C. An Introduction. tO Probability Theory and Its Applications. WILLIAM FELLER ( ). Eugene Higgins Professor of Mathematics. Princeton University. To Probability Theory And Its Applications Vol I Feller W Pdf previous post An Introduction To Pattern Recognition Michael Alder Pdf. An Introduction to Probability Theory and Its Applications. WILLIAM FELLER ( - ). Eugene Higgins Professor of Mathematics. Princeton University.

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An Introduction to Probability Theory by William Feller - Ebook download as PDF File .pdf) or read book online. Ed. W. Feller - Ebook download as PDF File .pdf) or read book online. Introduction to Probability Theory and Its Applications Vol II- William Feller - 3ed, 3 Ed. The text can also be used in a discrete probability course. The material Anyone writing a probability text today owes a great debt to William Feller, who taught.

Quotes[ edit ] An Introduction To Probability Theory And Its Applications Third Edition [ edit ] When this book was first conceived more than 25 years ago few mathematicians outside the Soviet Union recognized probability as a legitimate branch of mathematics. Preface to the Third Edition, p. The results concerning fluctuations in coin tossing show the widely held beliefs about the law of large numbers are fallacious. They were so amazing and so at variance with common intuition that even sophisticated colleagues doubted that coins actually misbehave as theory predicts. Note on the Use of this Book, p. The bewildered novice in chess moves cautiously, recalling individual rules, whereas the experienced player absorbs a complicated situation at a glance and is unable to account rationally for his intuition. In like manner mathematical intuition grows with experience, and it is possible to develop a natural feeling for concepts such as four dimensional space. Introduction, The Nature of Probability Theory, p. The manner in which mathematical theories are applied does not depend on preconceived ideas; it is a purposeful technique depending on, and changing with, experience. The philosophy of the foundations of probability must be divorced from mathematics and statistics, exactly as the discussion of our intuitive space concept is now divorced from geometry. Historically, the original purpose of the theory of probability was to describe the exceedingly narrow domain of experience connected with games of chance, and the main effort was directed to the calculation of certain probabilities. Only yesterday the practical things of today were decried as impractical, and the theories which will be practical tomorrow will always be branded as valueless games by the practical man of today. When a coin is tossed, it does not necessarily fall heads or tails; it can roll away or stand on its edge. Chapter I, The Sample Space, p. Using a coin for the same purpose may save feeding and training expenses and free the monkeys for other monkey business.

Radic's publishing house was in Jurisiceva 1, that is, in the Elsa Fluid dom. With kind permission of prof. Apotechary E. Photo from www. Vilim Feller was born on 7 July, in Zagreb, in time of greatest prosperity of the family. This can be seen in the register of births, Ilica 25, Zagreb many thanks to prof. Marta Zdenkovic for this information.

The name of Vilibald was given to him according to St Vilibald, ie. Willibald , whose feastday is on 7 July. See more information about Sv. Vilibald in Croatian. The church of St. Marko, Zagreb, where William Feller was baptised; the roof has been decorated by the Croatian Coat of Arms since photo by Hippo ; on the right of the church is the building of the Croatian Parliament Hrvatski Sabor.

He was baptised on 19th July, in the church of St. Marko in the Upper Town in Zagreb, by rev. Petar Mrzljak. His godparents were Dr. Entering the University of Zagreb in he changed his name to Vilim Feller. Vilibald Srecko Feller in ? He was the youngest one of eight brothers, and he also had four sisters three sisters were born after him:.

The huge and hard working family lived happily in Jurjevska 31a, Zagreb, in a beautifully organized house. It is interesting that this family building, surrounded with a cultivated park and rare plants, had among others an oval room for music and concerts Musik-Zimmer. Today the house and the park are in a sad shape, devastated since during the ex-Yugoslav Communist period. Vilibald Srecko Feller bottom right , the youngest among eight brothers: Schilling and Wojbor A. When young Vilibald Srecko Feller was at the age of a secondary school pupil, as a gifted child he had regular private lessons in mathematics from dr.

