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A timeline of key algebraic developments are as follows: | |||
{| class="wikitable" style="width:100%;" | |||
|- | |||
! style="width:15%" | Year || Event | |||
|- | |||
| Circa 1800 BC || The [[First Babylonian Dynasty|Old Babylonian]] [[Strassburg tablet]] seeks the solution of a quadratic elliptic equation.{{Citation needed|date=April 2007}} | |||
|- | |||
| Circa 1800 BC || The ''[[Plimpton 322]]'' tablet gives a table of [[Pythagorean triples]] in [[Babylonia]]n [[Cuneiform script]].{{Citation needed|date=July 2007}} | |||
|- | |||
| 1800 BC || [[Berlin papyrus 6619]] (19th dynasty) contains a quadratic equation and its solution. [http://www.math.buffalo.edu/mad/Ancient-Africa/mad_ancient_egyptpapyrus.html#berlin] | |||
|- | |||
</ | | 800 BC || [[Baudhayana]], author of the Baudhayana [[Sulba Sutras|Sulba Sutra]], a [[Vedic Sanskrit]] geometric text, contains [[quadratic equations]], and calculates the [[square root]] of 2 correct to five decimal places | ||
|- | |||
| Circa 300 BC || In Book II of his Elements, [[Euclid]] gives a geometric construction with Euclidean tools for the solution of the quadratic equation for positive real roots. The construction is due to the Pythagorean School of geometry.{{Citation needed|date=April 2007}} | |||
|- | |||
| Circa 300 BC || A geometric construction for the solution of the cubic is sought (doubling the cube problem). It is now well known that the general cubic has no such solution using [[Euclidean tools]].{{Citation needed|date=April 2007}} | |||
|- | |||
| 150 BC || [[Jainism|Jain]] mathematicians in [[History of India|India]] write the “Sthananga Sutra”, which contains work on the theory of numbers, arithmetical operations, [[geometry]], operations with [[fractions]], simple equations, [[cubic equations]], quartic equations, and [[permutations]] and [[combinations]] | |||
|- | |||
| Circa 100 BC || Algebraic equations are treated in the Chinese mathematics book ''[[The Nine Chapters on the Mathematical Art|Jiuzhang suanshu]]'' (''The Nine Chapters on the Mathematical Art''), which contains solutions of linear equations solved using the [[False position method|rule of double false position]], geometric solutions of quadratic equations, and the solutions of matrices equivalent to the modern method, to solve systems of simultaneous linear equations.{{Citation needed|date=April 2007}} | |||
|- | |||
| 1st century || [[Heron of Alexandria]], the earliest fleeting reference to square roots of negative numbers. | |||
|- | |||
| Circa 150 || Greek mathematician [[Hero of Alexandria]], treats algebraic equations in three volumes of mathematics.{{Citation needed|date=April 2007}} | |||
|- | |||
| Circa 200 || Hellenistic mathematician [[Diophantus]] lived in Alexandria and is often considered to be the "father of algebra", writes his famous ''[[Arithmetica]]'', a work featuring solutions of algebraic equations and on the theory of numbers.{{Citation needed|date=April 2007}} | |||
|- | |||
| 499 || Indian mathematician [[Aryabhata]], in his treatise ''Aryabhatiya'', obtains whole-number solutions to linear equations by a method equivalent to the modern one, describes the general integral solution of the indeterminate linear equation, gives integral solutions of simultaneous indeterminate linear equations, and describes a [[differential equation]].{{Citation needed|date=April 2007}} | |||
|- | |||
| Circa 625 || Chinese mathematician [[Wang Xiaotong]] finds numerical solutions to certain cubic equations.<ref>{{MacTutor|id=Wang_Xiaotong |title=Wang Xiaotong}}</ref> | |||
|- | |||
| Circa 7th century<br>Dates vary from the 3rd to the 12th centuries.<ref>{{Harv|Hayashi|2005|p=371}} Quote:"The dates so far proposed for the Bakhshali work vary from the third to the twelfth centuries AD, but a recently made comparative study has shown many similarities, particularly in the style of exposition and terminology, between Bakhshalī work and Bhāskara I's commentary on the ''Āryabhatīya''. This seems to indicate that both works belong to nearly the same period, although this does not deny the possibility that some of the rules and examples in the Bakhshālī work date from anterior periods."</ref> || The ''[[Indian mathematics#Bakhshali Manuscript|Bakhshali Manuscript]]'' written in [[Middle kingdoms of India|ancient India]] uses a form of algebraic notation using letters of the alphabet and other signs, and contains cubic and quartic equations, algebraic solutions of [[linear equations]] with up to five unknowns, the general algebraic formula for the quadratic equation, and solutions of indeterminate quadratic equations and simultaneous equations.{{Citation needed|date=April 2007}} | |||
|- | |||
| 7th century || [[Brahmagupta]] invents the method of solving indeterminate equations of the second degree and is the first to use algebra to solve astronomical problems. He also develops methods for calculations of the motions and places of various planets, their rising and setting, conjunctions, and the calculation of eclipses of the sun and the moon | |||
|- | |||
| 628 || [[Brahmagupta]] writes the ''[[Brahmasphutasiddhanta|Brahmasphuta-siddhanta]]'', where zero is clearly explained, and where the modern [[place-value]] [[Indian numerals|Indian numeral]] system is fully developed. It also gives rules for manipulating both [[negative and positive numbers]], methods for computing [[square roots]], methods of solving [[linear equation|linear]] and [[quadratic equation]]s, and rules for summing [[series (mathematics)|series]], [[Brahmagupta's identity]], and the [[Brahmagupta theorem]] | |||
|- | |||
| 700s || [[Virasena]] gives explicit rules for the [[Fibonacci sequence]], gives the derivation of the [[volume]] of a [[frustum]] using an [[Infinity|infinite]] procedure, and also deals with the [[logarithm]] to [[base 2]] and knows its laws | |||
|- | |||
| Circa 800 || The [[Abbasid]] patrons of learning, [[al-Mansur]], [[Haroun al-Raschid]], and [[al-Mamun]], had Greek, Babylonian, and Indian mathematical and scientific works translated into Arabic and began a cultural, scientific and mathematical awakening after a century devoid of mathematical achievements.<ref name="Boyer Intro Islamic Algebra">{{cite book|last=Boyer|authorlink=Carl Benjamin Boyer|title=|year=1991|chapter=The Arabic Hegemony|page=227|quote=The first century of the Muslim empire had been devoid of scientific achievement. This period (from about 650 to 750) had been, in fact, perhaps the nadir in the development of mathematics, for the Arabs had not yet achieved intellectual drive, and concern for learning in other parts of the world had faded. Had it not been for the sudden cultural awakening in Islam during the second half of the eighth century, considerably more of ancient science and mathematics would have been lost. To Baghdad at that time were called scholars from Syria, Iran, and Mesopotamia, including Jews and Nestorian Christians; under three great Abbasid patrons of learning - al Mansur, Haroun al-Raschid, and al-Mamun - The city became a new Alexandria. It was during the caliphate of al-Mamun (809-833), however, that the Arabs fully indulged their passion for translation. The caliph is said to have had a dream in which Aristotle appeared, and as a consequence al-Mamun determined to have Arabic versions made of all the Greek works that he could lay his hands on, including Ptolemy's ''Almagest'' and a complete version of Euclid's ''Elements''. From the Byzantine Empire, with which the Arabs maintained an uneasy peace, Greek manuscripts were obtained through peace treaties. Al-Mamun established at Baghdad a "House of Wisdom" (Bait al-hikma) comparable to the ancient Museum at Alexandria.}}</ref> | |||
|- | |||
| 820 || The word ''algebra'' is derived from operations described in the treatise written by the [[Mathematics in medieval Islam|Persian mathematician]], {{Unicode|[[Muhammad ibn Musa al-Khwarizmi|Muḥammad ibn Mūsā al-Ḵhwārizmī]]}}, titled ''[[The Compendious Book on Calculation by Completion and Balancing|Al-Kitab al-Jabr wa-l-Muqabala]]'' (meaning "The Compendious Book on Calculation by Completion and Balancing") on the systematic solution of [[linear equation|linear]] and quadratic equations. Al-Khwarizmi is often considered the "father of algebra", for founding algebra as an independent discipline and for introducing the methods of "[[Reduction (mathematics)|reduction]]" and "balancing" (the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation) which was what he originally used the term ''al-jabr'' to refer to.<ref name=Boyer-229>{{Harv|Boyer|1991|loc="The Arabic Hegemony" p. 229}} "It is not certain just what the terms ''al-jabr'' and ''muqabalah'' mean, but the usual interpretation is similar to that implied in the translation above. The word ''al-jabr'' presumably meant something like "restoration" or "completion" and seems to refer to the transposition of subtracted terms to the other side of an equation; the word ''muqabalah'' is said to refer to "reduction" or "balancing" - that is, the cancellation of like terms on opposite sides of the equation."</ref> His algebra was also no longer concerned "with a series of [[problem]]s to be resolved, but an [[Expository writing|exposition]] which starts with primitive terms in which the combinations must give all possible prototypes for equations, which henceforward explicitly constitute the true object of study." He also studied an equation for its own sake and "in a generic manner, insofar as it does not simply emerge in the course of solving a problem, but is specifically called on to define an infinite class of problems."<ref name=Rashed-Armstrong>{{Cite book | last1=Rashed | first1=R. | last2=Armstrong | first2=Angela | year=1994 | title=The Development of Arabic Mathematics | publisher=[[Springer Science+Business Media|Springer]] | isbn=0-7923-2565-6 | oclc=29181926 | pages=11–2 | ref=harv}}</ref> | |||
