As a complete introduction to all of the important areas in discrete mathematics - and as preparation for advanced courses in computer science or electrical engineering with discrete mathematics as a prerequisite - this text is ideal. The authors are well-known, highly respected mathematicians with many years of practical experience. They have included all parts of the subject that are essential for all practical applications, plus some less directly applicable topics which are intellectually challenging and fun (combinatorics, Euler's V-E+F=2 theorem, and mathematical games). More than 200 worked examples, 1,500 problems, and 600 figures are included.

Introduction to Discrete Mathematics

Science & Math

Ash, Carol

Ash, Robert B.

McEliece, Robert J.

Ash, Robert

McEliece, Robert

Mathematics

Mcgraw-Hill College

Real Analysis and Probability (Probability & Mathematical Statistics) [Jun 01, 1972] Ash, Robert B. ...

Real Analysis and Probability

Academic Pr

Real Analysis and Probability (Probability and Mathematical Statistics Ser.)

Random House, Inc.

Excellent introduction treats three major areas: analysis of channel models and proof of coding theorems; study of specific coding systems; and study of statistical properties of information sources. Appendix summarizes Hilbert space background and results from the theory of stochastic processes. Advanced undergraduate to graduate level. Bibliography.

Information Theory

Computers & Technology

Ash, R. B.

Computer Science

Horizon Pubs & Distributors Inc

The Calculus Tutoring Book

Jameson, William

IEEE

Designed for a first course in real variables, this text encourages intuitive thinking and offers background for more advanced mathematical work. Topics include complex variables, measure theory, differential equations, functional analysis, and probability. Detailed solutions to the problems appear at the back of the book, making it ideal for independent study. 1993 edition.

Real Variables: With Basic Metric Space Topology

Real Analysis and Solutions to Problems presents solutions to problems in real analysis and probability. Topics covered range from measure and integration theory to functional analysis and basic concepts of probability; the interplay between measure theory and topology; conditional probability and expectation; the central limit theorem; and strong laws of large numbers in terms of martingale theory.\nComprised of eight chapters, this volume begins with problems and solutions for the theory of measure and integration, followed by various applications of the basic integration theory. Subsequent chapters deal with functional analysis, paying particular attention to structures that can be defined on vector spaces; the connection between measure theory and topology; basic concepts of probability; and conditional probability and expectation. Strong laws of large numbers are also taken into account, first from the classical viewpoint, and then via martingale theory. The final chapter is devoted to the one-dimensional central limit problem, with emphasis on the fundamental role of Prokhorov's weak compactness theorem.\nThis book is intended primarily for students taking a graduate course in probability.

Real Analysis and Probability: Probability and Mathematical Statistics: a Series of Monographs and Textbooks

Academic Press

Measure, Integration, and Functional Analysis

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Books by Ash, Robert B.