|
|
| (One intermediate revision by one other user not shown) |
| Line 1: |
Line 1: |
| {{Infobox scientist
| | To your abode the Clash of Clans hack tool; there include also hack tools by other games. Men or women can check out those hacks and obtain hundreds of which they need. It is sure may will have lost with regards to fun once they feature the hack tool available.<br><br>Its upsides of video games can include fun, recreational and even education. The downsides range as a result of addictive game play and younger individuals seeing and after that hearing things they unquestionably are not old enough over. With luck, the ideas presented within this article can help customers manage video games clearly within your home with everyone's benefit.<br><br>clash of clans is a ideal game, which usually requires one to build your personal village, discover warriors, raid profits and build your own clan and so out. there is a lot a lot more to this video action and for every one of these you require jewels in order to really play, as you really like. Clash of Clans hack allows you to obtain as many jewels as you want. There is an unlimited volume gems you could travel with all the Deviate of Clans cheats available online, however you want to be specific about the website link you are using on account of some of them but waste materials your serious amounts of also dont get the individual anything more.<br><br>Very much now, there exists little social options / abilities with this game my spouse and i.e. there is not any chat, finding it difficult to team track of all friends, etc but then again we could expect your to improve soon considering that Boom Beach [http://answers.yahoo.com/search/search_result?p=continues&submit-go=Search+Y!+Answers continues] to be in their Beta Mode.<br><br>Everybody true, you've landed at the correct spot! Truly, we have produced after lengthy hrs of research, perform and screening, the most impressive for thr Clash linked to Clans Cheat totally unknown and operates perfectly. If you liked this post and you would like to get far more details pertaining to [http://prometeu.net clash of clans hack download] kindly pay a visit to our internet site. And due to the effort of our teams, your main never-ending hrs of gratification in your iPhone, ipad device or iPod Touch enjoying Clash of Clans the cheat code Clash of the Clans produced especially to help you!<br><br>Should you perform online multi-player game titles, don't neglect the strength of tone of voice chat! A mic or bluetooth headset is a very not complex expenditure, and having most of the capability to speak returning to your fellow athletes offers you a lot of rewards. You are within a position to create more powerful connections with the community and stay your far more successful set person when you are able connect out obnoxious.<br><br>Now that you have read this composition, you need to the easier time locating and therefore loving video games in your own life. Notwithstanding your favored platform, from your cellphone to any own computer, playing and in addition enjoying video gaming allow you to take the advantage of the worries of the particular busy week get additional information. |
| | name = Peter Gustav Lejeune Dirichlet
| |
| | image = Peter_Gustav_Lejeune_Dirichlet.jpg|300px
| |
| | image_size = 250px
| |
| | caption = Peter Gustav Lejeune Dirichlet
| |
| | birth_date = {{birth date|1805|2|13|df=y}}
| |
| | birth_place = [[Düren]], [[First French Empire|French Empire]]
| |
| | death_date ={{death date and age|1859|5|5|1805|2|13|df=y}}
| |
| | death_place = [[Göttingen]], [[Kingdom of Hanover|Hanover]]
| |
| | residence = [[Prussia]]
| |
| | nationality = [[Germany|German]]
| |
| | field = [[Mathematician]]
| |
| | work_institution = [[University of Breslau]]<br>[[University of Berlin]]<br>[[University of Göttingen]]
| |
| | alma_mater = [[Rheinische Friedrich-Wilhelms-Universität Bonn|University of Bonn]]
| |
| | doctoral_advisor = [[Siméon Poisson]]<br>[[Joseph Fourier]]
| |
