from

**mathematics**to physiology, and his positive analysis of social evolution, which is the base of philo= sociology.He worked hard at his classical lessons, and supplemented the ordinary business of the school by studying

**mathematics**in the holidays.He holds a high place in the history of humanism by the foundation of the College de France; he did not found an actual college, but after much hesitation instituted in 1530, at the instance of Guillaume Bude (Budaeus), Lecteurs royaux, who in spite of the opposition of the Sorbonne were granted full liberty to teach Hebrew, Greek, Latin,

**mathematics**, &c. The humanists Bude, Jacques Colin and Pierre Duchatel were the king's intimates, and Clement Marot was his favourite poet.In 1724 he was offered the chair of

**mathematics**in the university of Upsala, which he declined, on the ground that it was a mistake for mathematicians to be limited to theory.After acting for a short time as assistant in Harvard College Observatory, he was appointed assistant professor of

**mathematics**in the U.S. Naval Academy in 1866, and in the following year became director of the Allegheny Observatory at Pittsburg, a position which he held until his selection in 1887 as secretary of the Smithsonian.At Oxford, as at Eton, he read literature from natural liking, and he paid some attention to

**mathematics**.While he taught during the day at Stote's Hall, he studied

**mathematics**in the evening at a school in Newcastle.In 1773 he was appointed professor of

**mathematics**at the Royal Military Academy, Woolwich, and in the following year he was elected F.R.S.After his Tables of the Products and Powers of Numbers, 1781, and his Mathematical Tables, 1785, he issued, for the use of the Royal Military Academy, in 1787 Elements of Conic Sections, and in 1798 his Course of

**Mathematics**.His Mathematical and Philosophical Dictionary, a valuable contribution to scientific biography, was published in 1795 (2nd ed., 1815), and the four volumes of Recreations in

**Mathematics**and Natural Philosophy, mostly a translation from the French, in 1803.Here he heard Luther preach, but was more attracted by Melanchthon, who interested him in

**mathematics**and astrology.This practice continued to prevail till the 17th century, when, at the instance of the Jesuit Schall, president of the tribunal of

**mathematics**, they adopted the European method of dividing the day into twenty-four hours, each hour into sixty minutes, and each minute into sixty seconds.In science and theology,

**mathematics**and poetry, metaphysics and law, he is a competent and always a fair if not a profound critic. The bent of his own mind is manifest in his treatment of pure literature and of political speculation - which seems to be inspired with stronger personal interest and a higher sense of power than other parts of his work display.In the course of a century eight of its members successfully cultivated various branches of

**mathematics**, and contributed powerfully to the advance of science.While at Geneva he taught a blind girl several branches of science, and also how to write; and this led him to publish A Method of Teaching

**Mathematics**to the Blind.Chemistry, as well as

**mathematics**, seems to have been the object of his early attention; and in the year 1690 he published a dissertation on effervescence and fermentation.His independent discoveries in

**mathematics**are numerous and important.His inaugural discourse was on the "new analysis," which he so successfully applied in investigating various problems both in pure and applied

**mathematics**.It is, however, his works in pure

**mathematics**that are the permanent monuments of his fame.Meanwhile the study of

**mathematics**was not neglected, as appears not only from his giving instruction in geometry to his younger brother Daniel, but from his writings on the differential, integral, and exponential calculus, and from his father considering him, at the age of twenty-one, worthy of receiving the torch of science from his own hands.Both were appointed at the same time professors of

**mathematics**in the academy of St Petersburg; but this office Nicolas enjoyed for little more then eight months.After his'return,though only twenty-four years of age, he was invited to become president of an academy then projected at Genoa; but, declining this honour, he was, in the following year, appointed professor of

**mathematics**at St Petersburg.He studied law and

**mathematics**, and, of ter travelling in France,was for five years professor of eloquence in the university of his native city.On the death of his father he succeeded him as professor of

**mathematics**.In Italy he formed a friendship with Lorgna, professor of

**mathematics**at Verona, and one of the founders of the Societe' Italiana for the encouragement of the sciences.His fame now rests, however, entirely upon his achievements in

**mathematics**.He then devoted himself with astonishing ardour to

**mathematics**, chemistry, natural history, technology and even political economy.In 1842 he took a "double-first" and was elected fellow of B alliol, and lecturer in

**mathematics**and logic. Four years later he took orders, and with the aim of helping forward the education of the very poor, he accepted the headship of Kneller Hall, a college which the government formed for the training of masters of workhouse and penal schools.He graduated at Harvard in 1817, was tutor in

**mathematics**there in 1820-1821, was admitted to practice in the court of common pleas in December 1821, and began the practice of law in Newburyport, Mass., in 1824.In this way the principle of continuity, which is the basis of the method of Fluxions and the whole of modern

**mathematics**, may be applied to the analysis of problems connected with material bodies by assuming them, for the purpose of this analysis, to be homogeneous.Of his sons, Thomas (1616-1680) was born at Copenhagen, where, after a long course of study in various universities of Europe, he was appointed successively professor of

**mathematics**(1647) and anatomy (1648).Another son, Erasmus (1625-1698), born at Roskilde, spent ten years in visiting England, Holland, Germany and Italy, and filled the chairs of