|- | |||
| Circa 850 || [[Persian people|Persian]] mathematician [[al-Mahani]] conceived the idea of reducing geometrical problems such as [[Doubling the cube|duplicating the cube]] to problems in algebra.{{Citation needed|date=April 2007}} | |||
|- | |||
| Circa 990 || Persian mathematician [[Al-Karaji]] (also known as al-Karkhi), in his treatise ''Al-Fakhri'', further develops algebra by extending Al-Khwarizmi's methodology to incorporate integral powers and integral roots of unknown quantities. He replaces geometrical operations of algebra with modern arithmetical operations, and defines the [[monomial]]s x, x<sup>2</sup>, x<sup>3</sup>, .. and 1/x, 1/x<sup>2</sup>, 1/x<sup>3</sup>, .. and gives rules for the products of any two of these.<ref name=Al-Karaji/> He also discovered the first numerical solution to equations of the form ax<sup>2n</sup> + bx<sup>n</sup> = c.<ref name="Boyer al-Karkhi ax2n">{{Harv|Boyer|1991|loc="The Arabic Hegemony" p. 239}} "Abu'l Wefa was a capable algebraist aws well as a trionometer. [..] His successor al-Karkhi evidently used this translation to become an Arabic disciple of Diophantus - but without Diophantine analysis! [..] In particular, to al-Karaji is attributed the first numerical solution of equations of the form ax<sup>2n</sup> + bx<sup>n</sup> = c (only equations with positive roots were considered),"</ref> Al-Karaji is also regarded as the first person to free algebra from [[Geometry|geometrical]] operations and replace them with the type of [[arithmetic]] operations which are at the core of algebra today. His work on algebra and [[polynomial]]s, gave the rules for arithmetic operations to manipulate polynomials. The [[History of mathematics|historian of mathematics]] F. Woepcke, in ''Extrait du Fakhri, traité d'Algèbre par Abou Bekr Mohammed Ben Alhacan Alkarkhi'' ([[Paris]], 1853), praised Al-Karaji for being "the first who introduced the theory of algebraic [[calculus]]". Stemming from this, Al-Karaji investigated [[binomial coefficients]] and [[Pascal's triangle]].<ref name=Al-Karaji>{{MacTutor|id=Al-Karaji|title=Abu Bekr ibn Muhammad ibn al-Husayn Al-Karaji}}</ref> | |||
|- | |||
| 895 || [[Thabit ibn Qurra]]: the only surviving fragment of his original work contains a chapter on the solution and properties of [[cubic equation]]s. He also generalized the [[Pythagorean theorem]], and discovered the [[Thabit number|theorem]] by which pairs of [[amicable number]]s can be found, (i.e., two numbers such that each is the sum of the proper divisors of the other). | |||
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| 953 || [[Al-Karaji]] is the “first person to completely free [[algebra]] from geometrical operations and to replace them with the arithmetical type of operations which are at the core of algebra today. He was first to define the [[monomial]]s <math>x</math>, <math>x^2</math>, <math>x^3</math>, … and <math>1/x</math>, <math>1/x^2</math>, <math>1/x^3</math>, … and to give rules for [[product (mathematics)|products]] of any two of these. He started a school of algebra which flourished for several hundreds of years”. He also discovered the [[binomial theorem]] for [[integer]] [[exponent]]s, which “was a major factor in the development of [[numerical analysis]] based on the decimal system.” | |||
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| ca. 1000 || [[Abū Sahl al-Qūhī]] (Kuhi) solves [[equation]]s higher than the [[Quadratic equation|second degree]]. | |||
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| Circa 1050 || Chinese mathematician [[Jia Xian]] finds numerical solutions of polynomial equations of arbitrary degree.<ref>{{MacTutor|id=Jia_Xian|title=Jia Xian}}</ref> | |||
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| 1070 || [[Omar Khayyám]] begins to write ''Treatise on Demonstration of Problems of Algebra'' and classifies cubic equations. | |||
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| 1072 || Persian mathematician [[Omar Khayyam]] gives a complete classification of cubic equations with positive roots and gives general geometric solutions to these equations found by means of intersecting conic sections.<ref name="Boyer Omar Khayyam positive roots">{{cite book|last=Boyer|authorlink=Carl Benjamin Boyer|title=|year=1991|chapter=The Arabic Hegemony|pages=241–242|quote=Omar Khayyam (ca. 1050-1123), the "tent-maker," wrote an ''Algebra'' that went beyond that of al-Khwarizmi to include equations of third degree. Like his Arab predecessors, Omar Khayyam provided for quadratic equations both arithmetic and geometric solutions; for general cubic equations, he believed (mistakenly, as the sixteenth century later showed), arithmetic solutions were impossible; hence he gave only geometric solutions. The scheme of using intersecting conics to solve cubics had been used earlier by Menaechmus, Archimedes, and Alhazan, but Omar Khayyam took the praiseworthy step of generalizing the method to cover all third-degree equations (having positive roots).}}</ref> | |||
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| 1100s || [[Bhaskara II|Bhaskara Acharya]] writes the “[[Bijaganita]]” (“[[Algebra]]”), which is the first text that recognizes that a positive number has two square roots | |||
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| 1130 || [[Al-Samawal]] gave a definition of algebra: “[it is concerned] with operating on unknowns using all the arithmetical tools, in the same way as the arithmetician operates on the known.”<ref name=MacTutor/> | |||
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| 1135 || [[Sharafeddin Tusi]] followed al-Khayyam's application of algebra to geometry, and wrote a treatise on [[cubic equation]]s which “represents an essential contribution to another [[algebra]] which aimed to study [[curve]]s by means of [[equation]]s, thus inaugurating the beginning of [[algebraic geometry]].”<ref name=MacTutor>[http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Arabic_mathematics.html Arabic mathematics], ''[[MacTutor History of Mathematics archive]]'', [[University of St Andrews]], Scotland</ref> | |||
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| Circa 1200 || [[Sharaf al-Dīn al-Tūsī]] (1135–1213) wrote the ''Al-Mu'adalat'' (''Treatise on Equations''), which dealt with eight types of cubic equations with positive solutions and five types of cubic equations which may not have positive solutions. He used what would later be known as the "[[Ruffini's rule|Ruffini]]-[[Horner scheme|Horner]] method" to [[Numerical analysis|numerically]] approximate the [[root of a function|root]] of a cubic equation. He also developed the concepts of the [[maxima and minima]] of curves in order to solve cubic equations which may not have positive solutions.<ref>{{MacTutor|id=Al-Tusi_Sharaf|title=Sharaf al-Din al-Muzaffar al-Tusi}}</ref> He understood the importance of the [[discriminant]] of the cubic equation and used an early version of [[Gerolamo Cardano|Cardano]]'s formula<ref>{{Cite book | last1=Rashed | first1=Roshdi | last2=Armstrong | first2=Angela | year=1994 | title=The Development of Arabic Mathematics | publisher=Springer | isbn=0-7923-2565-6 | pages=342–3 | ref=harv}}</ref> to find algebraic solutions to certain types of cubic equations. Some scholars, such as Roshdi Rashed, argue that Sharaf al-Din discovered the [[derivative]] of cubic polynomials and realized its significance, while other scholars connect his solution to the ideas of Euclid and Archimedes.<ref name=Berggren>{{Cite journal|first=J. L.|last=Berggren|year=1990|title=Innovation and Tradition in Sharaf al-Din al-Tusi's Muadalat|journal=Journal of the American Oriental Society|volume=110|issue=2|pages=304–9|quote=Rashed has argued that Sharaf al-Din discovered the derivative of cubic polynomials and realized its significance for investigating conditions under which cubic equations were solvable; however, other scholars have suggested quite difference explanations of Sharaf al-Din's thinking, which connect it with mathematics found in Euclid or Archimedes.|doi=10.2307/604533|jstor=604533|author2=Al-Tūsī, Sharaf Al-Dīn|last3=Rashed|first3=Roshdi|last4=Al-Tusi|first4=Sharaf Al-Din|ref=harv}}</ref> | |||
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| 1202 || Algebra is introduced to [[Europe]] largely through the work of [[Leonardo Fibonacci]] of [[Pisa]] in his work ''[[Liber Abaci]]''.{{Citation needed|date=April 2007}} | |||
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| Circa 1300 || Chinese mathematician [[Zhu Shijie]] deals with [[polynomial algebra]], solves quadratic equations, simultaneous equations and equations with up to four unknowns, and numerically solves some quartic, [[Quintic equation|quintic]] and higher-order polynomial equations.{{Citation needed|date=April 2007}} | |||