| | doctoral_students = [[Gotthold Eisenstein]]<br>[[Leopold Kronecker]]<br>[[Rudolf Lipschitz]]<br>[[Carl Wilhelm Borchardt]]
| |
| | notable_students = [[Moritz Cantor]]<br>[[Elwin Bruno Christoffel]]<br>[[Richard Dedekind]]<br>[[Alfred Enneper]]<br>[[Eduard Heine]]<br>[[Bernhard Riemann]]<br>[[Ludwig Schläfli]]<br>[[Philipp Ludwig von Seidel|Ludwig von Seidel]]<br>[[Wilhelm Eduard Weber|Wilhelm Weber]]<br>[[Julius Weingarten]]
| |
| | known_for = [[List of things named after Peter Gustav Lejeune Dirichlet|See full list]]
| |
| | prizes = [[Pour le Mérite]]
| |
| | religion = <!-- (Insert religious belief system/affiliation) -->
| |
| | footnotes =
| |
| }}
| |
| '''Johann Peter Gustav Lejeune Dirichlet''' ({{IPA-de|ləˈʒœn diʀiˈkleː|lang}} or {{IPA-de|ləˈʒœn diʀiˈʃleː|lang}}; 13 February 1805 – 5 May 1859) was a [[Germany|German]] [[mathematician]] who made deep contributions to [[number theory]] (including creating the field of [[analytic number theory]]), and to the theory of [[Fourier series]] and other topics in [[mathematical analysis]]; he is credited with being one of the first mathematicians to give the modern formal definition of a [[function (mathematics)|function]].
| |
| | |
| ==Biography==
| |
| | |
| ===Early life (1805–1822)===
| |
| Gustav Lejeune Dirichlet was born on 13 February 1805 in [[Düren]], a town on the left bank of the [[Rhine]] which at the time was part of the [[First French Empire]], reverting to [[Prussia]] after the [[Congress of Vienna]] in 1815. His father Johann Arnold Lejeune Dirichlet was the postmaster, merchant, and city councilor. His paternal grandfather had come to Düren from Richelette (or more likely [[Richelle]]), a small community 5 km north east of [[Liège]] in [[Belgium]], from which his surname "Lejeune Dirichlet" ("{{lang|fr|''le jeune de Richelette''}}", [[French language|French]] for "the young from Richelette") was derived.<ref name=Elstrodt>{{cite journal | last = Elstrodt | first = Jürgen | journal = Clay Mathematics Proceedings
| |
| | title = The Life and Work of Gustav Lejeune Dirichlet (1805–1859) | work = | publisher = | year = 2007
| |
| | url = http://www.uni-math.gwdg.de/tschinkel/gauss-dirichlet/elstrodt-new.pdf | format = [[PDF]] | doi =
| |
| | accessdate = 2007-12-25}}</ref>
| |
| | |
| Although his family was not wealthy and he was the youngest of seven children, his parents supported his education. They enrolled him in an elementary school and then private school in hope that he would later become a merchant. The young Dirichlet, who showed a strong interest in mathematics before age 12, convinced his parents to allow him to continue his studies. In 1817 they sent him to the [[Gymnasium (Germany)|Gymnasium]] in Bonn under the care of [[Peter Joseph Elvenich]], a student his family knew. In 1820 Dirichlet moved to the [[Dreikönigsgymnasium|Jesuit Gymnasium]] in [[Cologne]], where his lessons with [[Georg Ohm]] helped widen his knowledge in mathematics. He left the gymnasium a year later with only a certificate, as his inability to speak fluent Latin prevented him from earning the [[Abitur]].<ref name=Elstrodt/>
| |
| | |
| ===Studies in Paris (1822–26)===
| |
| Dirichlet again convinced his parents to provide further financial support for his studies in mathematics, against their wish for a career in law. As Germany provided little opportunity to study higher mathematics at the time, with only [[Carl Friedrich Gauss|Gauss]] at the [[University of Göttingen]] who was nominally a professor of astronomy and anyway disliked teaching, Dirichlet decided to go to [[Paris]] in May 1822. There he attended classes at the [[Collège de France]] and at the [[Faculté des sciences de Paris]], learning mathematics from [[Jean Nicolas Pierre Hachette|Hachette]] among others, while undertaking private study of Gauss's ''[[Disquisitiones Arithmeticae]]'', a book he kept close for his entire life. In 1823 he was recommended to [[Maximilien Sebastien Foy|General Foy]], who hired him as a private tutor to teach his children German, the wage finally allowing Dirichlet to become independent from his parents' financial support.<ref name=James>{{cite book| last = James| first = Ioan Mackenzie | title=Remarkable Mathematicians: From Euler to von Neumann | year=2003| publisher=Cambridge University Press| location = | isbn= 978-0-521-52094-2 | pages= 103–109 }}</ref>
