Cantitate/Preț
Produs
Total produse
Vezi coșul
Problems in Probability de Albert N. Shiryaev

Problems in Probability: Problem Books in Mathematics

Autor Albert N. Shiryaev Traducere de Andrew Lyasoff
en Limba Engleză Paperback – 19 sep 2014

Observăm în volumul Problems in Probability o abordare riguroasă a interdisciplinarității matematice, unde teoria probabilităților se intersectează organic cu analiza funcțională, combinatorica și teoria potențialului. Această lucrare, publicată de Springer, nu este doar un auxiliar, ci o sinteză a metodologiei rusești de predare la nivel universitar, fiind fundamentată pe experiența de decenii a lui Albert N. Shiryaev la Universitatea de Stat din Moscova.

Suntem de părere că structura cărții reflectă o maturitate pedagogică remarcabilă. Începând cu bazele elementare, conținutul avansează coerent spre fundamentele matematice ale teoriei probabilităților, tratând extensiv convergența măsurilor de probabilitate și variabilele aleatorii independente. Capitolele dedicate martingalelor și lanțurilor Markov (capitolele 7 și 8) sunt deosebit de valoroase pentru studenții de la nivel masteral, oferind un nivel de profunzime care depășește exercițiile standard de curs.

În contextul operei autorului, această ediție separată a exercițiilor completează teoretic volumele Probability-1 și Probability-2, oferind instrumentarul practic necesar pentru asimilarea conceptelor abstracte dezvoltate în acele manuale. Față de Recent Developments in Stochastic Methods and Applications, care este o colecție de lucrări de conferință, volumul de față este un instrument de lucru structurat, axat pe formarea competențelor de calcul și demonstrație.

Ca alternativă la One Thousand Exercises in Probability de Geoffrey Grimmett pentru cursurile de statistică și probabilități, lucrarea lui Shiryaev aduce avantajul unei ancorări mai adânci în școala matematică rusă, punând un accent sporit pe rigoarea analitică și pe demonstrații complexe, fiind susținută de o anexă densă de notații și rezultate auxiliare.

Citește tot Restrânge

Din seria Problem Books in Mathematics

  • Graph Theory
    Preț: 33846 lei
  • 15% University of Toronto Mathematics Competition (2001-2015)
    Preț: 39203 lei
  • 15% Problems in Real and Complex Analysis
    Preț: 62615 lei
  • 15% Pell’s Equation
    Preț: 55832 lei
  • Problems in Analysis
    Preț: 37026 lei
  • Exercises in Probability
    Preț: 37438 lei
  • 15% Problem Book for First Year Calculus
    Preț: 62636 lei
  • 15% The IMO Compendium: A Collection of Problems Suggested for The International Mathematical Olympiads: 1959-2009 Second Edition
    Preț: 58645 lei
  • 15% Winning Solutions
    Preț: 55971 lei
  • 18% Exercises in Analysis
    Preț: 90229 lei
  • 18% Contests in Higher Mathematics: Miklós Schweitzer Competitions 1962–1991
    Preț: 92543 lei
  • 20% Exercises in Number Theory
    Preț: 47989 lei
  • Theory of Stochastic Processes
    Preț: 37818 lei
  • 15% Analysis and Algebra on Differentiable Manifolds
    Preț: 64255 lei
  • Functional Equations and How to Solve Them
    Preț: 43036 lei
  • 15% Theorems and Counterexamples in Mathematics
    Preț: 51365 lei
  • 8% A Problem Book in Real Analysis
    Preț: 46540 lei
  • 17% A Sequence of Problems on Semigroups
    Preț: 30323 lei
  • 15% Algebraic Logic
    Preț: 62575 lei
  • 15% Exercises in Computational Mathematics with MATLAB
    Preț: 39431 lei
  • Demography Through Problems
    Preț: 37303 lei
  • 15% Problems in Geometry
    Preț: 45059 lei
  • 18% Problem-Solving Strategies
    Preț: 70763 lei
  • 15% Problems and Theorems in Classical Set Theory
    Preț: 46883 lei
  • A Sequence of Problems on Semigroups
    Preț: 37040 lei
  • Principles of Partial Differential Equations
    Preț: 39866 lei
  • An Outline of Set Theory
    Preț: 36445 lei
  • 15% Exercises in Classical Ring Theory
    Preț: 62375 lei
  • 15% An Introduction to Hilbert Space and Quantum Logic
    Preț: 49891 lei
  • 15% Dynamical Systems I: Ordinary Differential Equations and Smooth Dynamical Systems
    Preț: 61441 lei
  • 15% Problems in Geometry
    Preț: 45815 lei
  • 15% Limits, Series, and Fractional Part Integrals
    Preț: 45688 lei
  • A Cp-Theory Problem Book
    Preț: 39724 lei
  • 15% Exercises in Modules and Rings
    Preț: 62590 lei
  • Theorems and Problems in Functional Analysis
    Preț: 44070 lei
  • 18% Probability Through Problems
    Preț: 95968 lei
  • 15% Polynomials
    Preț: 67677 lei
  • 19% The IMO Compendium
    Preț: 55288 lei
  • 15% Problem-Solving Through Problems
    Preț: 56214 lei
  • 17% Berkeley Problems in Mathematics
    Preț: 41141 lei

