Stochastic Differential Equations: An Introduction with Applications
Average customer rating: 4 out of 5 stars
  • A very good book!
  • Excellent introduction on Stochastic Differential Equations
  • OK intro to stochastic analysis
  • Very good book - would not mind more on finance
  • good intro book
Stochastic Differential Equations: An Introduction with Applications
Bernt K. Oksendal
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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ASIN: 3540637206

Book Description

This book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start from some basic results (without proofs) of the easier cases and develop the theory from there, and to concentrate on the proofs of the easier case (which nevertheless are often sufficiently general for many purposes) in order to be able to reach quickly the parts of the theory which is most important for the applications. The new feature of this 5th edition is an extra chapter on applications to mathematical finance.

Customer Reviews:

5 out of 5 stars A very good book!.......2007-07-05

I read this book after I had read Karatzas' and Shreve's book "Stochastic Calculus..." and it is probably better to do it the other way round. The mathematical prerequisites are not high, however a good intuitive understanding of measure theory is probably necessary. The pace of the book is leasurely, the proofs are such, that pencil and paper is rarely needed, however no rigor is lost.
The book quickly moves to interesting applications of the theory, which is motivated very well.
It contains a few typographical errors, mostly in the last chapter, and mostly of a harmless nature.

With the necessary mathematical background, it seems to be an ideal introduction to this highly interesting topic of stochastic differential equations!

5 out of 5 stars Excellent introduction on Stochastic Differential Equations.......2007-05-08

A well written book in Mathematics
Stochastic Differential Equations is a branch of mathematics. This book is not just for financial derivatives analysis or modeling. Oksendal first introduces the subject by raising a few stochastic problems (population growth; electric charge in RLC circuit; filtering problems, Dirichlet problems; asset management; optimal portfolio and options pricing) in the first chapter. The subsequent chapters develop notions and techniques which are able to solve wide varieties of stochastic problems (not just those mentioned in the first chapters). The arrangement is impressive in particular for readers who have no previous knowledge about the subject. The readers at least know the target for developing the techniques and would not lose the way when manipulating tons of symbols. Hints and answers to selected problems are invaluable to students for self-study.
To achieve a sound background on stochastic equations is extremely important especially in quantitative finance. It is not an easy job however. QF students may consider going through this book before seriously take Shreve's books on Stochastic Calculus for Finance.

3 out of 5 stars OK intro to stochastic analysis.......2007-03-14

This is a standard work (it is the one I read when I first started looking at this sort of thing) but having taken it off the shelf recently again, I think it is overrated, for several reasons.

First, it is very notation heavy - TeX has seduced Mr. Oksendahl into all sorts of bad habits - I can very easily imagine that the earlier editions (mine is the 5th), which were written with a typewriter, are much more readable.

Second, the proofs are very formal, developed mostly in terms of classical functional analysis (square integrable real functions, geometry of real Hilbert spaces etc.). From the point of view of rigor this is fine, but from the point of view of intuition, not so much, esp. when combined with the heavyweight notation. In fact note that unless you have a decent background in functional analysis, of the sort you are more likely to pick up in a mathematics degree than a finance degree, then you are going to get precisely nowhere with this book.

I don't want to be too negative, and there is lots of good stuff here - just to warn that Oksendahl is not (as one might think) a royal road to the theory of SDEs (depressingly, it may be that Oksendahl is, nevertheless, the best of the bunch out there - it is certainly, all criticism not-withstanding, more accessible than Karatzas and Shreve).

4 out of 5 stars Very good book - would not mind more on finance.......2007-02-08

Very good book. However the math prerequisite is at quite a high level. Especially the probability theory introduction could be a little less fast-paced. As my main interest was on the financial application I would not have minded a little more on that topic and a little less on e.g. filtering or stochatsic control in return.