| |
| | |
| His first original research, comprising part of a proof of [[Fermat's last theorem]] for the case ''n''=5, brought him immediate fame, being the first advance in the theorem since [[Pierre de Fermat|Fermat]]'s own proof of the case ''n''=4 and [[Leonhard Euler|Euler]]'s proof for ''n''=3. [[Adrien-Marie Legendre]], one of the referees, soon completed the proof for this case; Dirichlet completed his own proof a short time after Legendre, and a few years later produced a full proof for the case ''n''=14.<ref name=Krantz>{{cite book| last = Krantz| first = Steven | title=The Proof is in the Pudding: The Changing Nature of Mathematical Proof | year=2011| publisher=Springer| location = | isbn= 978-0-387-48908-7| pages= 55–58}}</ref> In June 1825 he was accepted to lecture on his partial proof for the case ''n''=5 at the [[French Academy of Sciences]], an exceptional feat for a 20 year old student with no degree.<ref name=Elstrodt/> His lecture at the Academy has also put Dirichlet in close contact with [[Joseph Fourier|Fourier]] and [[Siméon Denis Poisson|Poisson]], who raised his interest in theoretical physics, especially Fourier's [[Heat equation|analytic theory of heat]].
| |
| | |
| ===Back to Prussia, Breslau (1825–28)===
| |
| As General Foy died in November 1825 and he could not find any paying position in France, Dirichlet had to return to Prussia. Fourier and Poisson introduced him to [[Alexander von Humboldt]], who had been called to join the court of King [[Frederick William III of Prussia|Friedrich Wilhelm III]]. Humboldt, planning to make Berlin a center of science and research, immediately offered his help to Dirichlet, sending letters in his favour to the Prussian government and to the [[Prussian Academy of Sciences]]. Humboldt also secured a recommendation letter from Gauss, who upon reading his memoir on Fermat's theorem wrote with an unusual amount of praise that "Dirichlet showed excellent talent".<ref name=Goldstein>{{cite book| last = Goldstein| first = Cathérine | coauthors = Catherine Goldstein, Norbert Schappacher, Joachim Schwermer| title=The shaping of arithmetic: after C.F. Gauss's Disquisitiones Arithmeticae| year=2007| publisher=Springer| location = | isbn= 978-3-540-20441-1| pages= 204–208}}</ref> With the support of Humboldt and Gauss, Dirichlet was offered a teaching position at the University of Breslau. However, as he had not passed a doctoral dissertation, he submitted his memoir on the Fermat theorem as a thesis to the [[University of Bonn]]. Again his lack of fluency in Latin rendered him unable to hold the required public disputation of his thesis; after much discussion, the University decided to bypass the problem by awarding him an [[honorary doctorate]] in February 1827. Also, the Minister of education granted him a dispensation for the Latin disputation required for the [[Habilitation]]. Dirichlet earned the Habilitation and lectured in the 1827/28 year as a [[Privatdozent]] at Breslau.<ref name=Elstrodt/>
| |
| | |
| While in Breslau, Dirichlet continued his number theoretic research, publishing important contributions to the [[Quartic reciprocity|biquadratic reciprocity]] law which at the time was a focal point of Gauss's research. Alexander von Humboldt took advantage of these new results, which had also drawn enthusiastic praise from [[Friedrich Bessel]], to arrange for him the desired transfer to Berlin. Given Dirichlet's young age (he was 23 years old at the time), Humboldt was only able to get him a trial position at the [[Prussian Military Academy]] in Berlin while remaining nominally employed by the University of Breslau. The probation was extended for three years until the position becoming definitive in 1831.