Preț: 38134 lei

Puncte Express: 572
Paperback 38134 lei
Hardback 49297 lei

Carte tipărită la comandă

Livrare economică 21 mai-04 iunie

 Adaugă în coș

Wish list
Gift list
Am citit!
Adaugă în listă

Specificații

ISBN-13: 9781489999412
ISBN-10: 1489999418
Pagini: 440
Ilustrații: XII, 428 p. With Original Russian Edition of "Probability": Shir\t{ia}ev, Al’bert Nikolaevich, Zadachi po Teorii Vero\t{ia}tnoste\u{i}, Moscow: MCCME, ©2006..
Dimensiuni: 155 x 235 x 23 mm
Greutate: 0.61 kg
Ediția:2012
Editura: Springer
Colecția Springer
Seria Problem Books in Mathematics

Locul publicării:New York, NY, United States

Public țintă

Graduate

De ce să citești această carte

Această carte este esențială pentru studenții de masterat și doctorat care doresc să stăpânească tehnicile avansate ale teoriei probabilităților. Cititorul câștigă acces la o colecție vastă de probleme verificate în mediul academic de elită, beneficiind de indicii utile pentru rezolvare. Este un instrument indispensabil pentru cei care utilizează volumele teoretice ale lui Shiryaev, oferind puntea necesară între teoria abstractă și aplicația matematică riguroasă.

Despre autor

Albert N. Shiryaev este un matematician rus de renume mondial, profesor la Universitatea de Stat din Moscova și membru al Academiei Ruse de Științe. Elev al celebrului Andrei Kolmogorov, Shiryaev a adus contribuții fundamentale în domeniul statisticii matematice, al proceselor stocastice și al matematicii financiare. Opera sa, care include titluri de referință precum Probability-1 și Essentials of Stochastic Finance, Volume 3, este recunoscută internațional pentru claritatea expunerii și rigoarea logică, influențând generații de matematicieni prin manualele și seminarele sale de cercetare.

Descriere scurtă

For the first two editions of the book Probability (GTM 95), each chapter included a comprehensive and diverse set of relevant exercises. While the work on the third edition was still in progress, it was decided that it would be more appropriate to publish a separate book that would comprise all of the exercises from previous editions, in addition to many new exercises.
Most of the material in this book consists of exercises created by Shiryaev, collected and compiled over the course of many years while working on many interesting topics. Many of the exercises resulted from discussions that took place during special seminars for graduate and undergraduate students.  Many of the exercises included in the book contain helpful hints and other relevant information.
Lastly, the author has included an appendix at the end of the book that contains a summary of the main results, notation and terminology from Probability Theory that are used throughout the present book.  This Appendix also contains additional material from Combinatorics, Potential Theory and Markov Chains, which is not covered in the book, but is nevertheless needed for many of the exercises included here.