**mathematics**and medicine at Copenhagen.The sciences of

**mathematics**, astronomy and medicine were also cultivated with assiduity and success at Alexandria, but they can scarcely be said to have their origin there, or in any strict sense to form a part of the peculiarly Alexandrian literature.Alexandria continued to be celebrated as a school of

**mathematics**and science long after the Christian era.In 1827 he became extraordinary and in 1829 ordinary professor of

**mathematics**at Konigsberg, and this chair he filled till 1842, when he visited Italy for a few months to recruit his health.It was in analytical development that Jacobi's peculiar power mainly lay, and he made many important contributions of this kind to other departments of

**mathematics**, as a glance at the long list of papers that were published by him in Crelle's Journal and elsewhere from 1826 onwards will sufficiently indicate.In 1836 he entered Marischal College, and came under the influence of John Cruickshank, professor of

**mathematics**, Thomas Clark, professor of chemistry, and William Knight, professor of natural philosophy.His college career was distinguished, especially in mental philosophy,

**mathematics**and physics.In 1845 he was appointed professor of

**mathematics**and natural philosophy in the Andersonian University of Glasgow.This classification, though it is of high value in the clearing up of our conceptions of the essential contrasted with the accidental, the relation of genus, differentia and definition and so forth, is of more significance in connexion with abstract sciences, especially

**mathematics**, than for the physical sciences.This being so, not only were physics and

**mathematics**impossible as sciences of necessary objective truth, but our apparent consciousness of a permanent self and object alike must be delusive.The students number some 750, and there are five faculties of theology, law, medicine,

**mathematics**and science, and letters.His great reputation and the influence of Sir William Boswell, the English resident, with the states-general procured his election in 1643 to the chair of

**mathematics**in Amsterdam, whence he removed in 1646, on the invitation of the prince of Orange, to Breda, where he remained till 1652.It might, therefore, be described as that branch of

**mathematics**which deals with formulae for calculating the numerical measurements of curved lengths, areas and volumes, in terms of numerical data which determine these measurements.Vitality can only be retained by close association with more abstract branches of

**mathematics**.He was educated at the university of Moscow, and in 1859 became professor of

**mathematics**in the university of St Petersburg, a position from which he retired in 1880.Having studied literature, he afterwards devoted himself entirely to

**mathematics**and natural philosophy.He became professor of philosophy,

**mathematics**, and Oriental languages at Wurzburg, whence he was driven (1631) by the troubles of the Thirty Years' War to Avignon.Through the influence of Cardinal Barberini he next (1635) settled in Rome, where for eight years he taught

**mathematics**in the Collegio Romano, but ultimately resigned this appointment to study hieroglyphics and other archaeological subjects.His voluminous writings in philology, natural history, physics and

**mathematics**often accordingly have a good deal of the historical interest which attaches to pioneering work, however imperfectly performed; otherwise they now take rank as curiosities of literature merely.Next follow chapters on the literary renaissance of the nation, its progress in art,

**mathematics**, chemistry and natural science; the magnificent development of agriculture, modern industry, commerce and finance; and in particular its flourishing selfgovernment, " which will be exercised in the fullest freedom," and in which " the communal organization embodies in the highest degree the conception of self-government " (p. 234), and " the independent sphere of activity unlimited in its fundamental principle " (p. 235) in that " State control is exercised seldom and discreetly " (p. 236).Varenius studied at the gymnasium of Hamburg (1640-42), and at Konigsberg (1643-45) and Leiden (1645-49) universities, where he devoted himself to

**mathematics**and medicine, taking his medical degree at Leiden in 1649.In 181 9 he was appointed professor of

**mathematics**at the athenaeum of Brussels; in 1828 he became lecturer at the newly created museum of science and literature, and he continued to hold that post until the museum was absorbed in the free university in 1834.In 1788 he entered the corps of noble cadets in the artillery and engineering department, where his ability, especially in

**mathematics**, soon attracted attention.Despite extreme penury, he then continued to study indefatigably ancient and modern languages, history and literature, finally turning his attention to

**mathematics**and astronomy.In 1613 he succeeded his father Rudolph Snell (1546-1613) as professor of

**mathematics**in the university of Leiden.Soon afterwards he was appointed professor of

**mathematics**in the Ecole Militaire at Paris, and he was afterwards professor in the Ecole Normale.It will thus be seen that Legendre's works have placed him in the very foremost rank in the widely distinct subjects of elliptic functions, theory of numbers, attractions, and geodesy, and have given him a conspicuous position in connexion with the integral calculus and other branches of

**mathematics**.He studied theology, and was for some years a dissenting minister at Tonbridge, but on the death of his father he devoted himself to the congenial study of

**mathematics**.Meanwhile, at Oxford a proposal practically making Greek optional with all undergraduates was rejected, in November 1902, by 189 votes to 166; a preliminary proposal permitting students of

**mathematics**or natural science to offer one or more modern languages in lieu of Greek was passed by 164 to 162 in February 1904, but on the 29th of November the draft of a statute to this effect was thrown out by 200 to 164.The law of the 1st of May 1802 brought the lycees into existence, the subjects being, in Napoleon's own phrase, " mainly Latin and