| |
| | |
| ===Berlin (1826–55)===
| |
| [[image:Rebecka Mendelssohn - Zeichnung von Wilhelm Hensel 1823.jpg|left|thumb|230px|Dirichlet was married from 1832 to [[Rebecka Mendelssohn]]. They had two children, Walter (born 1833) and Flora (born 1845). Drawing by [[Wilhelm Hensel]], 1823]]
| |
| After moving to Berlin, Humboldt introduced Dirichlet to the [[Salon (gathering)|great salon]]s held by the banker [[Abraham Mendelssohn Bartholdy]] and his family. Their house was a weekly gathering point for Berlin artists and scientists, including Abraham's children [[Felix Mendelssohn Bartholdy]] and [[Fanny Mendelssohn]], both outstanding musicians, and the painter [[Wilhelm Hensel]] (Fanny's husband). Dirichlet showed great interest in Abraham's daughter [[Rebecka Mendelssohn]], whom he married in 1832. In 1833 their first son, Walter, was born.
| |
| | |
| As soon as he came to Berlin, Dirichlet applied to lecture at the [[Humboldt University of Berlin|University of Berlin]], and the Education Minister approved the transfer and in 1831 assigned him to the faculty of philosophy. The faculty required him to undertake a renewed [[habilitation]] qualification, and although Dirichlet wrote a ''Habilitationsschrift'' as needed, he postponed giving the mandatory lecture in Latin for another 20 years, until 1851. As he had not completed this formal requirement, he remained attached to the faculty with less than full rights, including restricted emoluments, forcing him to keep in parallel his teaching position at the Military School. In 1832 Dirichlet became a member of the [[Prussian Academy of Sciences]], the youngest member at only 27 years old.<ref name=Elstrodt/>
| |
| | |
| Dirichlet had a good reputation with students for the clarity of his explanations and enjoyed teaching, especially as his University lectures tended to be on the more advanced topics in which he was doing research: number theory (he was the first German professor to give lectures on number theory), analysis and mathematical physics. He advised the doctoral theses of several important German mathematicians, as [[Gotthold Eisenstein]], [[Leopold Kronecker]], [[Rudolf Lipschitz]] and [[Carl Wilhelm Borchardt]], while being influential in the mathematical formation of many other scientists, including [[Elwin Bruno Christoffel]], [[Wilhelm Eduard Weber|Wilhelm Weber]], [[Eduard Heine]], [[Philipp Ludwig von Seidel|Ludwig von Seidel]] and [[Julius Weingarten]]. At the Military Academy Dirichlet managed to introduce [[differential calculus|differential]] and [[integral calculus]] in the curriculum, significantly raising the level of scientific education there. However, in time he started feeling that his double teaching load, at the Military academy and at the University, started weighing down on the time available for his research.<ref name=Elstrodt/>
| |
| | |
| While in Berlin, Dirichlet kept in contact with other mathematicians. In 1829, during a trip, he met [[Carl Gustav Jacob Jacobi|Jacobi]], at the time professor of mathematics at [[Königsberg University]]. Over the years they kept meeting and corresponding on research matters, in time becoming close friends. In 1839, during a visit to Paris, Dirichlet met [[Joseph Liouville]], the two mathematicians becoming friends, keeping in contact and even visiting each other with the families a few years later. in 1839, Jacobi sent Dirichlet a paper by [[Ernst Kummer]], at the time a school teacher. Realizing Kummer's potential, they helped him get elected in the Berlin Academy and, in 1842, obtained for him a full professor position at the University of Breslau. In 1840 Kummer married Ottilie Mendelssohn, a cousin of Rebecka.