I express my sincere gratitude to dr. Photo and data from [ Prva Gimnazija u Zagrebu ]. Feller finished his secondary schooling in at the First Gymnasium in Zagreb. He had private lessons, and went to annual exams to that gymansium. Matriculation form of fourth semester of Vilim Feller's study of mathematics at the University of Zagreb, , with kind permission of prof.

We underline the fact that the regular study of mathematics lasted for four years. According to the obituary published in [ The Annals of Math. Statistics ], Feller finished his studies at the University of Zagreb with a degree equivalent to today's Master of Science, but this claim is wrong. First of all, Feller completed the first two years of study of Mathematics in Zagreb, and at that time, there was not the degree of "Master of Science".

Data filled in in by Vilim Feller, student of the University of Zagreb. A few n ames of his professors at the University of Zagreb, filled in by Vilim Feller in Now there comes the list of lectures that he attended, with the coresponding names of the lecturers:. As we see, young Feller had altogether 29 working hours of lectures weekly 5 days , that is, at the pace of nearly 6 hours each working day.

Vilim Feller in rowing; with kind permission of prof. A few words about Feller's professors in Zagreb. It is to be noted Dr. Vladimir Varicak at that time was already an established scientist of international reputation, one of the leading European specialists in Einstein's theory of relativity.

Also Stanko Hondl was known as an excellent professor of physics, whose lectures had strong emphasis on concrete experiments. Central Physics Library, Zagreb. Hondl was a successor of professor Vinko Dvorzak , outstanding Czech physicist and a student of Ernst Mach , who founded the study of physics at the University of Zagreb in It is very probable that Feller also attanded Hondl's special courses on the theory of relativity and atomic physics, as well as at other professors.

University of Zagreb , founded in , where Feller studied from till photos by D. Feller's professor Stjepan Bohnicek was a specialist in number theory. All this shows that young Feller had good professors, and obtained a solid grounding in mathematics and physics during his studies in Zagreb, which resulted with an equivalent of the title of Master of Science at the very young age of Here are two more matriculation forms filled in by Vilim Feller 2nd and 3rd semsester, University of Zagreb, and In [ Science in Croatia 2, p.

Marije Kiseljak, , from which the program of Mathematical Analysis for students of mathematics at the University of Zagreb could be seen in time when Feller was a student. But young Vilim Feller needed much stronger scientific environment. It is natural to assume that this happened under the advice and recommendation of his professors in Zagreb.

His adviser was a famous mathematician Richard Courant , who was a student of David Hilbert. Feller became acquainted with David Hilbert , one of the greatest mathematicians of all times, who was also teaching there. Hilbert was always his ideal mathematician. As we have said, in November 3, , the oral exam was held, and members of the committee were R. Courant, G. Herglotz and J.

I express my deep gratitude to Dr. The thesis was published under the same title in Mathematische Zeitschrift in , Vol 27, pp. According to [ Vranic , p. He reported his original results at the Geometric Seminar led by his professor Marije Kiseljak, Zagreb, who inspired young Feller's interest in this topic. As we have already mentioned, Feller completed his studies of mathematics in Zagreb with the title equivalent to today's Master of Science.

The assistants promptly alerted Courant to the presence of Willy Feller. After the third calculus lecture, to Feller's amazement, the professor - an unbeleivably august personage to a European student of that day - approached. Questioning the boy about his education in his native land, Courant discovered that Feller was already doing mathematics on his own.

He told him to bring his work to the next lecture. Even thus instructed, Feller was too bashful to produce his papers on the appointed day. The next morning he was awakened by commotion on the stairs leading to his attic room. There was a knock on the door.

Courant entered and left a few moments later with the desired papers. After Feller was "discovered" in the Praktikum, he was an accepted member of the new "in group" which gathered around Courant. It seems to be little known that William Feller wrote a review of the famous book by outstanding Russian mathematician A. Kolmogorov , Grundbegriffe der Wahrscheinlichkeitsrechnung [ English translation of the book ], , in which theoretical foundations of Probability Theory have been laid down:.

