Marek Capinski, Peter E. Kopp, Measure, Integral and Probability

Springer, 2007. - 218 pages. Introductory Probability is a pleasure to read and provides a fine answer to the question: How do you construct Brownian motion from scratch, given that you are a competent analyst? There are at least two ways to develop probability theory. The more familiar path is to treat it as its own discipline, and work from intuitive examples such as coin flips and conundrums such as the Monty Hall problem. An alternative is...

Duxbury Press, 2004. - 512 Pages. This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 20...

Wiley, 1971. - 704 pages. At the time the first volume of this book was written the interest in probability was not yet widespread. Teaching was on a very limited scale and topics such as Markov chains, which are now extensively used in several disciplines, were highly specialized chapters of pure mathematics. The first volume may therefore be likened to an all-purpose travel guide to a strange country. To describe the nature of probability it h...

Open Court, 2005. - 470 pages. In this clearly reasoned defense of Bayes's Theorem — that probability can be used to reasonably justify scientific theories — Colin Howson and Peter Urbach examine the way in which scientists appeal to probability arguments, and demonstrate that the classical approach to statistical inference is full of flaws. Arguing the case for the Bayesian method with little more than basic algebra, the authors show that it av...

Wiley, 1996. - 189 pages. 2nd Edition. The brand new edition of this classic text - with more exercises and easier to use than ever Like the first edition, this new version of Lamperti's classic text succeeds in making this fascinating area of mathematics accessible to readers who have limited knowledge of measure theory and only some familiarity with elementary probability. Streamlined for even greater clarity and with more exercises to help de...

Springer-Verlag, 2010. - 436 pages. This textbook on applied probability is intended for graduate students in applied mathematics, biostatistics, computational biology, computer science, physics, and statistics. It presupposes knowledge of multivariate calculus, linear algebra, ordinary differential equations, and elementary probability theory. Given these prerequisites, Applied Probability presents a unique blend of theory and applications, wi...

Wiley-Interscience, 608 pages, 1995. Now in its new third edition, Probability and Measure offers advanced students, scientists, and engineers an integrated introduction to measure theory and probability. Retaining the unique approach of the previous editions, this text interweaves material on probability and measure, so that probability problems generate an interest in measure theory and measure theory is then developed and applied to probabilit...

Academic Press, 2006. - 400 pages. Features exceptionally clear explanations of the mathematics of probability theory and explores its many diverse applications through numerous interesting and motivational examples. This book is an introductory textbook in probability. No prior knowledge in probability is required; however, previous exposure to an elementary precalculus course in probability would prove beneficial in that the student would no...

For Dummies, 2006. - 384 pages. Packed with practical tips and techniques for solving probability problems Increase your chances of acing that probability exam -- or winning at the casino! Whether you're hitting the books for a probability or statistics course or hitting the tables at a casino, working out probabilities can be problematic. This book helps you even the odds. Using easy-to-understand explanations and examples, it demystifies pro...

SIAM, 1987. - 180 pages. Topics include: ways modern statistical procedures can yield estimates of pi more precisely than the original Buffon procedure traditionally used; the question of density and measure for random geometric elements that leave probability and expectation statements invariant under translation and rotation; the number of random line intersections in a plane and their angles of intersection; developments due to W. L. Stevens'...