Geared toward upper-level undergraduates and graduate students, this two-part treatment deals with the foundations of multivariate analysis as well as related models and applications.
Starting with a look at practical elements of matrix theory, the text proceeds to discussions of continuous multivariate distributions, the normal distribution, and Bayesian inference; multivariate large sample distributions and approximations; the Wishart and other continuous multivariate distributions; and basic multivariate statistics in the normal distribution. The second half of the text moves from...

This even-handed treatment addresses the decades-old dispute among probability theorists, asserting that both statistical and inductive probabilities may be treated as sentence-theoretic measurements, and that the latter qualify as estimates of the former. Discusses sentence theory, set theory, statistical probabilities, inductive probabilities, more. Illustrations and footnotes elucidate definitions, theorems, and technicalities. 1962 edition.

This introductory text presents detailed accounts of the different forms of the theory developed by Stroock and Bismut, discussions of the relationship between these two approaches, and a variety of applications. 1987 edition.

In the mathematical subfield of numerical analysis, interpolation is a procedure that assists in -reading between the lines- in a set of tables by constructing new data points from existing points. This rigorous presentation employs only formulas for which it is possible to calculate error limits. Subjects include displacement symbols and differences, divided differences, formulas of interpolation, factorial coefficients, numerical differentiation, and construction of tables. Additional topics include inverse interpolation, elementary methods of summation, repeated summation, mechanical...

Newly revised by the author, this undergraduate-level text introduces the mathematical theory of probability and stochastic processes. Using both computer simulations and mathematical models of random events, it comprises numerous applications to the physical and biological sciences, engineering, and computer science. Subjects include sample spaces, probabilities distributions and expectations of random variables, conditional expectations, Markov chains, and the Poisson process. Additional topics encompass continuous-time stochastic processes, birth and death processes, steady-state...

Brief but rigorous, this text is geared toward advanced undergraduates and graduate students. It covers the coordinate system, planes and lines, spheres, homogeneous coordinates, general equations of the second degree, quadric in Cartesian coordinates, and intersection of quadrics. Mathematician, physicist, and astronomer, William H. McCrea conducted research in many areas and is best known for his work on relativity and cosmology. McCrea studied and taught at universities around the world, and this book is based on a series of his lectures.

This remarkable book develops the subject of linear algebra in a novel fashion. A logically interconnected sequence of propositions and problems--some 2,400 in all--appears without proofs. Assisted only by hints and pointers, students must work out formal proofs systematically, proceeding from simple verifications to relatively advanced strategies and techniques of proof.
This volume also presents insights into functional analysis, which may be formulated as linear analysis without an infinite dimensional framework. As students allow their consideration of the propositions to move toward...

Combining three books into a single volume, this text comprises Multicolor Problems, dealing with several of the classical map-coloring problems; Problems in the Theory of Numbers, an elementary introduction to algebraic number theory; and Random Walks, addressing basic problems in probability theory. The book's primary aim is not so much to impart new information as to teach an active, creative attitude toward mathematics. The sole prerequisites are high-school algebra and (for Multicolor Problems) a familiarity with the methods of mathematical induction. The book is designed for the...

Suitable for upper-level undergraduates and graduate students, this treatment of complex analysis focuses on function theory on a finitely connected planar domain. Clear and complete, it emphasizes domains bounded by a finite number of disjoint analytic simple closed curves. The author is Professor of Mathematics at Northwestern University. 1983 edition.

This study of basic number systems explores natural numbers, integers, rational numbers, real numbers, and complex numbers. Written by a noted expert on logic and set theory, it assumes no background in abstract mathematical thought. Undergraduates and beginning graduate students will find this treatment an ideal introduction to number systems, particularly in terms of its detailed proofs.
Starting with the basic facts and notions of logic and set theory, the text offers an axiomatic presentation of the simplest structure, the system of natural numbers. It proceeds, by set-theoretic...