William Feller: The calculus of probabilities is constructed axiomatically, with no gaps and in the greatest generality, and for the frst time systematically integrated, fully and naturally, with abstract measure theory.

The axiom system is certainly the simplest imaginable.

The great generality is noteworthy; probabilities in infinite dimensional spaces of arbitrary cardinality are dealt with. The presentation is very precise, but rather terse, directed to the reader who is not unfamiliar with the material. Measure theory is assumed. It is to be noted that Feller was only 27 years old when this book was published, while Kolmogorov was On 25 September , Andrej N. Kolmogorov was a guest of the Institute of Mathematics of the University of Zagreb, where he had a lecture "On the foundations of the Theory of Probability".

Kolmogorov bio je gost u Zagrebu Compare with its new French edition from According to a Swedish mathematician Ulf Grenander in his interview published in Statistical Science ,. Feller came from Germany and Cramer took him under his wings.

I think it was Cramer who told him that he should not continue working on differential geometry, which he did before. Cramer advised him to move to probability theory, the field of the future, and then Feller started working on probability theory.

Cramer certainly had impact on Feller, but as we saw, Feller published his first work on probability already in , and Feller was very well acquainted with Kolmogorov's classic monograph, which he reviewd for Zentralblatt. Also, according to Professor Ulrich Krengel , Feller started his work in probability theory already in Kiel, that is, in at the latest. Vili Feller with his mother, , in Bad Gastein spa, Austria; with kind permission of prof.

Feller defended his habilitation thesis in , and obtained the position of Privat Dozent in Kiel. He remained in Kiel until , when he left Germany due to the arrival of Nazism. In he married Clara Nielsen, who had been his student already in Kiel. In Feller's emigrated to the USA. Vilim Feller in , when he started to work in Stockholm; his father Eugen Viktor died the same year in Zagreb, and his mother two years later; with kind permission of prof. The proceedings were published by Hermann in eight fascicles in their series Actualites Scientifiques et Industrielles.

The first seven fascicles appeared in as numbers through For more information see [ Shaffer, Vovk ]. Clara Nielsen i Willy Feller in s. According to personal information I obtained from Marta and Nikola Zdenkovic in , Zagreb their grandfather Ferdinand was William Feller's brother , William Feller was on friendly terms with Albert Einstein , despite a difference of almost 30 years. Since , they were both in Princeton, USA: In Feller became associate professor at Brown University Providence, Rhode Island , and there he started his work on issuing Mathematical Reviews.

In he became citizen of the USA. In Feller became a professor at Cornell University, where he worked for five years. In he obtained the position of Eugene Higgins Professor of Mathematics at Princeton , where he remained until his death in Princeton University photos by Mihay. Clara Nielsen, , Feller's student in Kiel they married in , with kind permission of prof. He wrote both articles in the Croatian language:.

This is indicated under the title of the second article, where his name is written as. We provide an excerpt from an article by an American mathematician Michael Golomb, Terror and Exile and a Letter About it A report from Volume 4, 1, of TopCom , which was a part of a special exhibition organized during the International Congress of Mathematicians in Berlin, The List of Expelled Berlin mathematicians contains 53 names.

It contains names. It is a surprise to me, and probably also to many readers, that as many as 75 German mathematicians, many of them world-renowned, emigrated to this country in the thirties. I choose from the list names that are universally recognized: The great Albert Einstein, himself an emigrant from Berlin, is not included because he is classified as a Physicist, not a mathematician.

By their own work and as teachers of a generation of brilliant young American mathematicians these emigrees from Nazi Germany have made the US the great center of mathematics in the world that it is today. William Feller, photo from [ Vladimir Vranic ]. In addition to his own work, he discussed progress by Hadamard, Hostinsky, Doeblin and Kolmogorov. He also stressed the fact that by now probability was equally exact as other branches of mathematics, and that many mathematical subjects "integral equations, group theory" etc.