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| Circa 1400 || [[Jamshīd al-Kāshī]] developed an early form of [[Newton's method]] to numerically solve the equation <math>x^P - N = 0</math> to find roots of ''N''.<ref>Tjalling J. Ypma (1995), "Historical development of the Newton-Raphson method", ''SIAM Review'' '''37''' (4): 531–51, {{doi|10.1137/1037125}}</ref> | |||
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| Circa 1400 || Indian mathematician [[Madhava of Sangamagrama]] finds the solution of [[Transcendental function|transcendental equations]] by [[iteration]], [[iterative method]]s for the solution of non-linear equations, and solutions of differential equations.{{Citation needed|date=April 2007}} | |||
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| 15th century || [[Nilakantha Somayaji]], a [[Kerala school of astronomy and mathematics|Kerala school]] mathematician, writes the “Aryabhatiya Bhasya”, which contains work on infinite-series expansions, problems of algebra, and spherical geometry | |||
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| 1412–1482 || Arab mathematician [[Abū al-Hasan ibn Alī al-Qalasādī]] took "the first steps toward the introduction of [[Mathematical notation|algebraic symbolism]]." He used "short Arabic words, or just their initial letters, as mathematical symbols."<ref name=Qalasadi>{{MacTutor Biography|id=Al-Qalasadi|title= Abu'l Hasan ibn Ali al Qalasadi}}</ref> | |||
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| 1535 || [[Niccolò Fontana Tartaglia]] and others mathematicians in Italy independently solved the general cubic equation.<ref name="Stewart">{{cite book|first=Ian|last=Stewart|title=Galois Theory|edition=Third|publisher=Chapman & Hall/CRC Mathematics|year=2004}}</ref> | |||
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| 1545 || Girolamo [[Cardano]] publishes ''Ars magna'' -''The great art'' which gives Fontana's solution to the general quartic equation.<ref name="Stewart" /> | |||
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| 1572 || [[Rafael Bombelli]] recognizes the complex roots of the cubic and improves current notation.{{Citation needed|date=April 2007}} | |||
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| 1591 || [[Franciscus Vieta]] develops improved symbolic notation for various powers of an unknown and uses vowels for unknowns and consonants for constants in ''In artem analyticam isagoge''.{{Citation needed|date=April 2007}} | |||
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| 1619 || [[René Descartes]] discovers [[analytic geometry]] ([[Pierre de Fermat]] claimed that he also discovered it independently), | |||
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| 1631 || [[Thomas Harriot]] in a posthumous publication is the first to use symbols < and > to indicate "less than" and "greater than", respectively.<ref>{{cite book |first=Carl B. |last=Boyer |authorlink=Carl Benjamin Boyer |title=A History of Mathematics |edition=Second |publisher=John Wiley & Sons, Inc. |year=1991 |chapter=Prelude to Modern Mathematics |page=306 |isbn=0-471-54397-7 |quote=Harriot knew of relationships between roots and coefficients and between roots and factors, but like Viète he was hampered by failure to take note of negative and imaginary roots. In notation, however, he advanced the use of symbolism, being responsible for the signs > and < for "greater than" and "less than."}}</ref> | |||
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| 1637 || Pierre de Fermat claims to have proven [[Fermat's Last Theorem]] in his copy of [[Diophantus]]' ''Arithmetica'', | |||
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| 1637 || First use of the term [[imaginary number]] by [[René Descartes]]; it was meant to be derogatory. | |||
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| 1682 || [[Gottfried Leibniz|Gottfried Wilhelm Leibniz]] develops his notion of symbolic manipulation with formal rules which he calls ''characteristica generalis''.{{Citation needed|date=April 2007}} | |||
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| 1683 || Japanese mathematician [[Kowa Seki]], in his ''Method of solving the dissimulated problems'', discovers the [[determinant]],<ref name=MacTutorSeki/> discriminant,{{Citation needed|date=July 2008}} and [[Bernoulli number]]s.<ref name=MacTutorSeki>{{MacTutor|id=Seki|title=Takakazu Shinsuke Seki}}</ref> | |||
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| 1685 || Kowa Seki solves the general cubic equation, as well as some quartic and quintic equations.{{Citation needed|date=April 2007}} | |||
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| 1693 || [[Gottfried Wilhelm Leibniz|Leibniz]] solves systems of simultaneous linear equations using matrices and determinants.{{Citation needed|date=April 2007}} | |||
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| 1722 || [[Abraham de Moivre]] states [[de Moivre's formula]] connecting [[trigonometric function]]s and [[complex number]]s, | |||
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| 1750 || [[Gabriel Cramer]], in his treatise ''Introduction to the analysis of algebraic curves'', states [[Cramer's rule]] and studies [[algebraic curves]], matrices and determinants.<ref>{{MacTutor|id=Cramer|title=Gabriel Cramer}}</ref> | |||
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| 1797 || [[Caspar Wessel]] associates vectors with [[complex number]]s and studies complex number operations in geometrical terms, | |||
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| 1799 || Carl Friedrich Gauss proves the [[fundamental theorem of algebra]] (every polynomial equation has a solution among the complex numbers), | |||
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| 1799 || [[Paolo Ruffini]] partially proves the [[Abel–Ruffini theorem]] that [[Quintic equation|quintic]] or higher equations cannot be solved by a general formula, | |||
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| 1806 || [[Jean-Robert Argand]] publishes proof of the [[Fundamental theorem of algebra]] and the [[Argand diagram]], | |||
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| 1824 || [[Niels Henrik Abel]] proved that the general quintic equation is insoluble by radicals.<ref name="Stewart" /> | |||
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| 1832 || [[Galois theory]] is developed by [[Évariste Galois]] in his work on abstract algebra.<ref name="Stewart" /> | |||
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| 1847 || [[George Boole]] formalizes [[symbolic logic]] in ''The Mathematical Analysis of Logic'', defining what now is called [[Boolean algebra (logic)|Boolean algebra]], | |||
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| 1873 || [[Charles Hermite]] proves that [[e (mathematical constant)|e]] is transcendental, | |||
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| 1878 || Charles Hermite solves the general quintic equation by means of elliptic and modular functions | |||
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| 1981 || [[Mikhail Gromov (mathematician)|Mikhail Gromov]] develops the theory of [[hyperbolic group]]s, revolutionizing both infinite group theory and global differential geometry, | |||
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| 2007 || a team of researches throughout North America and Europe used networks of computers to map [[E8 (mathematics)]].<ref>Elizabeth A. Thompson, MIT News Office, ''Math research team maps E8'' http://www.huliq.com/15695/mathematicians-map-e8</ref> | |||
|} | |||
== | ==References== | ||
{{Reflist}} | |||
{{DEFAULTSORT:Timeline Of Algebra}} | |||
[[Category:History of algebra]] | |||
[[Category:Mathematics timelines|Algebra]] | |||
Revision as of 17:45, 1 February 2014
A timeline of key algebraic developments are as follows:
Year | Event |
---|---|
Circa 1800 BC | The Old Babylonian Strassburg tablet seeks the solution of a quadratic elliptic equation.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. |
Circa 1800 BC | The Plimpton 322 tablet gives a table of Pythagorean triples in Babylonian Cuneiform script.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. |
1800 BC | Berlin papyrus 6619 (19th dynasty) contains a quadratic equation and its solution. [1] |
800 BC | Baudhayana, author of the Baudhayana Sulba Sutra, a Vedic Sanskrit geometric text, contains quadratic equations, and calculates the square root of 2 correct to five decimal places |
Circa 300 BC | In Book II of his Elements, Euclid gives a geometric construction with Euclidean tools for the solution of the quadratic equation for positive real roots. The construction is due to the Pythagorean School of geometry.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. |
Circa 300 BC | A geometric construction for the solution of the cubic is sought (doubling the cube problem). It is now well known that the general cubic has no such solution using Euclidean tools.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. |
150 BC | Jain mathematicians in India write the “Sthananga Sutra”, which contains work on the theory of numbers, arithmetical operations, geometry, operations with fractions, simple equations, cubic equations, quartic equations, and permutations and combinations |
