With a unique approach and presenting an array of new and intriguing topics, Mathematical Quantization offers a survey of operator algebras and related structures from the point of view that these objects are quantizations of classical mathematical structures. This approach makes possible, with minimal mathematical detail, a unified treatment of a variety of topics.
Detailed here for the first time, the fundamental idea of mathematical quantization is that sets are replaced by Hilbert spaces. Building on this idea, and most importantly on the fact that scalar-valued functions on a set...

Adequate texts that introduce the concepts of abstract algebra are plentiful. None, however, are more suited to those needing a mathematical background for careers in engineering, computer science, the physical sciences, industry, or finance than Algebra: A Computational Introduction. Along with a unique approach and presentation, the author demonstrates how software can be used as a problem-solving tool for algebra.
A variety of factors set this text apart. Its clear exposition, with each chapter building upon the previous ones, provides greater clarity for the reader. The author first...

Provides a clear introduction to three related subjects whose interplay enhances intuitive understanding Focuses on geodesics as a tool for better understanding Riemannian geometry and as a source of examples in dynamical systems Offers a unique presentation of the very modern theory of the Conley index as a generalization of Morse theory and as a means for understanding topological dynamical systems Takes an example-based approach to the more cryptic notions of differential geometry Accessible, concise, and self-contained, this book offers an outstanding introduction to three related...

Theoretically, multiwavelets hold significant advantages over standard wavelets, particularly for solving more complicated problems, and hence are of great interest. Meeting the needs of engineers and mathematicians, this book provides a comprehensive overview of multiwavelets. The author presents the theory of wavelets from the viewpoint of general multiwavelets, which includes scalar m-band and standard wavelets as special cases, provides a more coherent approach, and provides alternative proofs and new insights even for standard wavelets. The treatment includes complete MATLAB routines...

A great deal of progress has been made recently in the field of asymptotic formulas that arise in the theory of Dirac and Laplace type operators. Asymptotic Formulae in Spectral Geometry collects these results and computations into one book. Written by a leading pioneer in the field, it focuses on the functorial and special cases methods of computing asymptotic heat trace and heat content coefficients in the heat equation. It incorporates the work of many authors into the presentation, and includes a complete bibliography that serves as a roadmap to the literature on the subject. Geometers,...

This book shows the power of the separation of variables technique by solving a variety of problems, many of which go well beyond the usual textbook problems. With a focus on the potential, heat, and wave equations throughout the book, the authors take a spectral expansion view of the technique and explore it in detail. Written at the advanced undergraduate level, the presentation requires a background in engineering mathematics, but no prior exposure to the method. The abundant worked examples provide guidelines for deciding whether and how to apply the method to any given problem, will help...

The finite element method has always been a mainstay for solving engineering problems numerically. The most recent developments in the field clearly indicate that its future lies in higher-order methods, particularly in higher-order "hp-"adaptive schemes. These techniques respond well to the increasing complexity of engineering simulations and satisfy the overall trend of simultaneous resolution of phenomena with multiple scales.

Higher-Order Finite Element Methods provides an thorough survey of intrinsic techniques and the practical know-how needed to implement higher-order finite element...

This third edition of Alfred Gray's famous textbook continues to offer an outstanding presentation of how to define and compute standard geometric functions along with a dialect of Mathematica for constructing new curves and surfaces from existing ones. Since Gray's death, authors Abbena and Salamon have stepped in to bring the book up to date. While maintaining Gray's intuitive approach, they have reorganized the material to provide a clearer division between the text and the Mathematica code, added a Mathematica notebook as an appendix to each chapter, and addressed important new topics,...

Collecting results scattered throughout the literature into one source, An Introduction to Quasigroups and Their Representations shows how representation theories for groups are capable of extending to general quasigroups and illustrates the added depth and richness that result from this extension.
To fully understand representation theory, the first three chapters provide a foundation in the theory of quasigroups and loops, covering special classes, the combinatorial multiplication group, universal stabilizers, and quasigroup analogues of abelian groups. Subsequent chapters deal with the...

Presents the analysis and synthesis of functions in terms of harmonics in a way that demonstrates the vitality, power, elegance, usefulness of the subject. This work covers the Fourier analysis of integrable and square integrable functions on R, distribution theory, and Fourier series, as well as functions defined on finite intervals.