Another important talk in Oslo was the one given by W. Feller on stochastic processes. He discussed his well known existence and uniqueness theorems for Markov processes with jumps. In the Conference [International Congress of Mathematicians , Cambridge, Massachussetts] chaired by von Neumann there were three talks related to probability: Certainly the last of these was a highlight.

Feller explained the ties between classical boundary problems for the heat equation and diffusion processes. He also spoke on Ito's theory of stochastic integration. This was possibly the first time that these topics were presented to a broad mathematical public. Vilim Feller on the right in Zagreb in , in Jurjevska 31a, where he spent his youth, with Ivo Zdenkovic, father of Marta and Nikola Zdenkovic Ivo's wife Eva is the daughter of Ferdinand, Vilim's brother ; with kind permission of prof.

Feller was among those who initiated publishing the important Mathematical Reviews journal in , and was one of its first executive editors ; the first editors were Otto Neugebauer , , and J. Tamarkin, According to Ulf Grenander in his very interesting interview published in Statistical Science , Feller had been the editor of Mathematische Zentralblatt.

When he arrived from Stockholm to Brown University USA in , he had a complete list of active mathematicians from all over the world with him, and that number at that time was ! Aided by this list, Neugebauer initiated editing the Mathematical Reviews from Brown. Later, Feller took over the editorial responsibilities and continued in that capacity for years until he left Brown and moved to Cornell. William Feller] deserves the gratitude of mathematicians for his six years of effort in establishing the new journal [i.

Reviews] , now the leading review of mathematics in the world. William Feller and Clara Nielsen Feller in Clara Nielsen Feller, with kind permission of prof. It is considered to be one of the best mathematical textbooks written in the 20th century. According to Feller's own words, he worked on Volume I for eight years, since till Probability is a mathematical discipline whose aims are akin to those, for example, of geometry or analytical mechanics.

In each field we must be careful to distinguish three aspects of the theory: The character, and the charm, of the whole structure cannot be appreciated without considering all three aspects in their proper relation.

Nowadays small boys betting and shooting dice, newspapers report on samples of public opinion, and the magic of statistics embraces all phases of life to the extent that young girls anxiously watch the statistics of their chances to get married.

The history of probability and of mathematics in general shows a stimulating interplay of theory and applications: William Feller , photo by Paul Halmos from his book I have a photographic memory Providence, ; Halmos provides also the photo of another outstanding Croatian mathematician - Zvonimir Janko. We provide an excerpt from the review of the first edition of Feller's book Volume I , written for Mathematical Reviews by R. From the review of the second edition of Feller's book Volume I , written by U.

Grenander for Mathematical Reviews:. As in the first edition the exposition is mathematically rigorous and at the same time elegant and lucid. This fascinating book will remain a standard textbook of mathematical probability for many years to come. Orey for Mathematical Reviews:.

This is the sequel to the popular first volume The reader of this book need not have any prior knowledge of probability beyond a few basic definitions, say as given in the first chapter of the first volume. Indeed it is the author's aim, admirably realized, to be of interest to a diverse audience, ranging from novice to expert. The book has a rich texture, derived from the wealth of problems treated as applications or illustrations of the theory.

The striking aspect is the apparent ease and elegance with which these problems are dispatched, frequently making obsolete the original treatment given in the research literature. Feller's book: Both volumes comprise altogether pages.

Both of them were substantially improved with respect to previous editions. The book seems even to acquire new friends. The fact that laymen are not deterred by passages which proved difficult to students of mathematics shows that the level of difficulty cannot be measured objectively; it depends on the type of information one seeks and the details one is prepared to skip.

The traveler often has the choice between climbing a peak or using a cable car. Here are the data about the latest editions of both Volumes from MathSciNet , which comprise altogether pp:. Feller, William: His wife Clara wrote on p. I am grateful to the publisher for providing a proofreader to compare the print against the manuscript and for compiling the index.