4 out of 5 stars good intro book.......2006-02-03

This is a good intro book. It brings you really fast to Ito's Formula and SDE. Somebody said that the Kolmogorov's backward eq in chapter 8 is wrong. This is false, it is just expressed in a different way than the usual form. However, with a change of time, you are all set.
Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations (Systems & Control: Foundations & Applications)
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    Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations (Systems & Control: Foundations & Applications)
    Martino Bardi , and Italo Capuzzo-Dolcetta
    Manufacturer: Birkhäuser Boston
    ProductGroup: Book
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    ASIN: 0817636404

    Book Description

    This book presents a self-contained and up-to-date account of the theory of viscosity solutions for first order partial differential equations of Hamilton-Jacobi type and its interplay with Bellman's Dynamic Programming approach to optimal control and differential games, as it developed after the beginning of the eighties with the pioneering work of M. Crandall and P.L. Lions. The book begins with a long introduction where the authors present in a rather informal way the main ideas and themes of the book, beginning with the classical derivation of the Hamilton-Jacobi-Bellman equation from the Dynamic Programming Optimality Principle and the characterization of the value function as the unique viscosity solution of this equation. This is followed by a treatment of the general theory of continuous viscosity solutions and its applications to a number of problems in deterministic optimal control theory for nonlinear systems(infinite and finite horizon, minimal time, optimal stopping, impulse control, problems with state constraints, etc.)The second part of the book develops the theory of discontinuous viscosity solutions and its applications to asymptotic problems (singular perturbations, ergodic problems, etc.), to some approximation schemes for the value function and for optimal feedback controls based on Dynamic Programming. The last chapter and appendix deal, respectively, with differential games and nonlinear H-infinity control.

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    Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control (Progress in Nonlinear Differential Equations and Their Appli)
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      Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control (Progress in Nonlinear Differential Equations and Their Appli)
      Piermarco Cannarsa , and Carlo Sinestrari
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      Calculus of Variations and Optimal Control/Differential Equations Set
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        Manufacturer: Chapman & Hall/CRC
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          Manufacturer: Birkhäuser Basel
          ProductGroup: Book
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          ASIN: 3764377208

          Book Description

          This volume contains selected contributions originating from the ‘Conference on Optimal Control of Coupled Systems of Partial Differential Equations’, held at the ‘Mathematisches Forschungsinstitut Oberwolfach’ in April 2005.

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          Differential Inclusions and Optimal Control (Mathematics and its Applications)
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            Michal Kisielewicz
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              Manufacturer: Birkhäuser Basel
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              ASIN: 3764321946

              Book Description

              While domain decomposition methods have a long history dating back well over one hundred years, it is only during the last decade that they have
              become a major tool in numerical analysis of partial differential equations.
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              Economic Dynamics: Applications of Difference Equations, Differential Equations and Optimal Control
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                Economic Dynamics: Applications of Difference Equations, Differential Equations and Optimal Control
                Amnon Levy-Livermore , and Amnon Levy
                Manufacturer: Avebury
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                From Nano to Space: Applied Mathematics Inspired by Roland Bulirsch
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                  From Nano to Space: Applied Mathematics Inspired by Roland Bulirsch

                  Manufacturer: Springer
                  ProductGroup: Book
                  Binding: Hardcover

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                  Graduate students and postgraduates in Mathematics, Engineering and the Natural Sciences want to understand Applied Mathematics for the solution of everyday problems. Scholars of Roland Bulirsch working at universities, at research institutions and in industry combine research and review papers in this anthology. Their work is summed up under the title "From Nano to Space – Applied Mathematics Inspired by Roland Bulirsch". More than 20 contributions are divided into scales: nano, micro, macro, space and real life. The contributions survey current research and present case studies very interesting and informative for both graduate students and postgraduates. The contributions show how modern Applied Mathematics influences our everyday lives. Several contributions include complex graphics and illustrations, many of them in color.