Circa 100 BC | Algebraic equations are treated in the Chinese mathematics book Jiuzhang suanshu (The Nine Chapters on the Mathematical Art), which contains solutions of linear equations solved using the rule of double false position, geometric solutions of quadratic equations, and the solutions of matrices equivalent to the modern method, to solve systems of simultaneous linear equations.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. |
1st century | Heron of Alexandria, the earliest fleeting reference to square roots of negative numbers. |
Circa 150 | Greek mathematician Hero of Alexandria, treats algebraic equations in three volumes of mathematics.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. |
Circa 200 | Hellenistic mathematician Diophantus lived in Alexandria and is often considered to be the "father of algebra", writes his famous Arithmetica, a work featuring solutions of algebraic equations and on the theory of numbers.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. |
499 | Indian mathematician Aryabhata, in his treatise Aryabhatiya, obtains whole-number solutions to linear equations by a method equivalent to the modern one, describes the general integral solution of the indeterminate linear equation, gives integral solutions of simultaneous indeterminate linear equations, and describes a differential equation.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. |
Circa 625 | Chinese mathematician Wang Xiaotong finds numerical solutions to certain cubic equations.[1] |
Circa 7th century Dates vary from the 3rd to the 12th centuries.[2] |
The Bakhshali Manuscript written in ancient India uses a form of algebraic notation using letters of the alphabet and other signs, and contains cubic and quartic equations, algebraic solutions of linear equations with up to five unknowns, the general algebraic formula for the quadratic equation, and solutions of indeterminate quadratic equations and simultaneous equations.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. |
7th century | Brahmagupta invents the method of solving indeterminate equations of the second degree and is the first to use algebra to solve astronomical problems. He also develops methods for calculations of the motions and places of various planets, their rising and setting, conjunctions, and the calculation of eclipses of the sun and the moon |
628 | Brahmagupta writes the Brahmasphuta-siddhanta, where zero is clearly explained, and where the modern place-value Indian numeral system is fully developed. It also gives rules for manipulating both negative and positive numbers, methods for computing square roots, methods of solving linear and quadratic equations, and rules for summing series, Brahmagupta's identity, and the Brahmagupta theorem |
700s | Virasena gives explicit rules for the Fibonacci sequence, gives the derivation of the volume of a frustum using an infinite procedure, and also deals with the logarithm to base 2 and knows its laws |
Circa 800 | The Abbasid patrons of learning, al-Mansur, Haroun al-Raschid, and al-Mamun, had Greek, Babylonian, and Indian mathematical and scientific works translated into Arabic and began a cultural, scientific and mathematical awakening after a century devoid of mathematical achievements.[3] |
820 | The word algebra is derived from operations described in the treatise written by the Persian mathematician, PROPERTY builders did not have the simplest year, what with the cooling measures imposed in January and the loan curbs in June, but some still managed to do effectively while others made their first foray abroad. As a public-listed company and a pioneer in the improvement of landed properties in Singapore, we have now been constructing some of Singapore's nicely-recognized, established residential estates for over 50 years. Our many developments in Singapore are an affidavit of our steady want to create not just high quality houses however communities for you and your family members Hotel Properties Limited (HPL) was listed on the Inventory Trade of Singapore in 1982. Beginning with simply the Hilton Lodge in Singapore, HPL has expanded rapidly through the years. As we speak HPL has pursuits in 19 resorts with almost 4000 rooms in 8 countries. An Choice or Settlement/Contract for the Buy of a Home or Flat will be formedin many ways e.g. A gaggle of persons, whether in partnership or otherwise Certainly one of Asia's premier property firms, Keppel Land is recognised for its sterling portfolio of award-profitable residential developments and funding-grade business properties as well as excessive requirements of company governance and transparency. Keppel Land is without doubt one of the largest listed property corporations by total assets on the Singapore Change. The Group's total assets amounted to about $13.eight billion as at 31 March 2014. Additionally it is a component of a number of stock indices including the FTSE ST Real Property Index, FTSE ST China Prime Index, FTSE All-World Index, FTSE Asia Pacific ex-Japan Index, FTSE EPRA/NAREIT World Real Estate Index and EPRA/NAREIT Index. 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It represents an outstanding achievement which developers, professionals and property house owners aspire to achieve. It bestows upon the winner the correct to use the coveted award emblem recognised extensively throughout the FIABCI network. ADRIA NON-PUBLIC CONDOMINIUM CONDOMINIUM DERBYSHIRE HIGHWAY, THOMSON ROAD, SINGAPORE (DISTRICT eleven) AMBER RESIDENCES (PREPARED HOUSES) PRIVATE CONDOMINIUM RESIDENCE AMBER STREET, SINGAPORE (DISTRICT 15) ARC AT TAMPINES GOVERNMENT CONDOMINIUM APARTMENT TAMPINES AVENUE 8, SINGAPORE (DISTRICT 18) ARDMORE RESIDENCE NON-PUBLIC CONDOMINIUM CONDO ARDMORE PARK, SINGAPORE (DISTRICT 10) ARISTO @ AMBER , THE PRIVATE CONDOMINIUM CONDOMINIUM AMBER STREET, SINGAPORE (DISTRICT 15) ASPEN LINQ NON-PUBLIC CONDOMINIUM RESIDENCE INSTITUTION HILL, SINGAPORE (DISTRICT 09) BARTLEY RESIDENCES NON-PUBLIC CONDOMINIUM HOUSE BARTLEY HIGHWAY, SINGAPORE (DISTRICT 19) BEACON HEIGHTS PERSONAL CONDOMINIUM CONDO MAR THOMA STREET, SINGAPORE (DISTRCT 12) title searches and authorized requisitions on the property; and Hongkong Land is a number one property funding, administration and growth group with a serious portfolio in Hong Kong and different property pursuits in Asia. As considered one of Singapore's largest property gamers, Singapore Land (SingLand) is synonymous with premier property developments in both prime and suburban areas. YHS made its first foray into property improvement with Tivoli Gardens, a 59-unit landed estate in District 19. This was adopted by the launch of The Sterling, a freehold condominium in Bukit Timah, and landed projects resembling Tai Keng Villas, Parry Inexperienced, Chuan Villas and Princeton Vale. Its newest growth is JARDIN, an exclusive property nestled alongside Bukit Timah/Dunearn Highway Learn More Can Singapore safely deflate its property market? GPS Funding Sales operates like an entrepreneur group drawing on wealth of experiences with in depth insight locally and having a global perspective. We are in a position to provide investment methods that tailor-made to the clients profile. Our purchasers starting from Wealth Fund managers, Multinational Companies, Small Medium Enterprise companies, Property Developers and Ultra Networth Individual. En-bloc Sales Department Sustainability, property growth, sustainability initiatives, tripple backside line, measuring sustainability, reporting, metrics and benchmarks When you've loved what you've got read thus far why not sign up for our FREE property alert and online journal PropertyWire Confidential. District 23, ninety nine years Leasehold condominium BUILD TO ALTER, titled Al-Kitab al-Jabr wa-l-Muqabala (meaning "The Compendious Book on Calculation by Completion and Balancing") on the systematic solution of linear and quadratic equations. Al-Khwarizmi is often considered the "father of algebra", for founding algebra as an independent discipline and for introducing the methods of "reduction" and "balancing" (the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation) which was what he originally used the term al-jabr to refer to.[4] His algebra was also no longer concerned "with a series of problems to be resolved, but an exposition which starts with primitive terms in which the combinations must give all possible prototypes for equations, which henceforward explicitly constitute the true object of study." He also studied an equation for its own sake and "in a generic manner, insofar as it does not simply emerge in the course of solving a problem, but is specifically called on to define an infinite class of problems."[5] |
Circa 850 | Persian mathematician al-Mahani conceived the idea of reducing geometrical problems such as duplicating the cube to problems in algebra.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. |
Circa 990 | Persian mathematician Al-Karaji (also known as al-Karkhi), in his treatise Al-Fakhri, further develops algebra by extending Al-Khwarizmi's methodology to incorporate integral powers and integral roots of unknown quantities. He replaces geometrical operations of algebra with modern arithmetical operations, and defines the monomials x, x2, x3, .. and 1/x, 1/x2, 1/x3, .. and gives rules for the products of any two of these.[6] He also discovered the first numerical solution to equations of the form ax2n + bxn = c.[7] Al-Karaji is also regarded as the first person to free algebra from geometrical operations and replace them with the type of arithmetic operations which are at the core of algebra today. His work on algebra and polynomials, gave the rules for arithmetic operations to manipulate polynomials. The historian of mathematics F. Woepcke, in Extrait du Fakhri, traité d'Algèbre par Abou Bekr Mohammed Ben Alhacan Alkarkhi (Paris, 1853), praised Al-Karaji for being "the first who introduced the theory of algebraic calculus". Stemming from this, Al-Karaji investigated binomial coefficients and Pascal's triangle.[6] |
