A Graduate Course in Probability
|Author:||Howard G. Tucker|
|Published:||Jan 23 2014|
|Posted:||Nov 19 2014|
|Book size:||15.85 MB|
Suitable for a graduate course in analytic probability theory, this text requires no previous knowledge of probability and only a limited background in real analysis. In addition to providing instruction for graduate students in mathematics and mathematical statistics, the book features detailed proofs that offer direct access to the basic theorems of probability theory for mathematicians of all interests.The treatment strikes a balance between measure-theoretic aspects of probability and distribution aspects, presenting some of the basic theorems of analytic probability theory in a cohesive manner. Statements are rendered as simply as possible in order to make them easy to remember and to demonstrate the essential idea behind each proof. Topics include probability spaces and distributions, stochastic independence, basic limiting operations, strong limit theorems for independent random variables, the central limit theorem, conditional expectation and Martingale theory, and an introduction to stochastic processes, particularly Brownian motion. Each section concludes with problems that reinforce the preceding material.
With a dynamic learn-by-doing focus, this laboratory manual encourages students to explore data structures by implementing them, a process through which students discover how data structures work and how they can be applied....
This is a substantially revised and updated introduction to arithmetic topics, both ancient and modern, that have been at the centre of interest in applications of number theory, particularly in cryptography. As such, no background in algebra or number theory is assumed, and the book begins with a discussion of the basic number theory that is needed. The approach taken is algorithmic, emphasising estimates of the efficiency of the techniques that arise from the theory, and one special feature is the inclusion of recent applications of the theory of elliptic curves. Extensive exercises and careful answers are an integral part all of the chapters....
A Short Course on the Basics
(Pearson Education) A hands-on guide to proficiency with Java, with clear explanations of fundamentals such as objects, classes and data structures. The CD-ROM contains 3 Java tutorial books in HTML, all major versions of the Java platform, and more. Softcover. DLC: Java (Computer program language)....
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