                  Generalized Characteristics of First Order PDEs:: Applications in Optimal Control and Differential Games
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                    Arik Melikyan
                    Manufacturer: Birkhauser
                    ProductGroup: Book
                    Binding: Hardcover

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                    ASIN: 0817639845

                    Locus Solus
                    Average customer rating: 5 out of 5 stars
                    • Tragically Hardly-ever-in-print
                    • Certain of his episodes outshine even Hugo or Napoleon!
                    • i read this a long time ago.
                    • A strange world of exhibits and the stories behind them
                    Locus Solus
                    Raymond Roussel
                    Manufacturer: Riverrun Press (New York, NY)
                    ProductGroup: Book
                    Binding: Paperback

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                    ASIN: 0714507342

                    Customer Reviews:

                    5 out of 5 stars Tragically Hardly-ever-in-print.......2006-08-20

                    There's a sea-horse race in this book. Not just a sea-horse race, but a sea-horse race inside a giant diamond-shaped tank of oxygenated fluid that also holds a beautiful submerged woman dancing and creating music with the movement of her locks of hair, sometimes enhancing the gyration of her head with sudden tosses and jostles of her hips. There's not only that, but several automaton devices that use flotation and buoyancy to drive their mechanic parts and act out various historical and mythological scenes. Like Voltaire suddenly doubting his atheistic doctrines, or Atlas kicking a celestial object, or Pilate being branded on the forehead.

                    All of that takes place inside the gigantic diamond-like tank of oxygenated fluid. A very lustrous fluid.

                    By the way, the English translation sometimes calls the sea-horses "hippocampi." Don't be confused: in context, it means sea-horses. It's not talking about parts of a brain. You might be thinking, "well there's no possible room for confusion there!", but au contraire. Because inside the tank is also a floating head/face of Danton, composed exclusively of the preserved nerves and musculuture, without any bones or skin. And re-animated with expertly applied electrical currents, courtesy of Canterel and his cat.

                    And they're not just any sea-horses. They're sea-horses equipped with "setons" attached to a shining golden sphere that they themselves created by kneading together small globulets of golden wine that Canterel pours into the tank and lets float down to them.

                    The entire episode I'm talking about took place long after the book had already left my jaw on the floor. In short: read it. You know that "dream-like" quality that hyped books supposedly possess? Say, like "Amnesia Moon"? Well Raymond Roussel accomplishes all that without any narrative tricks, without any deception, without any ill-defined or sensationally blurred "boundaries between dream and reality" or any of that nonsense. Roussel accomplishes his feats the old fashioned way: with elbow grease, and imagination. He accomplishes it by giving everything to you, not hiding things from you.

                    Who is the Canterel I mentioned above? Canterel-- a name that one should never utter aloud except on bended knee-- has the wealth and quirk of Willy Wonka, combined with the wealth and ingenuity of Bruce Wayne. Which makes for a very rich, very marvelous fellow. His estate and private collection puts both of those men's assets to shame, quite extravagantly.

                    As you already know, the book is a narrated trip through some of Canterel's exhibits. He aims to please, though. So don't think that the book will lack character, plot, or suspense just because it's a sort of museum-tour. There's stories within stories that explain the exhibits. And they have everything that archetypically good "stories" have, and more: love, betrayal, forgiveness, fantastic magnanimity, loss, disgrace, lust, vindication. I was breathless waiting for the resolutions of certain tales, practically jumping off my reading-bench to cheer for the characters, or otherwise immobilized by the revelations and vicissitudes.

                    Did I mention that nerves/musculuture of Danton's head are set into physiological motor motion by an electric current provided by a swimming cat whose hairless body acts as a battery after eating a specially-designed pill and is trained to stick its head into a long metal hat-like cone which becomes its electrode terminus?

                    And it's all described soberly, no tricks. By the way, Roussel (though there's a chance it's the translators doing, since I haven't and couldn't read the original French) tells his stories, tells the motivations and actions of characters, with a very skillful use of words, using strong descriptive verbs and nouns. The sentences held together with a unique power. Many times I took great pleasure in re-reading certain sentences, because they were said so absolutely perfectly. Of course, that should be the hallmark of a professional writer, but I don't find it too often.

