Perhaps uniquely among mathematical topics, complex analysis allows students to learn a thoroughly developed subject that is rich in both theory & applications. But for any of these profound results, the student is often left asking 'what does it mean?' In this text, Ullrich shows students how to think like an analyst.

Suitable for instructors for use as a companion volume to the book, A Modern Theory of Integration (AMS Graduate Studies in Mathematics series, Volume 32).

A survey of asymptotic methods set in the applied research context of wave propagation. It stresses rigorous analysis in addition to formal manipulations. It is suitable for a beginning graduate course on asymptotic analysis in applied mathematics and is a

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 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, classifi

This text presents the basic information about finite dimensional extension fields of the rational numbers, algebraic number fields, and the rings of algebraic integers in them. The important theorems regarding the units of the ring of integers and the class group are proved and illustrated with many examples given in detail. The completion of an algebraic number field at a valuation is discussed in detail and then used to provide economical proofs of global results. The book contains many concrete examples illustrating the computation of class groups, class numbers, and Hilbert class fields....

Symplectic geometry is a central topic of current research in mathematics. Indeed, symplectic methods are key ingredients in the study of dynamical systems, differential equations, algebraic geometry, topology, mathematical physics and representations of Lie groups. This book is an introduction to symplectic geometry, assuming only a general background in analysis and familiarity with linear algebra. It starts with the basics of the geometry of symplectic vector spaces. Then, symplectic manifolds are defined and explored. In addition to the essential classic results, such as Darboux's...

A guide to the qualitative theory of foliations. It features topics including: analysis on foliated spaces, characteristic classes of foliations and foliated manifolds. It is suitable as a supplementary text for a topics course at the advanced graduate level.

For a Riemannian manifold M, the geometry, topology and analysis are interrelated in ways that have become widely explored in modern mathematics. Bounds on the curvature can have significant implications for the topology of the manifold. The eigenvalues of the Laplacian are naturally linked to the geometry of the manifold. For manifolds that admit spin structures, one obtains further information from equations involving Dirac operators and spinor fields. In the case of four-manifolds, for example, one has the remarkable Seiberg-Witten invariants.

This book presents rigidity theory in a historical context. The combinatorial aspects of rigidity are isolated and framed in terms of a special class of matroids, which are a natural generalization of the connectivity matroid of a graph. The book includes an introduction to matroid theory and an extensive study of planar rigidity. The final chapter is devoted to higher dimensional rigidity, highlighting the main open questions. Also included is an extensive annotated bibiolography with over 150 entries. The book is aimed at graduate students and researchers in graph theory and combinatorics...