Goldman, A. Grunbaum, H. McKean, L.

Pitt, and A. Pittenger divided the book among themselves to check on the mathematics. Every mathematician knows what an incredible amount of work that entails. I express my deep gratitude to these men and extend my heartfelt thanks for their labor of love. The first Russian translation of Volume I appeared just a year after the appearance of the book in ! And also the first Russian translation of Volume II appeared just a year after the appearance of the book in !

Here is more detailed information based on Mathematical Reviews:. Feller, V. Diskretnye raspredeleniya. Russian [An introduction to probability theory and its applications. Discrete distributions. Inostrannoj Literatury, Moscow, Feller, V.: Vvedenie v teoriyu veroyatnostej i ee prilozheniya.

Tom 1. Dobrusin, A.

Juskevic and S. Edited by E.

Dynkin , with an introduction by A. Second edition, reprinted Izdat.

Tom 2. Prohorov Izdat.

Second edition. With a preface by A. Now we bring to the reader's attention the translation of the second English edition, improved and added to by the author in many details. It is precisely this choice of material which enables Feller's book to occupy an independent place in the literature on probability theory. By the choice of problems Feller brings to light their solving by "direct", and specifically probabilistic means.

This tendency to see behind analytical transformations their "probabilistic" sense, belongs to the most valuable features of Feller's book. Deserving our attention is also the author's effort in the book in clearly illustrating the character of effects of probabilistic laws on carefully chosen examples.

In many cases the author manages to introduce the reader into really interesting questions of comparation between statistical data and probabilistic theory of events. Professor Feller, having learned about the prepartion of the second volume, kindly sent us a list of many necessary corrections, that were included into the text.

I am very grateful to him for his kindness. It is surprising to read the following sentence of Yu. Prokhorov in his foreword to the Russian translation of the third English edition of Volume There is no any other book on probability theory comparable to this one - it so successfully comprises mathematical austerity, excellency of proofs, and the quantity of considered applications. Expounding the most complex mathematical questions, the author does not omit from sight the real world phenomena, where a developed theory can be applied.

The character of the book is such that it will not age for a very long time. Japanese translation of volume I of Feller's monograph has been published in two books issued in and I p. Limusa-Wiley, II p. Limusa, Wstep do rachunku prawdopodobienstwa. Tom I. Polish [Introduction to probability theory.

I] Translated from the second English language edition. Third revised edition! Panstwowe Wydawnictwo Naukowe, Warsaw, First edition in Tom II. II] Translated from the English. Second revised edition! Wstep do rachunku prawdopodobienstwa translated from the Third Edition , Wydawnictwo: Robert Bartoszynski.

Znakomity podrecznik rachunku prawdopodobienstwa! Wznowienie poszukiwanego od lat klasycznego podrecznika, nalezacego do kanonu literatury dotyczacej ksztalcenia probabilistycznego.

Zalety ksiazki to: In the first part of Feller's monograph had its 6th Polish edition, so the edition is already its seventh printing in Poland. Ts'e I. Chinese [Probability theory and its applications. William Feller in Chinese, from the Chinese edition of Volume 1. The edition has been printed in 9, copies, and subsequent Chinese editions seem to exist: Photo from Book. Feller's books have been reedited by Wiley-Eastern, New Delhi, for the needs of mathematicians in India:.

William Feller with his students; photo by J. Goldman, USA. According to [ Halmos , p. Feller's scientific interests in mathematics were very broad. He contributed to calculus, geometry, and functional analysis.

About half of his papers are in the field of probability theory. Especially important was his work in the period between and , when "W. Feller broke new grounds on the theory of diffusion and Kolmogorov was delighted. According to Mathematical Reviews , Feller's works are cited times by authors. The first part of his book is cited times, and the second part times. It should be noted that Math Reviews is reviewing math articles starting with the year , so that Feller's very productive scientific work before that that is, between and is not evidenced there.