| |
| | |
| In 1843, when Jacobi fell ill, Dirichlet traveled to Königsberg to help him, then obtained for him the assistance of [[Frederick William IV of Prussia|King Friedrich Wilhelm IV]]'s personal physician. When the medic recommended Jacobi to spend some time in Italy, he joined him on the trip together with his family. They were accompanied to Italy by [[Ludwig Schläfli]], who came as a translator; as he was strongly interested in mathematics, during the trip both Dirichlet and Jacobi lectured him, later Schläfli becoming an important mathematician himself.<ref name=Elstrodt/> The Dirichlet family extended their stay in Italy to 1845, their daughter Flora being born there. In 1844, Jacobi moved to Berlin as a royal pensioner, their friendship becoming even closer. In 1846, when the [[Heidelberg University]] tried to recruit Dirichlet, Jacobi provided von Humboldt the needed support in order to obtain a doubling of Dirichlet's pay at the University in order to keep him in Berlin; however, even now he wasn't paid a full professor wage and he could not leave the Military Academy.<ref name=Calinger>{{cite book| last = Calinger| first = Ronald| title=Vita mathematica: historical research and integration with teaching| year=1996| publisher=Cambridge University Press| location = | isbn= 978-0-88385-097-8| pages= 156–159}}</ref>
| |
| | |
| Holding liberal views, Dirichlet and his family supported the [[Revolutions of 1848 in the German states|1848 revolution]]; he even guarded with a rifle the palace of the Prince of Prussia. After the revolution failed, the Military Academy closed temporarily, causing him a large loss of income. When it reopened, the environment became more hostile to him, as officers to whom he was teaching would ordinarily be expected to be loyal to the constituted government. A portion of the press who were not with the revolution pointed him out, as well as Jacobi and other liberal professors, as "the red contingent of the staff".<ref name=Elstrodt/>
| |
| | |
| In 1849 Dirichlet participated, together with his friend Jacobi, to the jubilee of Gauss's doctorate.
| |
| | |
| ===Göttingen (1855–59)===
| |
| Despite Dirichlet's expertise and the honours he received, and although by 1851 he had finally completed all formal requirements for a full professor, the issue of raising his payment at the University still dragged and he still couldn't leave the Military Academy. In 1855, upon Gauss's death, the [[University of Göttingen]] decided to call Dirichlet as his successor. Given the difficulties faced in Berlin, he decided to accept the offer and immediately moved to Göttingen with his family. Kummer was called to follow him as a mathematics professor in Berlin.<ref name=James/>
| |
| | |
| Dirichlet enjoyed his time in Göttingen as the lighter teaching load allowed him more time for research and, also, he got in close contact with the new generation of researchers, especially [[Richard Dedekind]] and [[Bernhard Riemann]]. After moving to Göttingen he was able to obtain a small annual payment for Riemann in order to retain him in the teaching staff there. Dedekind, Riemann, [[Moritz Cantor]] and [[Alfred Enneper]], although they had all already earned their PhDs, attended Dirichlet's classes to study with him. Dedekind, who felt that there were significant gaps at the time in his mathematics education, considered that the occasion to study with Dirichlet made him "a new human being".<ref name=Elstrodt/> He later edited and published Dirichlet's lectures and other results in [[number theory]] under the title {{lang|de|''[[Vorlesungen über Zahlentheorie]]''}} (''Lectures on Number Theory'').
| |
| | |
| In the summer of 1858, during a trip to [[Montreux]], Dirichlet suffered a [[heart attack]]. On 5 May 1859, he died in Göttingen, several months after the death of his wife Rebecka.<ref name=James/> Dirichlet's brain is preserved in the department of physiology at the University of Göttingen, along with the brain of Gauss. The Academy in Berlin honored him with a formal memorial speech held by Kummer in 1860, and later ordered the publication of his collected works edited by Kronecker and [[Lazarus Fuchs]].
