Topics in Hyperplane Arrangements, Polytopes and Box-Splines brings together many areas of mathematics that focus on methods to compute the number of integral points in suitable families or variable polytopes. The topics introduced expand upon differential and difference equations, approximation theory, cohomology, and module theory. The discussion is divided into five extensive parts; the first of which provides basic material on convex sets, combinatorics, polytopes, Laplace and Fourier transforms, and the language of modules over the Weyl algebra. The following four sections focus on the differentiable case, discrete case, and several applications, e.i., two independent chapters explore the computations of De Rham cohomology for the complement of a hyperplane or toric arrangement. This book, written by two distinguished authors, engages a broad audience by providing a strong foundation in very important areas. This book may be used in a classroom setting as well as a reference for researchers.

Lie groups, named for the 19th century mathematician Sophus Lie, has been an increasing area of focus and rich research since the middle of the 20th century. Procesi's masterful approach to Lie groups through invariants and representations gives the reader a comprehensive treatment of the classical groups along with an extensive introduction to a wide range of topics associated with Lie groups: symmetric functions, theory of algebraic forms, Lie algebras, tensor algebra and symmetry, semisimple Lie algebras, algebraic groups, group representations, invariant, Hilbert theory, and binary forms with fields ranging from pure algebra to functional analysis.Key to this unique exposition is the large amount of background material presented so the book is accessible to a reader with relatively modest mathematical background. Historical information, examples, exercises are all woven into the text.Lie Groups: An Approach through Invariants and Representations will engage a broad audience, including advanced undergraduates, graduates, mathematicians in a variety of areas from pure algebra to functional analysis and physics.