Cuprins

Preface.- 1. Elementary Probability Theory.- 2. Mathematical Foundations of Probability Theory.- 3. Convergence of Probability Measures.- 4. Independent Random Variables.- 5. Stationary Random Sequences in Strict Sense.- 6. Stationary Random Sequences in Broad Sense.- 7. Martingales.- 8. Markov Chains.- Appendix.- References.

Recenzii

From the book reviews:
“The present book is a rich and comprehensive collection of problems compiled over many years for use in graduate courses at Moscow State University and other academic institutions in Russia. … Problems in Probability is an excellent source of exercises for graduate courses in probability. The exercises are diverse and very well chosen … .” (SIAM Review, Vol. 56 (4), December, 2014)
“This is an invaluable addition to the class of problem books; it will enable the beginning graduate student to tackle the more advanced continuous time counterparts of the material therein presented. It can also be used as a reference for specific results.” (Giuseppe Castellacci, Mathematical Reviews, January, 2014)
“The book includes a wide variety of problems that Shiryaev has written himself and collected from other ‘textbooks, lecture notes, exercise manuals, monographs, research papers, private communications, and such.’ … will serve as a good reference for readers who have already seen the topics. … Shiryaev’s book provides an excellent source of problems and will be a valuable resource to students who wish to learn probability at the graduate level.” (Darren Glass, MAA Reviews, June, 2013)
“This eight-chapter book contains problems on various aspects of probability that Shiryaev … carefully collected from diverse sources or created himself. … An attractive feature is the inclusion of hints/suggestions accompanying some of the difficult problems. … well-written book could be gainfully used as a supplementary text for an advanced course in probability theory or mathematics of finance. Researchers in probability would also find the book helpful. Summing Up: Highly recommended. Libraries serving universities with a strong program in probability theory; upper-division undergraduates through researchers/faculty.” (D. V. Chopra, Choice, Vol. 50 (8), April, 2013)

Notă biografică

Albert Shiryaev is an eminent mathematician who has written several texts on probability and stochastic calculus, which have been translated into several languages. He is the recipient of several honors and awards, including the Humboldt Research Award, Markov prize, and Kolmogorov prize.

Textul de pe ultima copertă

Problems in Probability  comprises one of the most comprehensive, nearly encyclopedic, collections of problems and exercises in probability theory. Albert Shiryaev has skillfully created, collected, and compiled  the exercises in this text over the course of many years while working on topics which interested him the most.   A substantial  number of the exercises resulted from diverse sources such as textbooks, lecture notes, exercise manuals, monographs, and discussions that took place during special seminars for graduate and undergraduate students. Many problems contain helpful hints and other relevant comments and a portion of the material covers some important applications from optimal control and mathematical finance. Readers of diverse backgrounds—from students to researchers—will find a great deal of value in this book and can treat the work as an exercise manual, a handbook, or as a supplementary text to a course in probability theory, control, and mathematical finance.
The problems and exercises in this book vary in nature and degree of difficulty. Some problems are meant to test the reader’s basic understanding, others are of medium-to-high degrees of difficulty and require more creative thinking. Other problems are meant to develop additional theoretical concepts and tools or to familiarize the reader with various facts that are not necessarily covered in mainstream texts. Additional problems are related to the passage from random walk to Brownian motions and Brownian bridges. The appendix contains a summary of the main results, notation and terminology that are used throughout the book.  It also contains additional material from combinatorics, potential theory and Markov chains—subjects that are not covered in the book, but are nevertheless needed for many of the exercises included here.

Caracteristici

Provides more than 1500 exercises and problems for professors using GTM 95 as a course text Volume is self-contained, although it can be used along with GTM 95 Covers traditional areas of probability theory, as well as recent developments Author is an experienced writer and a well-known expert in the field