**mathematics**."In these schools the subjects of study included

**mathematics**and natural sciences, geography and history, and modern languages (especially French), with riding, fencing and dancing; Latin assumed a subordinate place, and classical composition in prose or verse was not considered a sufficiently courtly accomplishment.The new gymnasium aimed at a wider education, in which literature was represented by Latin, Greek and German, by the side of

**mathematics**and natural science, history and religion.In 1875 Wiese was succeeded by Bonitz, the eminent Aristotelian scholar, who in 1849 had introduced

**mathematics**and natural science into the schools of Austria, and had substituted the wide reading of classical authors for the prevalent practice of speaking and writing Latin.In 1788 Pfaff became professor of

**mathematics**in Helmstedt, and so continued until that university was abolished in 1810.From that time till his death on the 21st of April 1825 he held the chair of

**mathematics**at Halle.His brother, Johann Wilhelm Andreas Pfaff (1774-1835), was professor of pure and applied

**mathematics**successively at Dorpat, Nuremberg, Wurzburg and Erlangen.At Harrow he obtained in 1842 a Lyon scholarship, and at Oxford in 1845 a first-class in

**mathematics**, in 1846 the junior and in 1847 the senior university mathematical scholarship. In 1846 he left Oxford to take his father's place in the business, in which he was engaged until his death.His papers, numbering over 100, were published principally in the Philosophical Transactions, Proceedings of the Royal Society, Quarterly Journal of

**Mathematics**, Proceedings of the London Mathematical Society and Crelle, and one or two in the Comptes rendus of the Paris Academy; a list of them, arranged according to the several journals in which they originally appeared, with short notes upon the less familiar memoirs, is given in Nature, xxvii.His Son, Johann Ernst Immanuel (1725-1778), studied Semitic languages at Jena, and also natural science and

**mathematics**.He graduated in 1865 at the Lawrence Scientific School of Harvard, where for the next two years he was a teacher of

**mathematics**.At Glasgow his favourite studies had been

**mathematics**and natural philosophy; but at Oxford he appears to have devoted himself almost entirely to moral and political science and to ancient and modern languages.At the age of eleven he was entered as a student at St Andrews, where he devoted himself almost exclusively to

**mathematics**.In May 1803, after attending further courses of lectures in Edinburgh, and acting as assistant to the professor of

**mathematics**at St Andrews, he was ordained as minister of Kilmany in Fifeshire, about 9 m.In 1805 he became a candidate for the vacant professorship of

**mathematics**at Edinburgh, but was unsuccessful.Between John Craig and John Napier a friendship sprang up which may have been due to their common taste for

**mathematics**.Now Mark Napier found in the library of the university of Edinburgh a mathematical work bearing a sentence in Latin which he translates, " To Doctor John Craig of Edinburgh, in Scotland, a most illustrious man, highly gifted with various and excellent learning, professor of medicine, and exceedingly skilled in the

**mathematics**, Tycho Brahe bath sent this gift, and with his own hand written this at Uraniburg, 2d November 1588."The introduction of infinite series into

**mathematics**effected a great change in the modes of calculation and the treatment of the subject.His early mastery of classical literature led him to the study of classic monuments in classic lands, while his equally conspicuous talent for

**mathematics**gave him the laws of form and proportion in architectural design.A vacancy among the fellows is filled up by the provost and a select number of the fellows, after examination comprised in five principal courses,

**mathematics**, experimental science, classics, mental and moral science and Hebrew.The scholars on the foundation (or "of the House") are chosen from among the undergraduates, for merit in classics,

**mathematics**or experimental science.From 1813 to 1820 he was extraordinary professor of astronomy and

**mathematics**at the new university and observer at the observatory, becoming in 1820 ordinary professor and director.John Casey, professor of

**mathematics**at the Catholic university of Dublin, has given elementary demonstrations founded on the theory of similitude and coaxal circles which are reproduced in his Sequel to Euclid; an analytical solution by Gergonne is given in Salmon's Conic Sections.Such persons have flourished at all times in the history of

**mathematics**; but the interest attaching to them is more psychological than mathematical.2 It is of recent years that the most important advances in the theory of circle-quadrature have been made.He had seen Cyrene from the sea, probably on his voyage from Puteoli to Alexandria, where he remained a long time, probably amassing materials, and studying astronomy and

**mathematics**.But at any rate the process was gradual; and Aristotle was advanced in metaphysics,

**mathematics**, physics, dialectics, rhetoric and poetics, before he became the founder of logic.Aristotle, who made this great discovery, must have had great difficulty in developing the new investigation of reasoning processes out of dialectic, rhetoric, poetics, grammar, metaphysics,

**mathematics**, physics and ethics; and in disengaging it from other kinds of learning.Having completed his education at the university of Edinburgh, where he was distinguished in

**mathematics**, Robert was induced to enter a banking-house in order to acquire a practical knowledge of business, but his ambition was really academic. In 1769 he gave up business pursuits and accepted the rectorship of Perth academy.For many years, however, by private arrangement with his colleague Professor Copland, Hamilton taught the class o £