His most cited article 37 times is. The parabolic differential equations and the associated semi-groups of transformations. Yosida ,. Besides two volumes of his famous book Feller wrote scientific papers, see the complete list in the memorial issue of [ Annals of Math.

Statistics ]. The list has been obtained using mathematical references from MathSciNet covering the period between since Feller's death and , citing Feller's name.

At the lowest level, it is personal interaction, after all, which produces great collaborations. Feller and Kolmogorov, across continents and ideologies, is the perfect example.

Feller-Tornier constant has been defined in Feller's paper written jointly with Erhard Tornier The constant is defined as the density of natural numbers whose prime factorization contains an even number of distinct primes to powers larger than the first. It is equal to 0. Tornier was 12 years older than Feller. In he became a Nazist, and ousted Feller from the University of Kiel in when he learned about his Jewish ancestry for more information see [ Thomas Hochkirchen ], Abraham A.

Lebenskreise , Deutsche Verlag-Anstalt, Stuttgart, , p. Kollegen in einer dunklen Zeit. Feller had another joint paper with Tornier, published also in Mathematische Annalen, Vol , Mass und Inhaltstheorie des Bairischen Nullraumes, pp. Feller in white suit with P. Loeve on his right, and with B. In Feller had a great honour to become a member of the international scientific committee which had to elect candidates for the Fields Medal.

Feller is the author or coauthor of two more books:. Feller in s, from Jay Goldman's Photo Album. Feller , William Feller was thesis advisor to 22 students in the period of to , and by he has as many as descendants.

Marta and Nikola Zdenkovic, Zagreb, informed me in that they do not know the meaning of initial "K. However, there exists a paper entitled Feller, W. Here are the names of Feller's PhD students:. Feller's unofficial PhD student was Frank Spitzer , see here. His another unofficial PhD student seems to be Joanne Elliott. She became a professional mathematician, and in one of her papers,.

Joanne Elliott: This problem, suggested by W. Feller, arises in the theory of stochastic processess. The author wishes to thank William Feller for many helpful discussions Joanne Elliott, William Feller: Joanne Elliott, photo by Paul Halmos on the same page Feller's photo appears I have a photographic memory Providence, She earned her PhD at Cornell in , and recall that Feller was professor there in the period of In Rutgers-New Brunswick Mathematics Graduate Faculty we found that she worked in potential theory, and that in she had a chair at Douglas College at Rutgers since, Professor of Mathematics since , retired since William Feller; photo from [ Croatian Biographical Lexicon ].

Shortly before his death he was elected as an honorary memebr of the London Mathematical Society. Mathematician; Educator. Many outstading mathematicians from Princeton University were elected as members of the National Academy of Sciences: Solomon Lefschetz , James W.

Wigner , Salomon Bochner , Howard P. Robertson , Norman E. Spencer , John W. Milnor , etc. See the complete list. Mathematics and Computer Science. The National Medal of Science award was established by the U. Congress as a Presidential award. It was conferred in by president Richard Nixon to Feller's wife Clara during the official ceremony held in the White House , a month after Feller's death at the age of Shelves: math I don't think it is necessary to seek "easier" introductions to probability than this classic.

The prose is quite readable, and the mathematics is accessible to a reader who has some calculus and is willing to stick with it. I took a peek at Volume 2, and I can't claim the same for it. The author clearly marks out what can be skipped, so you can strengthen your probabilistic intuitions without beating yourself up too much.

Amusingly, even Feller sometimes nods. On page 10 2nd ed, , while I don't think it is necessary to seek "easier" introductions to probability than this classic. On page 10 2nd ed, , while talking about the "Distribution of r balls in n cells", he states that "the number of possible arrangements increases rapidly with r and n.

On page 53, problem 6 b , we are to find, among others, the probability that there are 2 repetitions among 4 random digits. The repeated digit can be chosen 10 ways, and the remaining position can be filled in 9 ways. These are forgivable typos that don't affect the quality of the presentation.