Bøger i Graduate Studies in Mathematics serien

Comprehensive introduction consisting of two parts the core of the theory and then the more advanced topics.

Matrix theory is a classical topic of algebra that had originated, in its current form, in the middle of the 19th century. It is remarkable that for more than 150 years it continues to be an active area of research full of new discoveries and new applications. This presents modern perspectives of matrix theory at the level accessible to graduate students.

This book introduces graduate students and researchers in mathematics and the sciences to the multifaceted subject of the equations of hyperbolic type, which are used, in particular, to describe propagation of waves at finite speed. Among the topics presented are nonlinear geometric optics, the asymptotic analysis of short wavelength solutions, and nonlinear interaction of such waves.

Provides an introduction to hyperbolic geometry in dimension three, with motivation and applications arising from knot theory. The book was written to be interactive, with many examples and exercises. Some important results are left to guided exercises.

Offers a geometric introduction to the homology of topological spaces and the cohomology of smooth manifolds. This title introduces a class of stratified spaces, so-called stratifolds. It derives basic concepts from differential topology such as Sard's theorem, partitions of unity and transversality.

Algebraic number theory is one of the most refined creations in mathematics. This book presents the essential elements of algebraic number theory, including the theory of normal extensions up through a glimpse of class field theory.

Introduces the methods and language of functional analysis, including Hilbert spaces, Fredholm theory for compact operators and spectral theory of self-adjoint operators. This work presents the theorems and methods of abstract functional analysis and applications of these methods to Banach algebras and theory of unbounded self-adjoint operators.

Presents an introduction to differential geometry through differential forms, emphasizing their applications in various areas of mathematics and physics. This work focuses on Stokes' theorem, the classical integral formulas and their applications to harmonic functions and topology.

Focuses on linear equations of first and second order. An important feature of his treatment is that the majority of the techniques are applicable more generally. In particular, the author emphasizes a priori estimates throughout the text, even for those equations that can be solved explicitly.

Suitable for students in mathematics, physics, engineering, and computer science, this book explores contemporary approximation theory. It covers such topics as projections, interpolation paradigms, positive definite functions, interpolation theorems of Schoenberg and Micchelli, tomography, artificial neural networks, and thin-plate splines.

Offers a focused point of view on the differential geometry of curves and surfaces. This monograph treats the Gauss - Bonnet theorem and discusses the Euler characteristic. It also covers Alexandrov's theorem on embedded compact surfaces in R3 with constant mean curvature.

A companion volume to ""Graduate Algebra: Commutative View"", this book presents a unified approach to many important topics, such as group theory, ring theory, Lie algebras, and gives conceptual proofs of many basic results of noncommutative algebra.

Presents a comprehensive introduction to research on the applications of graph theory to real-world networks such as web graph. This book discusses both models of the web graph and algorithms for searching the web.

Presents an introduction to the theory of functions of several complex variables and their singularities, with special emphasis on topological aspects. This book includes such topics as Riemann surfaces, holomorphic functions of several variables, classification and deformation of singularities, and fundamentals of differential topology.

Fourier analysis encompasses a variety of perspectives and techniques. This book presents the real variable methods of Fourier analysis introduced by Calderon and Zygmund. It includes topics such as the Hardy-Littlewood maximal function and the Hilbert transform. It also covers the study of singular integral operators and multipliers.

Covers classical modular forms. This book is suitable to those who wish to use modular forms in applications, such as in the explicit solution of Diophantine equations.

Presents two essential and apparently unrelated subjects that include, microlocal analysis and the theory of pseudo-differential operators, a basic tool in the study of partial differential equations and in analysis on manifolds; and the Nash-Moser theorem, that is fundamentally important in geometry, dynamical systems, and nonlinear PDE.