895 | Thabit ibn Qurra: the only surviving fragment of his original work contains a chapter on the solution and properties of cubic equations. He also generalized the Pythagorean theorem, and discovered the theorem by which pairs of amicable numbers can be found, (i.e., two numbers such that each is the sum of the proper divisors of the other). |
953 | Al-Karaji is the “first person to completely free algebra from geometrical operations and to replace them with the arithmetical type of operations which are at the core of algebra today. He was first to define the monomials , , , … and , , , … and to give rules for products of any two of these. He started a school of algebra which flourished for several hundreds of years”. He also discovered the binomial theorem for integer exponents, which “was a major factor in the development of numerical analysis based on the decimal system.” |
ca. 1000 | Abū Sahl al-Qūhī (Kuhi) solves equations higher than the second degree. |
Circa 1050 | Chinese mathematician Jia Xian finds numerical solutions of polynomial equations of arbitrary degree.[8] |
1070 | Omar Khayyám begins to write Treatise on Demonstration of Problems of Algebra and classifies cubic equations. |
1072 | Persian mathematician Omar Khayyam gives a complete classification of cubic equations with positive roots and gives general geometric solutions to these equations found by means of intersecting conic sections.[9] |
1100s | Bhaskara Acharya writes the “Bijaganita” (“Algebra”), which is the first text that recognizes that a positive number has two square roots |
1130 | Al-Samawal gave a definition of algebra: “[it is concerned] with operating on unknowns using all the arithmetical tools, in the same way as the arithmetician operates on the known.”[10] |
1135 | Sharafeddin Tusi followed al-Khayyam's application of algebra to geometry, and wrote a treatise on cubic equations which “represents an essential contribution to another algebra which aimed to study curves by means of equations, thus inaugurating the beginning of algebraic geometry.”[10] |
Circa 1200 | Sharaf al-Dīn al-Tūsī (1135–1213) wrote the Al-Mu'adalat (Treatise on Equations), which dealt with eight types of cubic equations with positive solutions and five types of cubic equations which may not have positive solutions. He used what would later be known as the "Ruffini-Horner method" to numerically approximate the root of a cubic equation. He also developed the concepts of the maxima and minima of curves in order to solve cubic equations which may not have positive solutions.[11] He understood the importance of the discriminant of the cubic equation and used an early version of Cardano's formula[12] to find algebraic solutions to certain types of cubic equations. Some scholars, such as Roshdi Rashed, argue that Sharaf al-Din discovered the derivative of cubic polynomials and realized its significance, while other scholars connect his solution to the ideas of Euclid and Archimedes.[13] |
1202 | Algebra is introduced to Europe largely through the work of Leonardo Fibonacci of Pisa in his work Liber Abaci.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. |
Circa 1300 | Chinese mathematician Zhu Shijie deals with polynomial algebra, solves quadratic equations, simultaneous equations and equations with up to four unknowns, and numerically solves some quartic, quintic and higher-order polynomial equations.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. |
Circa 1400 | Jamshīd al-Kāshī developed an early form of Newton's method to numerically solve the equation to find roots of N.[14] |
Circa 1400 | Indian mathematician Madhava of Sangamagrama finds the solution of transcendental equations by iteration, iterative methods for the solution of non-linear equations, and solutions of differential equations.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. |
15th century | Nilakantha Somayaji, a Kerala school mathematician, writes the “Aryabhatiya Bhasya”, which contains work on infinite-series expansions, problems of algebra, and spherical geometry |
1412–1482 | Arab mathematician Abū al-Hasan ibn Alī al-Qalasādī took "the first steps toward the introduction of algebraic symbolism." He used "short Arabic words, or just their initial letters, as mathematical symbols."[15] |
1535 | Niccolò Fontana Tartaglia and others mathematicians in Italy independently solved the general cubic equation.[16] |
1545 | Girolamo Cardano publishes Ars magna -The great art which gives Fontana's solution to the general quartic equation.[16] |
1572 | Rafael Bombelli recognizes the complex roots of the cubic and improves current notation.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. |
1591 | Franciscus Vieta develops improved symbolic notation for various powers of an unknown and uses vowels for unknowns and consonants for constants in In artem analyticam isagoge.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. |
1619 | René Descartes discovers analytic geometry (Pierre de Fermat claimed that he also discovered it independently), |
1631 | Thomas Harriot in a posthumous publication is the first to use symbols < and > to indicate "less than" and "greater than", respectively.[17] |
1637 | Pierre de Fermat claims to have proven Fermat's Last Theorem in his copy of Diophantus' Arithmetica, |
1637 | First use of the term imaginary number by René Descartes; it was meant to be derogatory. |
1682 | Gottfried Wilhelm Leibniz develops his notion of symbolic manipulation with formal rules which he calls characteristica generalis.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. |
1683 | Japanese mathematician Kowa Seki, in his Method of solving the dissimulated problems, discovers the determinant,[18] discriminant,Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. and Bernoulli numbers.[18] |
1685 | Kowa Seki solves the general cubic equation, as well as some quartic and quintic equations.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. |
1693 | Leibniz solves systems of simultaneous linear equations using matrices and determinants.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. |
1722 | Abraham de Moivre states de Moivre's formula connecting trigonometric functions and complex numbers, |
1750 | Gabriel Cramer, in his treatise Introduction to the analysis of algebraic curves, states Cramer's rule and studies algebraic curves, matrices and determinants.[19] |
1797 | Caspar Wessel associates vectors with complex numbers and studies complex number operations in geometrical terms, |
1799 | Carl Friedrich Gauss proves the fundamental theorem of algebra (every polynomial equation has a solution among the complex numbers), |
1799 | Paolo Ruffini partially proves the Abel–Ruffini theorem that quintic or higher equations cannot be solved by a general formula, |
1806 | Jean-Robert Argand publishes proof of the Fundamental theorem of algebra and the Argand diagram, |
1824 | Niels Henrik Abel proved that the general quintic equation is insoluble by radicals.[16] |
1832 | Galois theory is developed by Évariste Galois in his work on abstract algebra.[16] |
1847 | George Boole formalizes symbolic logic in The Mathematical Analysis of Logic, defining what now is called Boolean algebra, |
1873 | Charles Hermite proves that e is transcendental, |
1878 | Charles Hermite solves the general quintic equation by means of elliptic and modular functions |
1981 | Mikhail Gromov develops the theory of hyperbolic groups, revolutionizing both infinite group theory and global differential geometry, |
2007 | a team of researches throughout North America and Europe used networks of computers to map E8 (mathematics).[20] |
References
43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.
- ↑ Can a new property agent make $eight,seven-hundred inside her first 2.5 months? (See bolded part above) A couple of yr ago, I joined one of the top actual property firms in Singapore, and happened to be recruited beneath one of many high-selling divisions. I later left the business for personal causes, but I still receive work related sales figures, and I can honestly say that yes it is completely doable. I've seen the figures.
Solely once you pass both paper in the RES exams, can you apply for the salesperson license with Council of Estate Agency through Knight Frank. An annual charge of $299.60 is payable to CEA for this license by means of Knight Frank. Create a Monetary Finances.is important given the up and down of this risky market place. Your monetary price range ought to plan for your advertising costs, any extra prices resembling training and your forecasted revenue. Fascinating, fascinated or still uncertain? Call Leon Low @ 9369 5588 and yow will discover out more on how he and his Staff members can assist you on this Actual Estate Business. See you actual quickly! By visitor contributor Getty Goh, Director of Ascendant Belongings , a real estate research and funding consultancy firm.