                    So anyway you'll feel like you're there. You won't even have any disbelief to suspend. At certain points, like a particular early exhibit that I won't name, I said to myself, "There's no going back, this is too fantastic, there's no POSSIBLE EXPLANATION of this, Roussel has crossed the line, this is uncanny and totally unrecoverable at this point, I feel exploited!," and I kept reading, kept reading-kept reading, "by god, no, by GOD HE'S DONE IT!, he's doing it, by god Canterel, Roussel, you've done it, my good holy god unbeliEVABLE!!! Whew. Wow." I had to close the book for a minute and lean against a fence, nodding my head uncontrollably. When you close this book and put it on your shelf when done, you'll keep suspecting that it's about to burst open and spill out its contents all over your room, neighborhood, and city-- and you'll feel like an angry god for actually having the ability to close the book and contain it.

                    Book will take your breath away. If not check your pulse. Or, try something else. Bye.

                    5 out of 5 stars Certain of his episodes outshine even Hugo or Napoleon!.......2004-03-06

                    I used to have so much fun reading this book. I remember I miraculously found a copy in some book shop on the far southside of Chicago for $8. One night I was drinking with some classmates shortly after class and I made the mistake of lending this irreplacable book to one of them, which of course the fool never returned nor probably ever read or if he did appreciated. May every curse be piled upon your perfidious little name, punk, which it is a blessing I can't remember it was so long ago.
                    I remember the first time I read Impressions of Africa, right after graduating high school. I was a naive young admirer of Duchamp at the time, and I kept seeing these references to Roussel, and the description of Impressions made it sound like a travel book. Had I known him then I might have expected something like a French William Cobbett. Ha! I don't think I realized something definitely strange was going on in those pages until I reached the part with the father and his sons echoing their voices off of each other's chests with their shirts being stuck to their skin "by some sticky substance", -- the word "substance" somehow set me laughing for a solid twenty, thirty minutes, and all the hilarity, the absurdity of the Incomporables' show that had gone on before were finally apparent to me. I have been a lover of Roussel ever since; the only casualty was my perspective of Duchamp's accomplishment, which is as Duchamp himself admitted greatly indebted to Roussel's.
                    Locus Solus is the book Roussel wrote after Impressions and the two make a pair unlike any other in literature. Locus is presided over by Martial Canteral, a figure right out of Jules Verne, who Roussel once said was a name that should not be spoken aloud "except on bended knee," -- hm, yes -- Canterel is a famous scientist and inventor, and the book is set at his estate where a group of distinguished figures have been invited to a tour of guided by none other than its owner and director. The book follows the tour as one of the eyewitnesses, and the sights along the way are so bizarre, the machinery so complex and beyond any reasonable utility, it quite defies any attempt to describe the effect here. One impression I think that merits a word or two is the apparent lack of emotion in the book. I would say that there is a great amount of sadness and tragedy in the book that adds a kind of under-layer parallel to the encoded sentences of Roussel's method. The vitallium episode, in which Canterel invents a "certain chemical" that makes the bodies of the dead become animate again (but are still dead) has a very particular strain of anguish and loss inherent in its concept. And then there is also the weariness of the visionary experienced by the reader, the author, and the characters being audience to so many impossibilities one after the other piled up so high there is an actual physical exhaustion after the conclusion. And then of course there is also the tragedy of the author himself, who had both novels lavishly adapted for the theater, and created two of the most colossal failures in the history of drama, causing riots and scandal at the showings and humiliation to the author. He ended up a pitiful man, addicted to drugs and having spent all his fortune, he killed himself in his forties with a great dream "of a glory that shall outshine that of Victor Hugo or Napoleon."
                    This is not a book for everyone, perhaps even for very few. However there is no good reason these two books are out of print. It is long past time they are reprinted and Roussel be given the honor he deserves.

                    5 out of 5 stars i read this a long time ago........1999-05-13

                    i read this book when i was about 13 and i have been wanting to read it again for 17 years. i remember it only vaguely, but i know it was good. please mister publisher, print it again.