**mathematics**.In each of these universities there are five faculties, namely, law, theology, medicine, science and

**mathematics**, and literature and philosophy, the courses for which are respectively four, five, eight, and six or seven years for the two last named.Among the literary and scientific associations of Copenhagen may be mentioned the Danish Royal Society, founded in 1742, for the advancement of the sciences of

**mathematics**, astronomy, natural philosophy, &c., by the publication of papers and essays; the Royal Antiquarian Society, founded in 1825, for diffusing a knowledge of Northern and Icelandic archaeology; the Society for the Promotion of Danish Literature, for the publication of works chiefly connected with the history of Danish literature; the Natural Philosophy Society; the Royal Agricultural Society; the Danish Church History Society; the Industrial Association, founded in 1838; the Royal Geographical Society, established in 1876; and several musical and other societies.John was educated at Leiden, and early displayed remarkable talents, more especially in

**mathematics**and jurisprudence.The propositions of

**mathematics**seem to be independent of this or that special fact of experience, and to remain unchanged even when the concrete matter of experience varies.Hume's theory of

**mathematics**- the only one, perhaps, which is compatible with his fundamental principle of psychology - is a practical condemnation of his empirical theory of perception.He studied at Geneva, Leyden and Paris, before becoming (1700) professor of philosophy and

**mathematics**at the academy of Lausanne, of which he was four times rector before 1724, when the theological disputes connected with the Consensus led him to accept a chair of philosophy and**mathematics**at Groningen.His scheme was first to work out, in a separate treatise De corpore, a systematic doctrine of Body, showing how physical phenomena were universally explicable in terms of motion, as motion or mechanical action was then (through Galileo and others) understood - the theory of motion being applied in the light of mathematical science, after quantity, the subject-matter of

**mathematics**, had been duly considered in its place among the fundamental conceptions of philosophy, and a clear indication had been given, at first starting, of the logical ground and method of all philosophical inquiry.Taking up

**mathematics**when not only his mind was already formed but his thoughts were crystallizing into a philosophical system, Hobbes had, in fact, never put himself to school and sought to work up gradually to the best knowledge of the time, but had been more anxious from the first to become himself an innovator with whatever insufficient means.All these controversial writings on

**mathematics**and physics represent but one half of his activity after the age of p y g Years.Upon every subject that came within the sweep of his system, except

**mathematics**and physics, his thoughts have been productive of thought.Pascal's work as a natural philosopher was not less remarkable than his discoveries in pure

**mathematics**.He was educated at the university of Turin, where he qualified as an engineer and became a doctor of

**mathematics**.He held many college offices, becoming successively lecturer in Greek (1651),

**mathematics**(1653),andhumanity('655), praelector (1657), junior dean (1657), and college steward (1659 and 1660); and according to the habit of the time, he was accustomed to preach in his college chapel and also at Great St Mary's before the university, long before he took holy orders.Besides the subjects taught at the Azhar university, instruction is given in literature,

**mathematics**and physical science.In later life, he gave up speculative thought and turned to scientific research, especially in

**mathematics**, physics and astronomy.Though the wish was not gratified, she lived from that time in a retirement almost conventual, avoiding all society and devoting herself entirely to the study of

**mathematics**.In 1804 he was appointed professor of

**mathematics**at the Lycee, in 1809 professor of analysis and mechanics, and in 1816 examiner at the Ecole Polytechnique.In addition to publishing a number of works on geometrical and mechanical subjects, Poinsot also contributed a number of papers on pure and applied

**mathematics**to Lionville's Journal and other scientific periodicals.He cared little for any of the professors, except Sir John Leslie, from whom he learned some

**mathematics**.He did not seek re-election in 1893, but devoted himself thenceforward to

**mathematics**, helping to make known in France the theories of Giusto Bellavitis.He landed at Macao in 1610, and while waiting a favourable opportunity to penetrate into China busied himself for three years in teaching

**mathematics**.His knowledge of

**mathematics**caused him to be employed on the coast survey in 1834.He followed his father's trade, but found time to acquire a knowledge of Latin, Greek,

**mathematics**, physics, anatomy and other subjects.His duties were light, and he employed his leisure in the study of philology,

**mathematics**, philosophy, history, political economy, natural science and natural history, for which he made large collections.These names have in the

**mathematics**tripos survived the procedure.A further distinction is important, especially in such subjects as

**mathematics**or foreign languages, in which it is legitimate to ask what precise power on the part of a candidate the passing of an examination shall signify.Of recent years the Thesls thesis has been introduced into lower examinations; it is required for the master's degree at London in the case of internal students, in subjects other than

**mathematics**(1910); both at Oxford and London, the B.Sc. degree, and at Cambridge the B.A.Having studied theology in the academy of the Moravian brethren at Niesky, and philosophy at Leipzig and Jena, he travelled for some time, and in 1806 became professor of philosophy and elementary

**mathematics**at Heidelberg.In 1816 he was invited to Jena to fill the chair of theoretical philosophy (including

**mathematics**and physics, and philosophy proper), and entered upon a crusade against the prevailing Romanticism.The grand-duke, however, continued to pay him his stipend, and in 1824 he was recalled to Jena as professor of

**mathematics**and physics, receiving permission also to lecture on philosophy in his own rooms to a select number of students.The word was reintroduced in modern philosophy probably by Rene Descartes (or by his followers) who, in the search for a definite self-evident principle as the basis of a new philosophy, naturally turned to the familiar science of