One to One Mentoring Free Caveat Listings Complete In-Home Programs Paxel-On The Job Coaching (Zero value to agent) Be taught and Earn Prog. State-Of-The Artwork Residential and Commercial Property Information Mission new condo launches singapore Launches - Native and Overseas These are high 6 ways that you can do to claim your PIC grant as knowledgeable property agent. There are some necessary documents that you have to undergo the IRAS, so your application could be authorized quickly. This PIC grant allows you to develop your property agency company from the tax deduction or money payout choices. KS Tan, property agent (HSR International/Knight Frank), 90060063 (Starhub) Vincent Ong , property agent with Knight Frank, 98531741 (Starhub) and 81876384 LLB (Honours), College of London
Resale Levy for Second-Timer Applicants – Previously second timers aren't required to pay a levy. This is applicable to only new EC land gross sales which are launched on or after 9th December 2013 Revision of Mortgage Loan Terms – From a earlier mortgage servicing ratio (MSR) stage of 60% to now 30% of a borrower's gross monthly revenue. The MSR cap will apply to EC purchases from at this time onwards. Property looking process is busy and thrilling, I am here to verify the expertise goes as smoothly as attainable by providing you with all of the provide help to need under one roof and to ensure your new home meets all of your expectations. Try to discover a companion to share an apartment through the next expatriate chat rooms. - Set Up A Digital Tour And Digital Open House Chesney Actual Property
All potential consumers might be fastidiously screened by a single agent together with your requirement and scheduling in thoughts thus ensuring a peace of mind advertising effort. An Unique Agent is authorised to barter on your behalf because you each have a customized advertising and marketing strategy, thus leading to a sooner closure at the very best price. For properties that include each residential and non-residential portions, solely the non-residential portion is subject to GST. If you received the rental payment. Whole rental of the furnished flat = $four,500 per thirty days He wished to take up a business course in a polytechnic, however his grades did not qualify him to do so. One month's rental for the goodfaith deposit Rental Period of 4 years (48 months) or MUCH LESS Total rental x zero.004
It is the sellers obligation to hand over the property upon authorized completion as agreed in the contract. Within the case of a HDB flat, vacant possession is a requirement. Plan your move early to prevent a final minute rush. Remove all your belongings and discard any unwanted furnishings and rubbish. Be sure that all fixtures and items within the inventory record are left behind. Invite the customer (as required by HDB) for an inspection earlier than completion. In the case of private properties, they are often sold with present tenancy or vacant possession. The gross sales contract will specify your authorized obligations. Examine with your agent in case you are in doubt.
Moreover dedicating himself to the IP profession, Moo Kwang additionally contributes to the coaching and growth of expectant IP professionals by acting as a mentor and providing practical guidance to patent agent trainees. Moo Kwang is presently an adjunct lecturer at the Nationwide University of Singapore. He lectures on intellectual capital management and IP rights to engineering undergraduates. In a separate statement, trade promotion agency IE Singapore mentioned the nation's key exports rose 28 per cent in the second quarter from the 12 months earlier than, accelerating from a 23 per cent rise within the first quarter. - CNA/vm The aged are easy targets who may be coaxed into promoting and buying their property. Member of Institute of Estate Agent Housing Builders Guidelines - ↑ Template:Harv Quote:"The dates so far proposed for the Bakhshali work vary from the third to the twelfth centuries AD, but a recently made comparative study has shown many similarities, particularly in the style of exposition and terminology, between Bakhshalī work and Bhāskara I's commentary on the Āryabhatīya. This seems to indicate that both works belong to nearly the same period, although this does not deny the possibility that some of the rules and examples in the Bakhshālī work date from anterior periods."
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ Template:Harv "It is not certain just what the terms al-jabr and muqabalah mean, but the usual interpretation is similar to that implied in the translation above. The word al-jabr presumably meant something like "restoration" or "completion" and seems to refer to the transposition of subtracted terms to the other side of an equation; the word muqabalah is said to refer to "reduction" or "balancing" - that is, the cancellation of like terms on opposite sides of the equation."
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ 6.0 6.1 Can a new property agent make $eight,seven-hundred inside her first 2.5 months? (See bolded part above) A couple of yr ago, I joined one of the top actual property firms in Singapore, and happened to be recruited beneath one of many high-selling divisions. I later left the business for personal causes, but I still receive work related sales figures, and I can honestly say that yes it is completely doable. I've seen the figures.
Solely once you pass both paper in the RES exams, can you apply for the salesperson license with Council of Estate Agency through Knight Frank. An annual charge of $299.60 is payable to CEA for this license by means of Knight Frank. Create a Monetary Finances.is important given the up and down of this risky market place. Your monetary price range ought to plan for your advertising costs, any extra prices resembling training and your forecasted revenue. Fascinating, fascinated or still uncertain? Call Leon Low @ 9369 5588 and yow will discover out more on how he and his Staff members can assist you on this Actual Estate Business. See you actual quickly! By visitor contributor Getty Goh, Director of Ascendant Belongings , a real estate research and funding consultancy firm.
One to One Mentoring Free Caveat Listings Complete In-Home Programs Paxel-On The Job Coaching (Zero value to agent) Be taught and Earn Prog. State-Of-The Artwork Residential and Commercial Property Information Mission new condo launches singapore Launches - Native and Overseas These are high 6 ways that you can do to claim your PIC grant as knowledgeable property agent. There are some necessary documents that you have to undergo the IRAS, so your application could be authorized quickly. This PIC grant allows you to develop your property agency company from the tax deduction or money payout choices. KS Tan, property agent (HSR International/Knight Frank), 90060063 (Starhub) Vincent Ong , property agent with Knight Frank, 98531741 (Starhub) and 81876384 LLB (Honours), College of London
Resale Levy for Second-Timer Applicants – Previously second timers aren't required to pay a levy. This is applicable to only new EC land gross sales which are launched on or after 9th December 2013 Revision of Mortgage Loan Terms – From a earlier mortgage servicing ratio (MSR) stage of 60% to now 30% of a borrower's gross monthly revenue. The MSR cap will apply to EC purchases from at this time onwards. Property looking process is busy and thrilling, I am here to verify the expertise goes as smoothly as attainable by providing you with all of the provide help to need under one roof and to ensure your new home meets all of your expectations. Try to discover a companion to share an apartment through the next expatriate chat rooms. - Set Up A Digital Tour And Digital Open House Chesney Actual Property
All potential consumers might be fastidiously screened by a single agent together with your requirement and scheduling in thoughts thus ensuring a peace of mind advertising effort. An Unique Agent is authorised to barter on your behalf because you each have a customized advertising and marketing strategy, thus leading to a sooner closure at the very best price. For properties that include each residential and non-residential portions, solely the non-residential portion is subject to GST. If you received the rental payment. Whole rental of the furnished flat = $four,500 per thirty days He wished to take up a business course in a polytechnic, however his grades did not qualify him to do so. One month's rental for the goodfaith deposit Rental Period of 4 years (48 months) or MUCH LESS Total rental x zero.004
It is the sellers obligation to hand over the property upon authorized completion as agreed in the contract. Within the case of a HDB flat, vacant possession is a requirement. Plan your move early to prevent a final minute rush. Remove all your belongings and discard any unwanted furnishings and rubbish. Be sure that all fixtures and items within the inventory record are left behind. Invite the customer (as required by HDB) for an inspection earlier than completion. In the case of private properties, they are often sold with present tenancy or vacant possession. The gross sales contract will specify your authorized obligations. Examine with your agent in case you are in doubt.
Moreover dedicating himself to the IP profession, Moo Kwang additionally contributes to the coaching and growth of expectant IP professionals by acting as a mentor and providing practical guidance to patent agent trainees. Moo Kwang is presently an adjunct lecturer at the Nationwide University of Singapore. He lectures on intellectual capital management and IP rights to engineering undergraduates. In a separate statement, trade promotion agency IE Singapore mentioned the nation's key exports rose 28 per cent in the second quarter from the 12 months earlier than, accelerating from a 23 per cent rise within the first quarter. - CNA/vm The aged are easy targets who may be coaxed into promoting and buying their property. Member of Institute of Estate Agent Housing Builders Guidelines - ↑ Template:Harv "Abu'l Wefa was a capable algebraist aws well as a trionometer. [..] His successor al-Karkhi evidently used this translation to become an Arabic disciple of Diophantus - but without Diophantine analysis! [..] In particular, to al-Karaji is attributed the first numerical solution of equations of the form ax2n + bxn = c (only equations with positive roots were considered),"
- ↑ Can a new property agent make $eight,seven-hundred inside her first 2.5 months? (See bolded part above) A couple of yr ago, I joined one of the top actual property firms in Singapore, and happened to be recruited beneath one of many high-selling divisions. I later left the business for personal causes, but I still receive work related sales figures, and I can honestly say that yes it is completely doable. I've seen the figures.
