Reflection groups and their invariant theory provide the main themes of this book and the first two parts focus on these topics. The first 13 chapters deal with reflection groups (Coxeter groups and Weyl groups) in Euclidean Space while the next thirteen chapters study the invariant theory of pseudo-reflection groups. The third part of the book studies conjugacy classes of the elements in reflection and pseudo-reflection groups. The book has evolved from various graduate courses given by the author over the past 10 years. It is intended to be a graduate text, accessible to students with a...

Thoroughly revised and updated in light of recent scholarship, the text introduces compelling perspectives on the French and Industrial Revolutions, integrates new discussions of cultural and social history, and expands coverage of southern and eastern Europe. While preserving the integrity of earlier editions, new coauthor Matthew Levinger broadens the analysis by exploring the everyday experiences of the working classes with those of the political and social elites.

Mathematical analysis offers a solid basis for many achievements in applied mathematics and discrete mathematics. This new textbook is focused on differential and integral calculus, and includes a wealth of useful and relevant examples, exercises, and results enlightening the reader to the power of mathematical tools. The intended audience consists of advanced undergraduates studying mathematics or computer science.

The author provides excursions from the standard topics to modern and exciting topics, to illustrate the fact that even first or second year students can understand...

Geometry is a classical core part of mathematics which, with its birth, marked the beginning of the mathematical sciences. Thus, not surprisingly, geometry has played a key role in many important developments of mathematics in the past, as well as in present times. While focusing on modern mathematics, one has to emphasize the increasing role of discrete mathematics, or equivalently, the broad movement to establish discrete analogues of major components of mathematics. In this way, the works of a number of outstanding mathema- cians including H. S. M. Coxeter (Canada), C. A. Rogers (United...

This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Coverage includes Radon-Nikodum property, finite-dimensional spaces and local theory on tensor products, and more.

This book is intended as a course in numerical analysis and approximation theory for advanced undergraduate students or graduate students, and as a reference work for those who lecture or research in this area. Its title pays homage to Interpolation and Approximation by Philip J. Davis, published in 1963 by Blaisdell and reprinted by Dover in 1976. My book is less g- eral than Philip Davis's much respected classic, as the quali?cation "by polynomials" in its title suggests, and it is pitched at a less advanced level. I believe that no one book can fully cover all the material that could...

1. The Inverse of a Nonsingular Matrix It is well known that every nonsingular matrix A has a unique inverse, ?1 denoted by A, such that ?1 ?1 AA = A A =I, (1) where I is the identity matrix. Of the numerous properties of the inverse matrix, we mention a few. Thus, ?1 ?1 (A ) = A, T ?1 ?1 T (A ) =(A ), ? ?1 ?1 ? (A ) =(A ), ?1 ?1 ?1 (AB) = B A, T ? where A and A, respectively, denote the transpose and conjugate tra- pose of A. It will be recalled that a real or complex number ? is called an eigenvalue of a square matrix A, and a nonzero vector x is called an eigenvector of A corresponding to...

Borwein is an authority in the area of mathematical optimization, and his book makes an important contribution to variational analysis

Provides a good introduction to the topic

The Kenneth May Lectures have never before been published in book form

Important contributions to the history of mathematics by well-known historians of science

Should appeal to a wide audience due to its subject area and accessibility

This book deals mainly with the study of convex functions and their behavior from the point of view of stability with respect to perturbations. We shall consider convex functions from the most modern point of view: a function is de?ned to be convex whenever its epigraph, the set of the points lying above the graph, is a convex set. Thus many of its properties can be seen also as properties of a certain convex set related to it. Moreover, we shall consider extended real valued functions, i. e., functions taking possibly the values and +?. The reason for considering the value +? is the powerful...