                    5 out of 5 stars A strange world of exhibits and the stories behind them.......1998-11-30

                    Roussel's novels are giant puzzles, in which he describes images and stories that have a unique carnival logic. Punning relationships generate textual rebuses (rebi?), in a way that makes the reader aware of the book as a mechanism, but Roussel gives too few clues to really understand it. In Locus Solus, Roussel gives a tour of the museum garden of an eccentric millionaire, who, like Roussel himself, collects with a frenetic and psychedelic rationalism. Please, Riverrun Press, reprint this book.
                    Asthetische Reflexionen in Raymond Roussels Romanen: Impressions d'Afrique und Locus solus (Abhandlungen zur Sprache und Literatur)
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                      Asthetische Reflexionen in Raymond Roussels Romanen: Impressions d'Afrique und Locus solus (Abhandlungen zur Sprache und Literatur)
                      Astrid Volmer
                      Manufacturer: Romanistischer
                      ProductGroup: Book
                      Binding: Paperback

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                      ASIN: 386143038X
                      Kniga Dlya Takih Kak Ya (Locus Solus)
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                        Max Fray
                        Manufacturer: Amfora
                        ProductGroup: Book
                        Binding: Hardcover

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                        ASIN: 5942786070

                        Product Description

                        V jetoj knige sobrany teksty, kotorye, pol'zujas' jazykom samogo avtora, mozhno nazvat' "temnoj storonoj Maksa Fraja". "Temnoj" ne potomu, konechno, chto chitatelju predstoit vstrecha s nekim zlovewim "misterom Hajdom", prjatavshimsja za spinoj obajatel'nogo "doktora Dzhekila", populjarnogo avtora romanov v zhanre fantasy. Prosto do sih por jeti teksty byli skryty ot shirokoj chitatel'skoj auditorii. Oni znakomy lish' starozhilam russkogo Interneta. Pri poverhnostnom prochtenii trudno poverit', chto romany o pohozhdenijah sjera Maksa i jesse o "knigrah" (avtorskaja proizvodnaja ot slov "knigi" i "igry") napisany odnim i tem zhe chelovekom; glubokij analiz pozvoljaet chitatelju vosprinimat' jesse Fraja kak prostrannyj "kommentarij" k ego zhanrovoj proze... ili dazhe naoborot. Sam Maks Fraj schitaet, chto mnogotomnaja jepopeja o prikljuchenijah sjera Maksa byla prosto pravil'no razrabotannym marshrutom "ne znaju kuda", gde i avtor, i chitatel' mogut najti nekoe nevyrazimoe, no pritjagatel'noe "nevedomo chto", kazhdyj - svoe. On polagaet, chto chitatel' i avtor - soobwniki. Esli vospol'zovat'sja futbol'noj terminologiej, pisatel' lish' daet pas, gol zhe vsegda zabivaet chitatel', pojetomu v konechnom schete rezul'tat zavisit imenno ot chitatel'skogo masterstva. A vnutrennee rodstvo dejstvujuwih lic mnogokratno uvelichivaet obwie shansy na uspeh. Delaja sobstvennuju istoriju chuzhim dostojaniem, rasskazchik ne prosto voskreshaet ee v pamjati, no i v nekotorom rode zanovo ovewestvljaet. Ona, konechno, i tak ne vydumka, i vse zhe prezhde, do slov, ej nedostavalo podlinnosti. V rezul'tate sovmestnyh usilij rasskazchika i slushatelja, ili chitatelja na perilah nevoobrazimogo Mosta Vremeni odna za drugoj pojavljajutsja zrimye i osjazaemye zarubki. Pojetomu vot vam istorija o Rybnike, rybake i rybke, i ewe o mokroj vorone, i o konce sveta zaodno, i, esli uzh na to poshlo, - o nachale sveta, i kak zhe horosho, chto u jetogo slova tak mnogo smyslov.
                        Locus Solus
                        Average customer rating: Not rated
                          Locus Solus
                          Raymond Roussell
                          Manufacturer: UNIV OF CA BERKELEY
                          ProductGroup: Book
                          Binding: Hardcover
                          ASIN: B000TXH3P8
                          LOCUS SOLUS III-IV NEW POETRY
                          Average customer rating: Not rated
                            LOCUS SOLUS III-IV NEW POETRY
                            John ASHBERY
                            Manufacturer: see notes for publisher info
                            ProductGroup: Book
                            Binding: Hardcover
                            ASIN: B000L6L8KO
                            LOCUS SOLUS V.
                            Average customer rating: Not rated
                              LOCUS SOLUS V.
                              John et al. (editors). Ashbery
                              Manufacturer: Kulchur,
                              ProductGroup: Book
                              Binding: Paperback
                              ASIN: B000UUAD0W
                              Petit Dictionnaire De Locus Solus (Faux Titre) (Faux Titre)
                              Average customer rating: Not rated
                                Petit Dictionnaire De Locus Solus (Faux Titre) (Faux Titre)
                                Patrick Besnier , and Pierre Bazantay
                                Manufacturer: Editions Rodopi
                                ProductGroup: Book
                                Binding: Paperback