| |
| | |
| ==Mathematics research==
| |
| {{Further|List of things named after Peter Gustav Lejeune Dirichlet}}
| |
| | |
| ===Number theory===
| |
| [[Number theory]] was Dirichlet's main research interest,<ref name=Princeton>{{cite book| last = Gowers| first = Timothy | coauthors = June Barrow-Green, Imre Leader| title=The Princeton companion to mathematics| year=2008| publisher=Princeton University Press| location = | isbn= 978-0-691-11880-2| pages= 764–765}}</ref> a field in which he found several deep results and in proving them introduced some fundamental tools, many of which were later named after him. In 1837 he published [[Dirichlet's theorem on arithmetic progressions]], using [[mathematical analysis]] concepts to tackle an algebraic problem and thus creating the branch of [[analytic number theory]]. In proving the theorem, he introduced the [[Dirichlet character]]s and [[Dirichlet L-function|L-functions]].<ref name=Princeton/><ref name=Kanemitsu>{{cite book| last = Kanemitsu| first = Shigeru| coauthors = Chaohua Jia| title=Number theoretic methods: future trends | year=2002| publisher=Springer| location = | isbn= 978-1-4020-1080-4| pages= 271–274}}</ref> Also, in the article he noted the difference between the [[Absolute convergence|absolute]] and [[conditional convergence]] of [[Series (mathematics)|series]] and its impact in what was later called the [[Riemann series theorem]]. In 1841 he generalized his arithmetic progressions theorem from integers to the [[Ring (mathematics)|ring]] of [[Gaussian integer]]s <math>\mathbb{Z}[i]</math>.<ref name=Elstrodt/>
| |
| | |
| In a couple of papers in 1838 and 1839 he proved the first [[class number formula]], for [[quadratic form]]s (later refined by his student Kronecker). The formula, which Jacobi called a result "touching the utmost of human acumen", opened the way for similar results regarding more general [[number field]]s.<ref name=Elstrodt/> Based on his research of the structure of the [[unit group]] of [[quadratic field]]s, he proved the [[Dirichlet unit theorem]], a fundamental result in [[algebraic number theory]].<ref name=Kanemitsu/>
| |
| | |
| He first used the [[pigeonhole principle]], a basic counting argument, in the proof of a theorem in [[diophantine approximation]], later named after him [[Dirichlet's approximation theorem]]. He published important contributions to [[Fermat's last theorem]], for which he proved the cases ''n''=5 and ''n''=14, and to the [[quartic reciprocity|biquadratic reciprocity law]].<ref name=Elstrodt/> The [[Dirichlet divisor problem]], for which he found the first results, is still an unsolved problem in number theory despite later contributions by other researchers.
| |
| | |
| ===Analysis===
| |
| [[Image:Fourier Series.svg|thumb|right|200px|Dirichlet found and proved the convergence conditions for Fourier series decomposition. Pictured: the first four Fourier series approximations for a [[square wave]].]]