**mathematics**.This collection, alphabetically arranged, comprised annotations on classical authors, passages from newspapers, treatises on morals and

**mathematics**from the standard works of the period.Besides philosophy, he once at least lectured on

**mathematics**.John is said to have owed his education in philosophy,

**mathematics**and theology to an Italian monk named Cosmas, whom Sergius had redeemed from a band of captive slaves.De Morgan was one of his colleagues, but he resigned in 1840 in order to become professor of

**mathematics**in the university of Virginia.But he failed to obtain either of two posts - the professorships of

**mathematics**at the Royal Military Academy and of geometry in Gresham College - for which he applied in 1854, though he was elected to the former in the following year on the death of his successful competitor.Three years later he was appointed professor of

**mathematics**in the Johns Hopkins University, Baltimore, stipulating for an annual salary of $5000, to be paid in gold.At Baltimore he gave an enormous impetus to the study of the higher

**mathematics**in America, and during the time he was there he contributed to the American Journal of**Mathematics**, of which he was the first editor, no less than thirty papers, some of great length, dealing mainly with modern algebra, the theory of numbers, theory of partitions and universal algebra.His early life was occupied in mastering the curriculum of theology, jurisprudence,

**mathematics**, medicine and philosophy, under the approved teachers of the time.He studied

**mathematics**and physics in his native town, Groningen, where in 1879 he took his doctor's degree on presenting a dissertation entitled New Proofs of the Earth's Rotation.That which is object of thought cannot be outside consciousness; just as in

**mathematics**-V - is an unreal quantity, so "things-in-themselves" are ex hypothesi outside consciousness, i.e.Complete or perfect knowledge is confined to the domain of pure thought, to logic and

**mathematics**.Jefferson carried with him from the college of William and Mary at Williamsburg, in his twentieth year, a good knowledge of Latin, Greek and French (to which he soon added Spanish, Italian and Anglo-Saxon), and a familiarity with the higher

**mathematics**and natural sciences only possessed, at his age, by men who have a rare natural taste and ability for those studies.Notwithstanding his many official duties, he found time to publish more than three hundred works, several of them extensive treatises, and many of them memoirs dealing with the most abstruse branches of pure and applied

**mathematics**.There are few branches of

**mathematics**to which he did not contribute something, but it was in the application of**mathematics**to physical subjects that his greatest services to science were performed.Born at Edinburgh in 1710 and originally educated for the church, Short attracted the attention of Maclaurin, professor of

**mathematics**at the university, who permitted him about 1732 to make use of his rooms in the college buildings for experiments in the construction of telescopes.At an early age he manifested a preference for the study of

**mathematics**, but this was gradually superseded by an interest in natural science, which led him ultimately to the study of medicine.The university, in Calle Uruguay, has faculties of law, medicine, letters,

**mathematics**, engineering, and some minor groups of studies, including agriculture and veterinary science.His father, Matthew Stewart (1715-1785), was professor of

**mathematics**in the university of Edinburgh (1747-1772).Dugald Stewart was educated in Edinburgh at the high school and the university, where he read

**mathematics**and moral philosophy under Adam Ferguson.After acting three years as his father's substitute he was elected professor of

**mathematics**in conjunction with him in 1775.To say, however, that Clarke simply confused

**mathematics**and morals by justifying the moral criterion on a mathematical basis is a mistake.He caused works on

**mathematics**, astronomy, medicine and philosophy to be translated from the Greek, and founded in Bagdad a kind of academy, called the "House of Science," with a library and an observatory.In 1828, after a year's special preparation, young Fremont entered the junior class of the college of Charleston, and here displayed marked ability, especially in

**mathematics**; but his irregular attendance and disregard of college discipline led to his expulsion from the institution, which, however, conferred upon him a degree in 1836.In 1833 he was appointed teacher of

**mathematics**on board the sloop of war "Natchez," and was so engaged during a cruise along the South American coast which was continued for about two and a half years.Soon after returning to Charleston he was appointed professor of

**mathematics**in the United States navy, but he chose instead to serve as assistant engineer of a survey undertaken chiefly for the purpose of finding a pass through the mountains for a proposed railway from Charleston to Cincinnati.The founder of logic anticipated the latest logic of science, when he recognized, not only the deduction of

**mathematics**, but also the experience of facts followed by deductive explanations of their causes in physics.On the whole, however, Aristotle, Bacon and Mill, purged from their errors, form one empirical school, gradually growing by adapting itself to the advance of science; a school in which Aristotle was most influenced by Greek deductive

**Mathematics**, Bacon by the rise of empirical physics at the Renaissance, and Mill by the Newtonian combination of empirical facts and mathematical principles in the Principia.In his definite classification of the sciences,'" into First Philosophy,

**Mathematics**and Physics, it has no place.Its axioms, such as the law of contradiction, belong to first philosophy, but the doctrine as a whole falls neither under 'this head nor yet, though the thought has been entertained, under that of

**mathematics**, since logic orders mathematical reasoning as well as all other.In the sphere of abstract form,

**mathematics**, the like may be allowed, abstraction being treated as an elimination of matter from the cn voXov by one act.But the divorce of science of nature from

