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Knowing the Odds: An Introduction to Probability (Graduate Studies in Mathematics), by John B. Walsh
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This book covers in a leisurely manner all the standard material that one would want in a full year probability course with a slant towards applications in financial analysis at the graduate or senior undergraduate honors level. It contains a fair amount of measure theory and real analysis built in but it introduces sigma-fields, measure theory, and expectation in an especially elementary and intuitive way. A large variety of examples and exercises in each chapter enrich the presentation in the text.
- Sales Rank: #349947 in Books
- Published on: 2012-09-06
- Original language: English
- Dimensions: 10.25" h x 7.25" w x 1.25" l, 2.00 pounds
- Binding: Hardcover
- 421 pages
Review
John Walsh, one of the great masters of the subject, has written a superb book on probability. It covers at a leisurely pace all the important topics that students need to know, and provides excellent examples. I regret his book was not available when I taught such a course myself, a few years ago. ----Ioannis Karatzas, Columbia University
In this wonderful book, John Walsh presents a panoramic view of Probability Theory, starting from basic facts on mean, median and mode, continuing with an excellent account of Markov chains and martingales, and culminating with Brownian motion. Throughout, the author's personal style is apparent; he manages to combine rigor with an emphasis on the key ideas so the reader never loses sight of the forest by being surrounded by too many trees. As noted in the preface, "To teach a course with pleasure, one should learn at the same time." Indeed, almost all instructors will learn something new from the book, (e.g. the potential-theoretic proof of Skorokhod embedding) and at the same time, it is attractive and approachable for students. ----Yuval Peres, Microsoft
With many examples in each section that enhance the presentation, this book is a welcome addition to the collection of books that serve the needs of advanced undergraduate as well as first year graduate students. The pace is leisurely which makes it more attractive as a text. ----Srinivasa Varadhan, Courant Institute, New York
Most helpful customer reviews
3 of 3 people found the following review helpful.
Excellent Book
By Alejandro Parada
I have taken several courses in probability in engineering and in the math department, and definitely I can assure that this is one of the most beautiful textbooks in probability. It is highly rigorous but written with a pleasant style. Before the reading of this book I really hated the probability, after the reading of this book I love that is related with probability.
0 of 0 people found the following review helpful.
A beautiful book on probaility
By d
This book really deserves to be more widely known - just one review so far is absurd for a book of this quality. It is one of the most vivid and engaging book on probability I've seen so far.
I cannot see that it really has much competition. All the books on probability (I've seen) that nurture your intuition have little to no measure theory; conversely most measure theory books assume you already have the intuition. But students of the subject who don't have the best probabilistic intuition AND are comfortable with abstract mathematics at the senior-undergrad-or-beginning-graduate level are not really served by any books on the market (again, as far as I know). For example, Ash, Billingsley, Resnick, Rosenthal et al don't help you with intuition. And on the other side, there are too many books to mention, but they typically don't tell you what a sigma algebra or for that matter a filtration is. Walsh does both - he gives you the intuition and the rigor.
I believe this book will work best for people who have the background described above. My own background is in machine learning, and Walsh's book is extremely well-suited to my needs. But I think it would also work beautifully for students who have done the basic course in probability and want to see more. Or perhaps people whose education in probability has been scattershot and uneven; Walsh will pull it together for you.
It's very clearly written, with an understated "aliveness" that is rare and doesn't distract from the subject.
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