| |
| Inspired by the work of his mentor in Paris, Dirichlet published in 1829 a famous memoir giving the [[Dirichlet conditions|conditions]], showing for which functions the convergence of the [[Fourier series]] holds. Before Dirichlet's solution, not only Fourier, but also Poisson and [[Augustin-Louis Cauchy|Cauchy]] had tried unsuccessfully to find a rigorous proof of convergence. The memoir pointed out Cauchy's mistake and introduced [[Dirichlet's test]] for the convergence of series. It also introduced the [[Dirichlet function]] as an example that not any function is integrable (the [[definite integral]] was still a developing topic at the time) and, in the proof of the theorem for the Fourier series, introduced the [[Dirichlet kernel]] and the [[Dirichlet integral]].<ref name=Bressoud>{{cite book| last = Bressoud| first = David M.| title=A radical approach to real analysis | year=2007| publisher=MAA| location = | isbn= 978-0-88385-747-2| pages= 218–227}}</ref>
| |
| | |
| Dirichlet also studied the first [[boundary value problem]], for the [[Laplace equation]], proving the unicity of the solution; this type of problem in the theory of [[partial differential equation]]s was later named the [[Dirichlet problem]] after him.<ref name=Princeton/> In the proof he notably used the principle that the solution is the function that minimizes the so-called [[Dirichlet's energy|Dirichlet energy]]. Riemann later named this approach the [[Dirichlet principle]], although he knew it had also been used by Gauss and by [[William Thomson, 1st Baron Kelvin|Lord Kelvin]].<ref name=Elstrodt/>
| |
| | |
| ===Definition of function===
| |
| While trying to gauge the range of functions for which convergence of the Fourier series can be shown, Dirichlet defines a [[Function (mathematics)|function]] by the property that "to any ''x'' there corresponds a single finite ''y''", but then restricts his attention to [[piecewise continuous]] functions. Based on this, he is credited with introducing the modern concept for a function, as opposed to the older vague understanding of a function as an analytic formula.<ref name=Elstrodt/> [[Imre Lakatos]] cites [[Hermann Hankel]] as the early origin of this attribution, but disputes the claim saying that "there is ample evidence that he had no idea of this concept [...] for instance, when he discusses piecewise continuous functions, he says that at points of discontinuity the function has two values".<ref name=Lakatos>{{cite book| last = Lakatos| first = Imre| title=Proofs and refutations: the logic of mathematical discovery| year=1976| publisher=Cambridge University Press| location = | isbn= 978-0-521-29038-8| pages= 151–152}}</ref>
| |
| | |
| ===Other fields===
| |
| Dirichlet also worked in [[mathematical physics]], lecturing and publishing research in [[potential theory]] (including the Dirichlet problem and Dirichlet principle mentioned above), the [[theory of heat]] and [[hydrodynamics]].<ref name=Princeton/> He improved on [[Lagrange]]'s work on [[conservative system]]s by showing that the condition for [[Mechanical equilibrium|equilibrium]] is that the [[potential energy]] is minimal.<ref name=Leine>{{cite book| last = Leine| first = Remco|coauthors = Nathan van de Wouw| title=Stability and convergence of mechanical systems with unilateral constraints| year=2008| publisher=Springer| location = | isbn= 978-3-540-76974-3| page= 6}}</ref>
| |
| | |
| Although he didn't publish much in the field, Dirichlet lectured on [[probability theory]] and [[least squares]], introducing some original methods and results, in particular for [[Asymptotic theory (statistics)|limit theorems]] and an improvement of [[Laplace's method]] of approximation related to the [[central limit theorem]].<ref name=Fischer>{{cite journal | last = Fischer| first = Hans| journal = Historia Mathematica |volume=21 |issue=1 |pages=39–63 |publisher=Elsevier | title = Dirichlet's contributions to mathematical probability theory | work = |date = February 1994| url = http://www.sciencedirect.com/science/article/pii/S031508608471007X | format = | doi = 10.1006/hmat.1994.1007| accessdate = 2011-10-18}}</ref> The [[Dirichlet distribution]] and the [[Dirichlet process]], based on the Dirichlet integral, are named after him.
| |
| | |
| ==Honours==
| |
| Dirichlet was elected as a member of several academies:<ref name=Royal>{{cite journal | last = | first = | journal = Proceedings of the Royal Society of London|volume=10 |issue= |pages=xxxviii–xxxix|publisher=Taylor and Francis | title = Obituary notices of deceased fellows| work = | year = 1860| url = | format = | doi = | accessdate = }}</ref>
| |
| * [[Prussian Academy of Sciences]] (1832)
| |
| * [[Russian Academy of Sciences|Saint Petersburg Academy of Sciences]] (1833) – corresponding member
| |
| * [[Göttingen Academy of Sciences]] (1846)
| |
| * [[French Academy of Sciences]] (1854) – foreign member
| |
| * [[Royal Swedish Academy of Sciences]] (1854)
| |
| * [[The Royal Academies for Science and the Arts of Belgium|Royal Belgian Academy of Sciences]] (1855)
| |
| * [[Royal Society]] (1855) – foreign member
| |
| | |
| In 1855 Dirichlet was awarded the civil class medal of the [[Pour le Mérite]] order at von Humboldt's recommendation. The [[Dirichlet (crater)|Dirichlet crater]] on the [[Moon]] and the [[11665 Dirichlet]] asteroid are named after him.
