- Tapa blanda: 364 páginas
- Editor: CRC Press; Edición: 1 (21 de febrero de 1994)
- Idioma: Inglés
- ISBN-10: 0201406861
- ISBN-13: 978-0201406863
- Valoración media de los clientes: Sé el primero en opinar sobre este producto
- Clasificación en los más vendidos de Amazon: nº304.727 en Libros en idiomas extranjeros (Ver el Top 100 en Libros en idiomas extranjeros)
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The Art Of Probability (Inglés) Tapa blanda – 21 feb 1994
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Offering accessible and nuanced coverage, Richard W. Hamming discusses theories of probability with unique clarity and depth. Topics covered include the basic philosophical assumptions, the nature of stochastic methods, and Shannon entropy. One of the best introductions to the topic, The Art of Probability is filled with unique insights and tricks worth knowing.
Every field of knowledge has its subject matter and its methods, along with a style for handling them. The field of Probability has a great deal of Art component in it - not only is the subject matter rather different from that of other fields, but at present the techniques are not well organized into systematic methods.
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I wish that I had known of this book when I was in graduate school. However, it has even more use for a practitioner or teacher than for a first time student, as it gives one new insights with each reading of the material.
One thing, when Hamming says to go and "work it out" to gain insight, take him at his word and go at it. He knew his stuff and you will too if you spend some serious time with this text.
The first five chapters in particular cover most of the usual topics of introductory probability (discrete and continuous distributions, generating functions, etc.), though in a more deliberate, patient manner. Because the approach favors depth rather than breadth, you will not find a systematic catalog of all distributions; for example, the negative binomial and hypergeometric distributions are not mentioned, nor are the gamma or beta distributions. But what you gain are more detailed examples, and instructive discussions of the meaning of the results of the calculations - not just the methods. (But make no mistake - calculation methods are discussed in great detail as well.)
Along the way, you will find careful, illuminating solutions and discussions of most of the "standards" (eg. birthday problem, hat check problem, Monty Hall, etc., etc.), though not always with the standard names. One notable feature is chapter 7, where you will find an interesting, very readable treatment of the basics of information theory. One idiosyncrasy of nomenclature: the author uses what he calls "state diagrams" to analyze what are more commonly referred to as "Markov processes."
Combined with a more standard text (I strongly recommend "Introduction to Probability, Statistics, and Random Processes" by Hossein Pishro-Nik, which is freely and legally available online), you can't go wrong with this gem.
There are many other unique things in this book, for example Hamming discusses sensitivity of particular probabilistic methods to small pertrubations of the initial probabilities, and many other similar potential tricky issues with practical applications of probability theory. Hamming worked at Los Alamos, and I think he understood better than most mathematicians the consequences mathematical considerations can yield, and this shows in those careful discussions of modelling issues scattered throughout the book, I would go as much as to say he is trying to instill some sense of social responsibility in you. Another interesting difference from the typical modern probability textbook is heavy use of generating functions in many places throughout the book. Hamming is also strong in developing intuition, for example there are many numerical tables showing numerical results of sample probability experiments, which is another thing about this book that reminded me of the Feynman lectures - typical math and physics book somehow avoid this type of numerical work.
As for disadvantages, the book doesn't cover all the subjects modern textbooks cover, especially the discussion of continuous sample spaces is rather brief. Some terminology is atypical, for example Markov chains are treated in the book, but they are called simply "state diagrams". Exercises only have numerical answers, and those immediately follow the text of the exercise, so you can only start the exercise with answer already in mind. Again, as in case of the Feynman lectures, Hamming can be incredibly clever sometimes, to the point it's hard to follow his train of thought. At places also more advanced mathematics appears (but some calculus is more than enough for most of the book). I think this book will work for you best if you supplement it, like I did, with one of the traditional, classroom-proven probability books - the Bertsekas/Tsitsiklis one or one by Sheldon Ross. Despite those disadvantages, I can't rate this book any lower than 5 stars, since the coverage of this book is so unique and the material not to be found anywhere else.