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Spacetime, Geometry and Gravitation (Progress in Mathematical Physics)
Spacetime, Geometry and Gravitation (Progress in Mathematical Physics)

Teaching Einstein’s general relativity at introductory level poses problems because students cannot begin to appreciate the basics of the theory unless they learn a sufficient amount of Riemannian geometry. Most elementary books take the easy course of telling the students a few working rules stripping the mathematical details to a minimum...

Mathematical Olympiad Challenges
Mathematical Olympiad Challenges
This significantly revised and expanded second edition of "Mathematical Olympiad Challenges" is a rich collection of problems put together by two experienced and well-known professors and coaches of the U.S. International Mathematical Olympiad Team. Hundreds of beautiful, challenging, and instructive problems from algebra, geometry,...
Functional Analysis Methods for Reliability Models (Pseudo-Differential Operators)
Functional Analysis Methods for Reliability Models (Pseudo-Differential Operators)
People are often concerned with the reliability of products they use and of the friends and associates with whom they interact daily in a myriad of ways. Although the term “reliability” may not occur in the description of a given product or interaction, it is often the attribute that the individual means in expression of...
Economic Models and Algorithms for Distributed Systems (Autonomic Systems)
Economic Models and Algorithms for Distributed Systems (Autonomic Systems)

Distributed computing paradigms for sharing resources such as Clouds, Grids, Peer-to-Peer systems, or voluntary computing are becoming increasingly popular. While there are some success stories such as PlanetLab, OneLab, BOINC, BitTorrent, and SETI@home, a widespread use of these technologies for business applications has not yet been achieved....

Four Short Courses on Harmonic Analysis: Wavelets, Frames, Time-Frequency Methods, and Applications to Signal and Image Analysis
Four Short Courses on Harmonic Analysis: Wavelets, Frames, Time-Frequency Methods, and Applications to Signal and Image Analysis

This state-of-the-art textbook examines four research directions in harmonic analysis and features some of the latest applications in the field, including cosmic microwave background analysis, human cortex image denoising, and wireless communication. The work is the first one that combines spline theory (from a numerical or...

Partial Differential Equations: Second Edition (Cornerstones)
Partial Differential Equations: Second Edition (Cornerstones)

This self-contained text offers an elementary introduction to partial differential equations (pdes), primarily focusing on linear equations, but also providing some perspective on nonlinear equations. The classical treatment is mathematically rigorous with a generally theoretical layout, though indications to some of the physical origins of pdes...

Nonlinear Partial Differential Equations with Applications (International Series of Numerical Mathematics)
Nonlinear Partial Differential Equations with Applications (International Series of Numerical Mathematics)

This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition leads the reader through the general theory based on abstract (pseudo-) monotone or accretive operators as fast as possible towards the analysis of concrete differential equations, which have...

Cluster Analysis for Data Mining and System Identification
Cluster Analysis for Data Mining and System Identification

Data clustering is a common technique for statistical data analysis, which is used in many fields, including machine learning, data mining, pattern recognition, image analysis and bioinformatics. Clustering is the classification of similar objects into different groups, or more precisely, the partitioning of a data set into subsets...

Geometric Optics: Theory and Design of Astronomical Optical Systems Using Mathematica®
Geometric Optics: Theory and Design of Astronomical Optical Systems Using Mathematica®

This book—unique in the literature—provides readers with the mathematical background needed to design many of the optical combinations that are used in astronomical telescopes and cameras. The results presented in the work were obtained by using a different approach to third-order aberration theory as well as the extensive use of the...

Geometric Problems on Maxima and Minima
Geometric Problems on Maxima and Minima
Questions of maxima and minima have great practical significance, with applications to physics, engineering, and economics; they have also given rise to theoretical advances, notably in calculus and optimization. Indeed, while most texts view the study of extrema within the context of calculus, this carefully constructed problem book takes a...
Introduction to Computational Biology: An Evolutionary Approach
Introduction to Computational Biology: An Evolutionary Approach
In 1982, the first release of the GenBank sequence database contained 601,438 residues. By 2005, this number had grown beyond and continues to increase exponentially. Far from regarding this as “information overload”, we believe the free availability of so much precise and fundamental data on the ultimate constituents of life to be the...
Families of Conformally Covariant Differential Operators, Q-Curvature and Holography (Progress in Mathematics)
Families of Conformally Covariant Differential Operators, Q-Curvature and Holography (Progress in Mathematics)
The central object of the book is Q-curvature. This important and subtle scalar Riemannian curvature quantity was introduced by Tom Branson about 15 year ago in connection with variational formulas for determinants of conformally covariant differential operators. The book studies structural properties of Q-curvature from an extrinsic point of view...
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