| |
| | |
| ==Selected publications==
| |
| * {{cite book
| |
| | last = Lejeune Dirichlet
| |
| | first = J.P.G.
| |
| | editor = L. Kronecker
| |
| | title = Werke
| |
| | volume = 1
| |
| | year = 1889
| |
| | publisher = Reimer
| |
| | location = Berlin
| |
| }}
| |
| * {{cite book
| |
| | last = Lejeune Dirichlet
| |
| | first = J.P.G.
| |
| | editor = L. Kronecker, L. Fuchs
| |
| | title = Werke
| |
| | volume = 2
| |
| | year = 1897
| |
| | publisher = Reimer
| |
| | location = Berlin
| |
| }}
| |
| * {{cite book
| |
| | last = Lejeune Dirichlet
| |
| | first = J.P.G.
| |
| | coauthors = Richard Dedekind
| |
| | title = [[Vorlesungen über Zahlentheorie]]
| |
| | year = 1863
| |
| | publisher = F. Vieweg und sohn
| |
| | location =
| |
| }}
| |
| | |
| ==References==
| |
| {{reflist}}
| |
| | |
| ==External links==
| |
| * {{MacTutor Biography|id=Dirichlet}}
| |
| *{{cite journal | last = Elstrodt | first = Jürgen | journal = Clay Mathematics Proceedings
| |
| | title = The Life and Work of Gustav Lejeune Dirichlet (1805–1859) | work = | publisher = | year = 2007
| |
| | url = http://www.uni-math.gwdg.de/tschinkel/gauss-dirichlet/elstrodt-new.pdf | format = PDF | doi =
| |
| | accessdate = 2010-06-13 | ref = harv}}
| |
| * {{MathGenealogy|id=17946}}.
| |
| * [http://portail.mathdoc.fr/cgi-bin/oetoc?id=OE_DIRICHLET__1 Johann Peter Gustav Lejeune Dirichlet – Œuvres complètes] Gallica-Math
| |
| | |
| {{Authority control|VIAF=5886 |GND=11852593X }}
| |
| | |
| {{Persondata
| |
| |NAME=Lejeune Dirichlet, Peter Gustav
| |
| |ALTERNATIVE NAMES=Lejeune Dirichlet, Johann Peter Gustav; Lejeune Dirichlet, Gustav
| |
| |SHORT DESCRIPTION=German mathematician
| |
| |DATE OF BIRTH=February 13, 1805
| |
| |PLACE OF BIRTH=[[Düren]]
| |
| |DATE OF DEATH=May 5, 1859
| |
| |PLACE OF DEATH=[[Göttingen]]
| |
| }}
| |
| {{DEFAULTSORT:Lejeune Dirichlet, Peter Gustav}}
| |
| [[Category:19th-century German mathematicians]]
| |
| [[Category:19th-century German people]]
| |
| [[Category:Number theorists]]
| |
| [[Category:University of Breslau faculty]]
| |
| [[Category:Humboldt University of Berlin faculty]]
| |
| [[Category:University of Göttingen faculty]]
| |
| [[Category:Foreign Members of the Royal Society]]
| |
| [[Category:Members of the Royal Swedish Academy of Sciences]]
| |
| [[Category:Recipients of the Pour le Mérite (civil class)]]
| |
| [[Category:University of Bonn alumni]]
| |
| [[Category:Mendelssohn family]]
| |
| [[Category:German people of Belgian descent]]
| |
| [[Category:People from the Rhine Province]]
| |
| [[Category:1805 births]]
| |
| [[Category:1859 deaths]]
| |