Solely once you pass both paper in the RES exams, can you apply for the salesperson license with Council of Estate Agency through Knight Frank. An annual charge of $299.60 is payable to CEA for this license by means of Knight Frank. Create a Monetary Finances.is important given the up and down of this risky market place. Your monetary price range ought to plan for your advertising costs, any extra prices resembling training and your forecasted revenue. Fascinating, fascinated or still uncertain? Call Leon Low @ 9369 5588 and yow will discover out more on how he and his Staff members can assist you on this Actual Estate Business. See you actual quickly! By visitor contributor Getty Goh, Director of Ascendant Belongings , a real estate research and funding consultancy firm.
One to One Mentoring Free Caveat Listings Complete In-Home Programs Paxel-On The Job Coaching (Zero value to agent) Be taught and Earn Prog. State-Of-The Artwork Residential and Commercial Property Information Mission new condo launches singapore Launches - Native and Overseas These are high 6 ways that you can do to claim your PIC grant as knowledgeable property agent. There are some necessary documents that you have to undergo the IRAS, so your application could be authorized quickly. This PIC grant allows you to develop your property agency company from the tax deduction or money payout choices. KS Tan, property agent (HSR International/Knight Frank), 90060063 (Starhub) Vincent Ong , property agent with Knight Frank, 98531741 (Starhub) and 81876384 LLB (Honours), College of London
Resale Levy for Second-Timer Applicants – Previously second timers aren't required to pay a levy. This is applicable to only new EC land gross sales which are launched on or after 9th December 2013 Revision of Mortgage Loan Terms – From a earlier mortgage servicing ratio (MSR) stage of 60% to now 30% of a borrower's gross monthly revenue. The MSR cap will apply to EC purchases from at this time onwards. Property looking process is busy and thrilling, I am here to verify the expertise goes as smoothly as attainable by providing you with all of the provide help to need under one roof and to ensure your new home meets all of your expectations. Try to discover a companion to share an apartment through the next expatriate chat rooms. - Set Up A Digital Tour And Digital Open House Chesney Actual Property
All potential consumers might be fastidiously screened by a single agent together with your requirement and scheduling in thoughts thus ensuring a peace of mind advertising effort. An Unique Agent is authorised to barter on your behalf because you each have a customized advertising and marketing strategy, thus leading to a sooner closure at the very best price. For properties that include each residential and non-residential portions, solely the non-residential portion is subject to GST. If you received the rental payment. Whole rental of the furnished flat = $four,500 per thirty days He wished to take up a business course in a polytechnic, however his grades did not qualify him to do so. One month's rental for the goodfaith deposit Rental Period of 4 years (48 months) or MUCH LESS Total rental x zero.004
It is the sellers obligation to hand over the property upon authorized completion as agreed in the contract. Within the case of a HDB flat, vacant possession is a requirement. Plan your move early to prevent a final minute rush. Remove all your belongings and discard any unwanted furnishings and rubbish. Be sure that all fixtures and items within the inventory record are left behind. Invite the customer (as required by HDB) for an inspection earlier than completion. In the case of private properties, they are often sold with present tenancy or vacant possession. The gross sales contract will specify your authorized obligations. Examine with your agent in case you are in doubt.
Moreover dedicating himself to the IP profession, Moo Kwang additionally contributes to the coaching and growth of expectant IP professionals by acting as a mentor and providing practical guidance to patent agent trainees. Moo Kwang is presently an adjunct lecturer at the Nationwide University of Singapore. He lectures on intellectual capital management and IP rights to engineering undergraduates. In a separate statement, trade promotion agency IE Singapore mentioned the nation's key exports rose 28 per cent in the second quarter from the 12 months earlier than, accelerating from a 23 per cent rise within the first quarter. - CNA/vm The aged are easy targets who may be coaxed into promoting and buying their property. Member of Institute of Estate Agent Housing Builders Guidelines - ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ 10.0 10.1 Arabic mathematics, MacTutor History of Mathematics archive, University of St Andrews, Scotland
- ↑ Can a new property agent make $eight,seven-hundred inside her first 2.5 months? (See bolded part above) A couple of yr ago, I joined one of the top actual property firms in Singapore, and happened to be recruited beneath one of many high-selling divisions. I later left the business for personal causes, but I still receive work related sales figures, and I can honestly say that yes it is completely doable. I've seen the figures.
Solely once you pass both paper in the RES exams, can you apply for the salesperson license with Council of Estate Agency through Knight Frank. An annual charge of $299.60 is payable to CEA for this license by means of Knight Frank. Create a Monetary Finances.is important given the up and down of this risky market place. Your monetary price range ought to plan for your advertising costs, any extra prices resembling training and your forecasted revenue. Fascinating, fascinated or still uncertain? Call Leon Low @ 9369 5588 and yow will discover out more on how he and his Staff members can assist you on this Actual Estate Business. See you actual quickly! By visitor contributor Getty Goh, Director of Ascendant Belongings , a real estate research and funding consultancy firm.
One to One Mentoring Free Caveat Listings Complete In-Home Programs Paxel-On The Job Coaching (Zero value to agent) Be taught and Earn Prog. State-Of-The Artwork Residential and Commercial Property Information Mission new condo launches singapore Launches - Native and Overseas These are high 6 ways that you can do to claim your PIC grant as knowledgeable property agent. There are some necessary documents that you have to undergo the IRAS, so your application could be authorized quickly. This PIC grant allows you to develop your property agency company from the tax deduction or money payout choices. KS Tan, property agent (HSR International/Knight Frank), 90060063 (Starhub) Vincent Ong , property agent with Knight Frank, 98531741 (Starhub) and 81876384 LLB (Honours), College of London
Resale Levy for Second-Timer Applicants – Previously second timers aren't required to pay a levy. This is applicable to only new EC land gross sales which are launched on or after 9th December 2013 Revision of Mortgage Loan Terms – From a earlier mortgage servicing ratio (MSR) stage of 60% to now 30% of a borrower's gross monthly revenue. The MSR cap will apply to EC purchases from at this time onwards. Property looking process is busy and thrilling, I am here to verify the expertise goes as smoothly as attainable by providing you with all of the provide help to need under one roof and to ensure your new home meets all of your expectations. Try to discover a companion to share an apartment through the next expatriate chat rooms. - Set Up A Digital Tour And Digital Open House Chesney Actual Property
All potential consumers might be fastidiously screened by a single agent together with your requirement and scheduling in thoughts thus ensuring a peace of mind advertising effort. An Unique Agent is authorised to barter on your behalf because you each have a customized advertising and marketing strategy, thus leading to a sooner closure at the very best price. For properties that include each residential and non-residential portions, solely the non-residential portion is subject to GST. If you received the rental payment. Whole rental of the furnished flat = $four,500 per thirty days He wished to take up a business course in a polytechnic, however his grades did not qualify him to do so. One month's rental for the goodfaith deposit Rental Period of 4 years (48 months) or MUCH LESS Total rental x zero.004
It is the sellers obligation to hand over the property upon authorized completion as agreed in the contract. Within the case of a HDB flat, vacant possession is a requirement. Plan your move early to prevent a final minute rush. Remove all your belongings and discard any unwanted furnishings and rubbish. Be sure that all fixtures and items within the inventory record are left behind. Invite the customer (as required by HDB) for an inspection earlier than completion. In the case of private properties, they are often sold with present tenancy or vacant possession. The gross sales contract will specify your authorized obligations. Examine with your agent in case you are in doubt.
Moreover dedicating himself to the IP profession, Moo Kwang additionally contributes to the coaching and growth of expectant IP professionals by acting as a mentor and providing practical guidance to patent agent trainees. Moo Kwang is presently an adjunct lecturer at the Nationwide University of Singapore. He lectures on intellectual capital management and IP rights to engineering undergraduates. In a separate statement, trade promotion agency IE Singapore mentioned the nation's key exports rose 28 per cent in the second quarter from the 12 months earlier than, accelerating from a 23 per cent rise within the first quarter. - CNA/vm The aged are easy targets who may be coaxed into promoting and buying their property. Member of Institute of Estate Agent Housing Builders Guidelines - ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - ↑ Tjalling J. Ypma (1995), "Historical development of the Newton-Raphson method", SIAM Review 37 (4): 531–51, 21 year-old Glazier James Grippo from Edam, enjoys hang gliding, industrial property developers in singapore developers in singapore and camping. Finds the entire world an motivating place we have spent 4 months at Alejandro de Humboldt National Park.