**mathematics**, the failure of biological inquiry to reach so elementary a conception as that of the nerves, the absence of chemistry from the circle of the sciences, disappointed the promise of the dawn and the relative achievement of the noon-day.In scientific method, then, it could but advance, provided physics and

**mathematics**did not again fail of accord.In the

**mathematics**we determine complex problems by a construction link by link from axioms and simple data clearly and distinctly conceived.The reality of

**mathematics**, equally with that of the ideals of morals drawn from within, does not extend to the " ectypes " of the outer world.Mill holds even the ideas of

**mathematics**to be hypothetical, and in theory knows nothing of a non-enumerative or non-associative universal.Leibnitz's treatment of the primary principles among truths of reason as identities, and his examples drawn inter alia from the " first principles " of

**mathematics**, influenced Kant by antagonism.The clue to the discovery of transcendental conditions Kant finds in the existence of judgments, most manifest in

**mathematics**and in the pure science of nature, which are certain, yet not trifling, necessary and yet not reducible to identities, synthetic therefore and a priori, and so accounted for neither by Locke nor by Leibnitz.In 1904 Alexander Macfarlane published a Bibliography of Quaternions and allied systems of

**Mathematics**for the International Association for promoting the study of Quaternions and allied systems of**Mathematics**(Dublin University Press); the pamphlet contains 86 pages.These works are lost; but their titles, combined with expressions in the letters of Synesius, who consulted her about the construction of an astrolabe and a hydroscope, indicate that she devoted herself specially to astronomy and

**mathematics**.Thus PS (or OR) is the abscissa of P. The word appears for the first time in a Latin work written by Stefano degli Angeli (1623-1697), a professor of

**mathematics**in Rome.North of this and extending to the boundary of the 1 The actual surveying and laying out of the city was done by Andrew Ellicott (1754-1820), a civil engineer, who had been employed in many boundary disputes, who became surveyor-general of the United States in 1792, and from 1812 until his death was professor of

**mathematics**at the United States Military Academy at West Point.In 1701 he resigned his living to become deputy at Cambridge to Sir Isaac Newton, `Thom two years later he succeeded as Lucasian professor of

**mathematics**.In 1861 he became professor of

**mathematics**in the United States navy, and was put in charge of the great 26-in.In 1884 he became professor of

**mathematics**and astronomy at the Johns Hopkins University, continuing, however, to reside at Washingtion.He was also editor of the American Journal of

**Mathematics**for many years.His education was only elementary and very defective, except in

**mathematics**, in which he was largely self-taught; and although at his death he left a considerable library, he was never an assiduous reader.These acts helped greatly to discredit the Moderate party, of whose spirit they were the outcome; and that party further injured their standing in the country by attacking Leslie, afterwards Sir John Leslie, on frivolous grounds - a phrase he had used about Hume's view of causation - when he applied for the chair of

**mathematics**in Edinburgh.In the

**mathematics**there is no reason why it should not be employed.Magee was appointed professor of

**mathematics**and senior fellow of Trinity in 1800, but in 1812 he resigned, and undertook the charge of the livings of Cappagh, Co.The faculties are four - philosophy and history, philology,

**mathematics**and natural sciences, and jurisprudence.He soon showed mathematical powers, but these were not fostered by the careful training mathematicians usually receive, and it may be said that in after years his attention was directed to the higher

**mathematics**mainly by force of circumstances.His investigations occupied almost the whole field of science, including physiology, physiological optics, physiological acoustics, chemistry,

**mathematics**, electricity and magnetism, meteorology and theoretical mechanics.In 1853 be became professor of

**mathematics**at the university, and in 1860 professor of mineralogy in the school of applied engineering.He graduated at the university of Pennsylvania in 1835, and was assistant professor of

**mathematics**(1836-1837), professor of**mathematics**(1837-1840), and professor of Latin and Greek (1840-1848) in Dickinson College, Carlisle, Pennsylvania.In

**mathematics**, an expression of the form a, 1/2 a2 b a 5 ..., where a 1, a 2, a 3,.Shapur I., who appears to have, had a broader outlook, added to the religious writings a collection of scientific treatises on medicine, asticonomy,

**mathematics**, philosophy, zoology, &c., partly from Indian and Greek sources.Showing decided military tastes Francois Arago was sent to the municipal college of Perpignan, where he began to study

**mathematics**in preparation for the entrance examination of the polytechnic school.He received instruction in

**mathematics**from Hobbes, and was early initiated into all the vices of the age by Buckingham and Percy.Having become senior moderator in

**mathematics**and a fellow of Trinity, he took holy orders, and was appointed regius professor of divinity in Dublin University in 1866, a position which he retained until 1888, when he was chosen provost of Trinity College.He now began to occupy himself with scientific pursuits, and gave some attention to

**mathematics**as well as to chemistry and mineralogy; but, having met with Adam Smith's great work, he threw himself with ardour into the study of political economy.Many of them were well versed in Aristotelian and Arabic philosophy, in astronomy,

**mathematics**, and especially in medicine.The complete catalogue may be roughly arranged under three heads - (1) belles lettres, (2) history and antiquities, (3) technical treatises on philosophy, law, grammar,

