Probability and Measure Theory, Second Edition, is a text for a graduate-level course in probability that includes essential background topics in analysis. It provides extensive coverage of conditional probability and expectation, strong laws of large numbers, martingale theory, the central limit theorem, ergodic theory, and Brownian motion.

• Clear, readable style
• Solutions to many problems presented in text
• Solutions manual for instructors
• Material new to the second edition on ergodic theory, Brownian motion, and convergence theorems used in...

This book fills an educational void by adapting unique classroom-tested techniques that students find most congenial...that strip the shroud of mystery from an esoteric subject...that prepare students for applications of calculus in later courses.

This introduction to more advanced courses in probability and real analysis emphasizes the probabilistic way of thinking, rather than measure-theoretic concepts. Geared toward advanced undergraduates and graduate students, its sole prerequisite is calculus.
Taking statistics as its major field of application, the text opens with a review of basic concepts, advancing to surveys of random variables, the properties of expectation, conditional probability and expectation, and characteristic functions. Subsequent topics include infinite sequences of random variables, Markov chains, and an...

This graduate-level text provides coverage for a one-semester course in algebraic number theory. It explores the general theory of factorization of ideals in Dedekind domains as well as the number field case. Detailed calculations illustrate the use of Kummer's theorem on lifting of prime ideals in extension fields.
The author provides sufficient details for students to navigate the intricate proofs of the Dirichlet unit theorem and the Minkowski bounds on element and ideal norms. Additional topics include the factorization of prime ideals in Galois extensions and local as well as global...

This brief course in statistical inference was extensively class tested by the author at the University of Illinois, and it requires only a basic familiarity with probability and matrix and linear algebra. Ninety problems with solutions make it an ideal choice for self-study as well as a helpful review of a wide range of statistical formulas with applications in business, government, public administration, and other fields.
The first eight chapters review results from basic probability that are important to statistics, including transformation of random variables, Jacobians,...