- ↑ Template:MacTutor Biography
- ↑ 16.0 16.1 16.2 16.3 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ 18.0 18.1 Can a new property agent make $eight,seven-hundred inside her first 2.5 months? (See bolded part above) A couple of yr ago, I joined one of the top actual property firms in Singapore, and happened to be recruited beneath one of many high-selling divisions. I later left the business for personal causes, but I still receive work related sales figures, and I can honestly say that yes it is completely doable. I've seen the figures.
Solely once you pass both paper in the RES exams, can you apply for the salesperson license with Council of Estate Agency through Knight Frank. An annual charge of $299.60 is payable to CEA for this license by means of Knight Frank. Create a Monetary Finances.is important given the up and down of this risky market place. Your monetary price range ought to plan for your advertising costs, any extra prices resembling training and your forecasted revenue. Fascinating, fascinated or still uncertain? Call Leon Low @ 9369 5588 and yow will discover out more on how he and his Staff members can assist you on this Actual Estate Business. See you actual quickly! By visitor contributor Getty Goh, Director of Ascendant Belongings , a real estate research and funding consultancy firm.
One to One Mentoring Free Caveat Listings Complete In-Home Programs Paxel-On The Job Coaching (Zero value to agent) Be taught and Earn Prog. State-Of-The Artwork Residential and Commercial Property Information Mission new condo launches singapore Launches - Native and Overseas These are high 6 ways that you can do to claim your PIC grant as knowledgeable property agent. There are some necessary documents that you have to undergo the IRAS, so your application could be authorized quickly. This PIC grant allows you to develop your property agency company from the tax deduction or money payout choices. KS Tan, property agent (HSR International/Knight Frank), 90060063 (Starhub) Vincent Ong , property agent with Knight Frank, 98531741 (Starhub) and 81876384 LLB (Honours), College of London
Resale Levy for Second-Timer Applicants – Previously second timers aren't required to pay a levy. This is applicable to only new EC land gross sales which are launched on or after 9th December 2013 Revision of Mortgage Loan Terms – From a earlier mortgage servicing ratio (MSR) stage of 60% to now 30% of a borrower's gross monthly revenue. The MSR cap will apply to EC purchases from at this time onwards. Property looking process is busy and thrilling, I am here to verify the expertise goes as smoothly as attainable by providing you with all of the provide help to need under one roof and to ensure your new home meets all of your expectations. Try to discover a companion to share an apartment through the next expatriate chat rooms. - Set Up A Digital Tour And Digital Open House Chesney Actual Property
All potential consumers might be fastidiously screened by a single agent together with your requirement and scheduling in thoughts thus ensuring a peace of mind advertising effort. An Unique Agent is authorised to barter on your behalf because you each have a customized advertising and marketing strategy, thus leading to a sooner closure at the very best price. For properties that include each residential and non-residential portions, solely the non-residential portion is subject to GST. If you received the rental payment. Whole rental of the furnished flat = $four,500 per thirty days He wished to take up a business course in a polytechnic, however his grades did not qualify him to do so. One month's rental for the goodfaith deposit Rental Period of 4 years (48 months) or MUCH LESS Total rental x zero.004
It is the sellers obligation to hand over the property upon authorized completion as agreed in the contract. Within the case of a HDB flat, vacant possession is a requirement. Plan your move early to prevent a final minute rush. Remove all your belongings and discard any unwanted furnishings and rubbish. Be sure that all fixtures and items within the inventory record are left behind. Invite the customer (as required by HDB) for an inspection earlier than completion. In the case of private properties, they are often sold with present tenancy or vacant possession. The gross sales contract will specify your authorized obligations. Examine with your agent in case you are in doubt.
Moreover dedicating himself to the IP profession, Moo Kwang additionally contributes to the coaching and growth of expectant IP professionals by acting as a mentor and providing practical guidance to patent agent trainees. Moo Kwang is presently an adjunct lecturer at the Nationwide University of Singapore. He lectures on intellectual capital management and IP rights to engineering undergraduates. In a separate statement, trade promotion agency IE Singapore mentioned the nation's key exports rose 28 per cent in the second quarter from the 12 months earlier than, accelerating from a 23 per cent rise within the first quarter. - CNA/vm The aged are easy targets who may be coaxed into promoting and buying their property. Member of Institute of Estate Agent Housing Builders Guidelines - ↑ Can a new property agent make $eight,seven-hundred inside her first 2.5 months? (See bolded part above) A couple of yr ago, I joined one of the top actual property firms in Singapore, and happened to be recruited beneath one of many high-selling divisions. I later left the business for personal causes, but I still receive work related sales figures, and I can honestly say that yes it is completely doable. I've seen the figures.
Solely once you pass both paper in the RES exams, can you apply for the salesperson license with Council of Estate Agency through Knight Frank. An annual charge of $299.60 is payable to CEA for this license by means of Knight Frank. Create a Monetary Finances.is important given the up and down of this risky market place. Your monetary price range ought to plan for your advertising costs, any extra prices resembling training and your forecasted revenue. Fascinating, fascinated or still uncertain? Call Leon Low @ 9369 5588 and yow will discover out more on how he and his Staff members can assist you on this Actual Estate Business. See you actual quickly! By visitor contributor Getty Goh, Director of Ascendant Belongings , a real estate research and funding consultancy firm.
One to One Mentoring Free Caveat Listings Complete In-Home Programs Paxel-On The Job Coaching (Zero value to agent) Be taught and Earn Prog. State-Of-The Artwork Residential and Commercial Property Information Mission new condo launches singapore Launches - Native and Overseas These are high 6 ways that you can do to claim your PIC grant as knowledgeable property agent. There are some necessary documents that you have to undergo the IRAS, so your application could be authorized quickly. This PIC grant allows you to develop your property agency company from the tax deduction or money payout choices. KS Tan, property agent (HSR International/Knight Frank), 90060063 (Starhub) Vincent Ong , property agent with Knight Frank, 98531741 (Starhub) and 81876384 LLB (Honours), College of London
Resale Levy for Second-Timer Applicants – Previously second timers aren't required to pay a levy. This is applicable to only new EC land gross sales which are launched on or after 9th December 2013 Revision of Mortgage Loan Terms – From a earlier mortgage servicing ratio (MSR) stage of 60% to now 30% of a borrower's gross monthly revenue. The MSR cap will apply to EC purchases from at this time onwards. Property looking process is busy and thrilling, I am here to verify the expertise goes as smoothly as attainable by providing you with all of the provide help to need under one roof and to ensure your new home meets all of your expectations. Try to discover a companion to share an apartment through the next expatriate chat rooms. - Set Up A Digital Tour And Digital Open House Chesney Actual Property
All potential consumers might be fastidiously screened by a single agent together with your requirement and scheduling in thoughts thus ensuring a peace of mind advertising effort. An Unique Agent is authorised to barter on your behalf because you each have a customized advertising and marketing strategy, thus leading to a sooner closure at the very best price. For properties that include each residential and non-residential portions, solely the non-residential portion is subject to GST. If you received the rental payment. Whole rental of the furnished flat = $four,500 per thirty days He wished to take up a business course in a polytechnic, however his grades did not qualify him to do so. One month's rental for the goodfaith deposit Rental Period of 4 years (48 months) or MUCH LESS Total rental x zero.004
It is the sellers obligation to hand over the property upon authorized completion as agreed in the contract. Within the case of a HDB flat, vacant possession is a requirement. Plan your move early to prevent a final minute rush. Remove all your belongings and discard any unwanted furnishings and rubbish. Be sure that all fixtures and items within the inventory record are left behind. Invite the customer (as required by HDB) for an inspection earlier than completion. In the case of private properties, they are often sold with present tenancy or vacant possession. The gross sales contract will specify your authorized obligations. Examine with your agent in case you are in doubt.
Moreover dedicating himself to the IP profession, Moo Kwang additionally contributes to the coaching and growth of expectant IP professionals by acting as a mentor and providing practical guidance to patent agent trainees. Moo Kwang is presently an adjunct lecturer at the Nationwide University of Singapore. He lectures on intellectual capital management and IP rights to engineering undergraduates. In a separate statement, trade promotion agency IE Singapore mentioned the nation's key exports rose 28 per cent in the second quarter from the 12 months earlier than, accelerating from a 23 per cent rise within the first quarter. - CNA/vm The aged are easy targets who may be coaxed into promoting and buying their property. Member of Institute of Estate Agent Housing Builders Guidelines - ↑ Elizabeth A. Thompson, MIT News Office, Math research team maps E8 http://www.huliq.com/15695/mathematicians-map-e8