**mathematics**, philology and other subjects.Residing at Paris as a teacher of

**mathematics**, he became a disciple of Comte, who appointed him his literary executor.He studied

**mathematics**, civil and military architecture, and astronomy, and became associate of the Academie des Sciences, professor of geometry, secretary to the Academy of Architecture and fellow of the Royal Society of London.Greek, and studying

**mathematics**and other sciences.From 1828 to 1839 Babbage was Lucasian professor of

**mathematics**at Cambridge.Until the abandonment of this experiment in 1847, Ripley was its leader, cheerfully taking upon himself all kinds of tasks, teaching

**mathematics**and philosophy in the school, milking cows and attending to other bucolic duties, and after June 1845 editing the weekly Harbinger, an organ of "association," which he continued to edit in New York from 1847 until it was discontinued in 1849.In 1871 he was appointed professor of

**mathematics**at University College, London, and in 1874 became fellow of the Royal Society.This diversion from his original bent gave him an inclination to the career of civil and mechanical engineering; and in the spring of 1826 he was elected by the trustees of the Albany Academy to the chair of

**mathematics**and natural philosophy in that institution.Beginning with metaphysics and ethics and passing on to

**mathematics**, he turned to chemistry at the end of 17 9 7, and within a few months of reading Nicholson's and Lavoisier's treatises on that science had produced a new theory of light and heat.He was called to the bar in 1849, and remained at the bar fourteen years, till 1863, when he was elected to the new Sadlerian chair of pure

**mathematics**in the university of Cambridge.He wrote upon nearly every subject of pure

**mathematics**, and also upon theoretical dynamics and spherical and physical astronomy.Another memoir of applied

**mathematics**is the Dioptrische Untersuchungen (1840).Of the memoirs in pure

**mathematics**, comprised for the most part in vols.He graduated in 1826, taking a first class in

**mathematics**and a second in classics.Kirchhoff's contributions to mathematical physics were numerous and important, his strength lying in his powers of stating a new physical problem in terms of

**mathematics**, not merely in working out the solution after it had been so formulated.At this time Madame Kovalevsky was at Stockholm, where Gustaf Mittag Leffler, also a pupil of Weierstrass, who had been recently appointed to the chair of

**mathematics**at the newly founded university, had procured for her a post as lecturer.Henceforth the Jewish past, - that one path back to the beginning of the world, - was marked out by the absolute laws of

**mathematics**and revelation.He was professor of

**mathematics**in the university of Deseret and wrote several books on this subject, these including Cubic and Biquadratic Equations (1866).In

**mathematics**, the "caustic surfaces" of a given surface are the envelopes of the normals to the surface, or the loci of its centres of principal curvature.The son graduated at Union College in 1818, and in 1821-1826 was professor of

**mathematics**and natural philosophy there.He graduated at Union College in 1826, was ordained a priest of the Protestant Episcopal Church in 1828, was rector for several months in Saco, Maine, and in 1828-1833 was professor of

**mathematics**and natural philosophy at Washington (now Trinity) College, Hartford, Connecticut.He was then called in 1834 as ordinary professor of

**mathematics**to Halle.In 1836 Plucker returned to Bonn as ordinary professor of

**mathematics**.Placed at the age of fifteen in a counting-house at Bremen, he was impelled by his desire to obtain a situation as supercargo on a foreign voyage to study navigation,

**mathematics**and finally astronomy.In pure

**mathematics**he enlarged the resources of analysis by the invention of Bessel's Functions.It comprises five faculties (literature and philosophy, jurisprudence,

**mathematics**, natural science and medicine), and is well equipped with zoological, mineralogical and geological museums, a physiological institute, a cabinet of anthropology, and botanical gardens.Arrived at Venice, he seems to have occupied himself chiefly with studies in

**mathematics**and cosmography.Aristotle himself includes under the title, besides

**mathematics**, all his physical inquiries.Thus

**mathematics**assumes space as an existent infinite, without investigating in what sense the existence or the infinity of this Unding, as Kant called it, can be asserted.He was referred in natural philosophy, including

**mathematics**, and obtained his degree only by a special but by no means infrequent act of indulgence.In 1 754 he published an anonymous treatise entitled Histoire des recherches sur la quadrature du cercle, and in 1758 the first part of his great work, Histoire des mathdmatiques, the first history of

**mathematics**worthy of the name.In 1853 he passed out at the head of the list of engineers, and, after a brief practical experience at Almeria and Granada, was appointed professor of pure and applied

**mathematics**in the school where he had lately been a pupil.He applies his

**mathematics**to the drama; no writer excels him in artful construction, in the arrangement of dramatic scenes, in mere theatrical technique, in the focusing of attention on his chief personages.There were universities in Bogota and Medellin, the former having faculties of letters and philosophy, jurisprudence and political science, medicine and natural sciences, and

**mathematics**and engineering, with an attendance of 1200 to 1500 students.After receiving preliminary instructions in

**mathematics**from his father, he was sent to the university of Basel, where geometry soon became his favourite study.In 1730 he became professor of physics, and in 1733 he succeeded Daniel Bernoulli in the chair of