                                GeneralGeneral | Criticism & Theory | History & Criticism | Literature & Fiction | Subjects | Books
                                FrenchFrench | World Literature | Literature & Fiction | Subjects | Books
                                FrenchFrench | Foreign Language Fiction | Literature & Fiction | Subjects | Books
                                All French BooksAll French Books | French | Foreign Language Books | Specialty Stores | Books
                                ASIN: 9051834934
                                Russkie inorodnye skazki-2. Antologiya (Locus solus)
                                Average customer rating: Not rated
                                  Russkie inorodnye skazki-2. Antologiya (Locus solus)
                                  M. Fraj
                                  Manufacturer: Amfora
                                  ProductGroup: Book
                                  Binding: Hardcover

                                  All Russian BooksAll Russian Books | Russian | Foreign Language Books | Specialty Stores | Books
                                  ASIN: 5942785031

                                  Product Description

                                  Eta antologiya sostavlena Maksom Fraem iz proizvedenij molodykh avtorov, kotorykh Fraj vydelyaet i kotorym simpatiziruet. V osnovnom, vse skazki, sostavivshie sbornik, esche ne publikovalis' v pechatnom vide.
                                  Zapiski o Peterburge (Locus solus)
                                  Average customer rating: Not rated
                                    Zapiski o Peterburge (Locus solus)
                                    E. Ignatova
                                    Manufacturer: Amfora
                                    ProductGroup: Book
                                    Binding: Hardcover

                                    All Russian BooksAll Russian Books | Russian | Foreign Language Books | Specialty Stores | Books
                                    ASIN: 5942787883

                                    Product Description

                                    `Zapiski o Peterburge` E.A.Ignatovoj posvyascheny istorii goroda - ot ego osnovaniya do 40-kh godov XX veka. Osobyj interes predstavlyaet ranee ne publikovavshayasya vtoraya kniga, vossozdayuschaya kartinu gorodskoj zhizni s 1917 po 1940 g. (na materiale arkhivnykh dokumentov, redkikh memuarnykh svidetel'stv, periodiki tekh let).
                                    Locus Solus, a novel.
                                    Average customer rating: Not rated
                                      Locus Solus, a novel.
                                      Raymond Roussel
                                      Manufacturer: University of California Press
                                      ProductGroup: Book
                                      Binding: Hardcover
                                      ASIN: B000JLGZJA

                                      Books:

                                      1. Test Methods for Explosives (Shock Wave and High Pressure Phenomena)
                                      2. The Far Side Gallery 2007 Off The Wall Page-a-Day Calendar
                                      3. The Finite Element Method in the 1990's: A Book Dedicated to O.C. Zienkiewicz
                                      4. The Geometry of the Word Problem for Finitely Generated Groups (Advanced Courses in Mathematics - CRM Barcelona)
                                      5. The Statistical Evaluation of Medical Tests for Classification and Prediction (Oxford Statistical Science Series)
                                      6. The World of Faery: An Inspirational Collection of Art for Faery Lovers
                                      7. Today's Business Math: A Text-Workbook
                                      8. Topological Degree Theory and Applications (Series in Mathematical Analysis and Applications)
                                      9. Two-Dimensional Separated Flows
                                      10. Understanding Nonlinear Dynamics

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