Books in the Undergraduate Texts in Mathematics series

this section gained proofs of the Schroeder-Bernstein theorem and the Trichotomy Law for Sets, and lost most of the material about finite and countable sets, which has now been moved to a new section devoted to those two types of sets.

The text was written with four pedagogical goals in mind: offer a variety of topics in one course, get to the main themes and tools as efficiently as possible, show the relationships between the different topics, and include recent results to convince students that mathematics is a living discipline.

This book is an informal and readable introduction to higher algebra at the post-calculus level. The new examples and theory are built in a well-motivated fashion and made relevant by many applications - to cryptography, coding, integration, history of mathematics, and especially to elementary and computational number theory.

The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and deep open problems.

For instance, when we apply the Laplace trans form method to a linear ordinary differential equation with constant coefficients, any(n) + an-lY(n-l) + * * * + aoy = f(t), why is it justified to take the Laplace transform of both sides of the equation (Theorem A.

Every mathematician agrees that every mathematician must know some set theory; The purpose of the book is to tell the beginning student of advanced mathematics the basic set theoretic facts of life, and to do so with the minimum of philosophical discourse and logical formalism.

A must-read for mathematicians, scientists and engineers who want to understand difference equations and discrete dynamicsContains the most complete and comprehenive analysis of the stability of one-dimensional maps or first order difference equations. Lucid and transparent writing style

Calculus and linear algebra are two dominant themes in contemporary mathematics and its applications. The aim of this book is to introduce linear algebra in an intuitive geometric setting as the study of linear maps and to use these simpler linear functions to study more complicated nonlinear functions.

Finally, the book illustrates the many connections between topology and other subjects, such as analysis and set theory, via the inclusion of "Extras" at the end of each chapter presenting a brief foray outside topology.

The fourth edition adds material related to mathematical finance as well as expansions on stable laws and martingales.From the reviews: "Almost thirty years after its first edition, this charming book continues to be an excellent text for teaching and for self study."

This is a gentle introduction to the vocabulary and many of the highlights of elementary group theory. Written in an informal style, the material is divided into short sections, each of which deals with an important result or a new idea. Includes more than 300 exercises and approximately 60 illustrations.

The advantages of using linear algebra both in the teaching of differential equations and in the teaching of multivariate calculus are by now widely recognized. Although most of the recent books do use linear algebra, it is only the algebra of ~3.