**mathematics**.At the commencement of his new career he enriched the academical collection with many memoirs, which excited a noble emulation between him and the Bernoullis, though this did not in any way affect their friendship. It was at this time that he carried the integral calculus to a higher degree of perfection, invented the calculation of sines, reduced analytical operations to a greater simplicity, and threw new light on nearly all parts of pure

**mathematics**.In 1741 Euler accepted the invitation of Frederick the Great to Berlin, where he was made a member of the Academy of Sciences and professor of

**mathematics**.It was not

**mathematics**but philology which was to settle the gathering doubts of Ernest Renan.During his university course, which began in 1740, Kant was principally attracted towards

**mathematics**and physics.Here, for the first time, appears definitely the distinction between synthesis and analysis, and in the distinction is found the reason for the superior certainty and clearness of

**mathematics**as opposed to philosophy.**Mathematics**, Kant thinks, proceeds synthetically, for in it the notions are constructed.Metaphysics, on the other hand, is analytical in method; in it the notions are given, and by analysis they are cleared up. It is to be observed that the description of

**mathematics**as synthetic is not an anticipation of the critical doctrine on the same subject.Might not

**mathematics**be a purely imaginary science?The foundation for pure or rational

**mathematics**, there being included under this the pure science of movement, is thus laid in the critical doctrine of space and time.It may well be that the whole abstract edifice of modern

**mathematics**is built on these biologically innate foundations.Relativist

**mathematics**, the criticism goes, by relinquishing absolutism amounts to ' anything goes ' .Or can visual images provide a genuine aide to understanding science and

**mathematics**?Anglophone philosopher who brought the history back into the philosophy of

**mathematics**.We have an aging population and a declining birthrate - the

**mathematics**say the money just won't be there.Much use is made of ICT in our teaching and each

**mathematics**classroom is equipped with a PC and an interactive whiteboard.Most of these teachers were also found to hold absolutist conceptions of

**mathematics**; images that matched their teaching styles.Chinese

**mathematics**was, like their language, very concise.Just as physical constants provide " boundary conditions " for the physical universe, mathematical constants somehow characterize the structure of

**mathematics**.To the best of my knowledge the term ' social constructivism ' appeared in

**mathematics**education from two sources.When teaching this important part of the

**mathematics**curriculum, this poster offers useful support.My poor progress in

**mathematics**was largely a result of my attention deficit.Holding a master's degree in

**mathematics**is related to gains in student achievement.It is

**Mathematics**purified from material dross and made spiritual.Professor Chris Jones has taken up a chair in nonlinear dynamics in the school of

**mathematics**.What are the implications of these trends for the attractions of statistics and

**mathematics**education to students?This was followed by three years as a

**mathematics**teacher educator for Volunteer Services Overseas in Dominica in the Caribbean.Whilst this makes it very accessible, it also means that most of its considerable bulk is dedicated to fairly elementary

**mathematics**.Burton, L. (1995) Moving toward a feminist epistemology of

**mathematics**.Eurydice briefing... more Where England stands in the Trends in International

**Mathematics**and Science Study (TIMSS) 2003.Predicate logic provides remarkable insight into these questions by providing a precise formalism capable of expressing all ordinary

**mathematics**.The point was then generalized to number patterns in

**mathematics**.Now one might reasonably ask what Sanskrit grammar has to do with

**mathematics**.The Euclidean paradigm of

**mathematics**as an objective, absolute, incorrigible and rigidly hierarchical body of knowledge is increasingly under question.We also meet teachers looking for better ideas for

**mathematics**homework.Indeed, on every subject beside

**mathematics**, he was profoundly ignorant.It has had a strongly interdisciplinary approach, involving courses in engineering, life sciences, and

**mathematics**across the two institutions.Students are required to attend introductory September courses in

**mathematics**, statistics, economics and econometrics before the main teaching program starts in October.Others take the view that

**mathematics**is purely man-made.He then introduced one of the greatest masterstrokes in the whole of

**mathematics**.A-level Statistics is not acceptable in place of A-level

**mathematics**because it does not contain enough pure maths.The Institute of

**Mathematics**and its Applications is the professional and learned society for qualified and practicing mathematicians.In fact, there are areas of

**mathematics**that have been developed by mathematicians on the assumption that the Riemann Hypothesis is true.Hardy was a pure mathematician who hoped his

**mathematics**could never be applied.We use ideas and tools from the broad fields of fluid mechanics, physics and applied

**mathematics**.After two years in the army he returned to the military academy to teach

**mathematics**.Examining the effects of different multiple representational systems in learning primary

**mathematics**.Humans invent abstract

**mathematics**, basically making it up out of their imaginations, yet math magically turns out to describe the world.Gilles Roberval began to study

**mathematics**at the age of 14 years.Nonlinear analysis has surely contributed major developments which nowadays shape the face of applied

**mathematics**.A basic grounding in discrete

**mathematics**will assumed during the lectures on security.The content consists of a number of strands of pure

**mathematics**with associated applications.Tutorial support for the elementary

**mathematics**needed for this module will be provided for those who require it.However Prof Van Vleck also has interests in other areas of nonlinear

**mathematics**, particularly shadowing.How can history of

**mathematics**be useful for the**mathematics**education researcher?