Books in the Universitext series

The book presents the central facts of the local, projective and intrinsic theories of complex algebraic plane curves, with complete proofs and starting from low-level prerequisites.

Aimed primarily at graduate students and beginning researchers, this book provides an introduction to algebraic geometry that is particularly suitable for those with no previous contact with the subject;

This book explains the mathematical background behind the Standard Model, translating ideas from physics into a mathematical language and vice versa. The first part of the book covers the mathematical theory of Lie groups and Lie algebras, fibre bundles, connections, curvature and spinors.

This established reference work continues to introduce its readers to some of the hottest topics in contemporary mathematical research. This sixth edition includes, among other new additions, a systematic treatment of eigenvalues of Riemannian manifolds.

This book is an introduction to stochastic analysis and quantitative finance; Stochastic Analysis for Finance with Simulations is designed for readers who want to have a deeper understanding of the delicate theory of quantitative finance by doing computer simulations in addition to theoretical study.

While the topic of principal bundles in differential geometry has become classic, even standard, material in the modern graduate mathematics curriculum, the unique approach taken in this text presents the material in a way that is intuitive for both students of mathematics and of physics.

Unlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity. The first part is a concise and self-contained introduction to the basics of manifolds, differential forms, metrics and curvature.

This book examines the central principles of abelian harmonic analysis: Pontryagin duality, the Plancherel theorem and the Poisson summation formula, as well as their respective generalizations to non-abelian groups, including the Selberg trace formula.

Simply put, quantum calculus is ordinary calculus without taking limits. As this book develops quantum calculus along the lines of traditional calculus, the reader discovers, with a remarkable inevitability, many important notions and results of classical mathematics.

Mathematical logic developed into a broad discipline with many applications in mathematics, informatics, linguistics and philosophy. This text introduces the fundamentals of this field, and this new edition has been thoroughly expanded and revised.

This graduate textbook provides a detailed introduction to the probabilistic interpretation of nonlinear potential theory, relying on the recently introduced notion of tug-of-war games with noise.The book explores both basic and more advanced constructions, carefully explaining the parallel between linear and nonlinear cases.

This book is a revised version of the first edition and is intended as a Linear Algebra sequel and companion volume to the fourth edition of (Graduate Texts in Mathematics 23). In this new version of Multilinear Algebra, Chapters 1-5 remain essen tially unchanged from the previous edition.

This book starts with illustrations of the ubiquitous character of optimization, and describes numerical algorithms in a tutorial way.

Make the reader aware of the fact that both principal incarnations of Fourier theory, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups.

This book is an introduction to Malliavin calculus as a generalization of the classical non-anticipating Ito calculus to an anticipating setting. It presents the development of the theory and its use in new fields of application.

Ordinary differential equations serve as mathematical models for many exciting real world problems. This textbook organizes material around theorems and proofs, comprising of 42 class-tested lectures that effectively convey the subject in easily manageable sections.

The book is an introductory textbook mainly for students of computer science and mathematics. Our guiding phrase is "what every theoretical computer scientist should know about linear programming". One of its main goals is to help the reader to see linear programming "behind the scenes".

In any case, for the development of a consistent and powerful mathematical theory, it seems to be necessary to concentrate solely on the internal problems and structures and to neglect the relations to other ?elds of scienti?c, even of mathematical study for a certain while.

Graduate mathematics students will find this book an easy-to-follow, step-by-step guide to the subject. Rotman's book gives a treatment of homological algebra which approaches the subject in terms of its origins in algebraic topology.

Given the ease with which computers can do iteration it is now possible for almost anyone to generate beautiful images whose roots lie in discrete dynamical systems. Images of Mandelbrot and Julia sets abound in publications both mathematical and not.

To the uninitiated, algebraic topology might seem fiendishly complex, but its utility is beyond doubt. No prior knowledge of algebraic topology is assumed, only a background in undergraduate mathematics, and the required topological notions and results are gradually explained.

An application of differential forms for the study of some local and global aspects of the differential geometry of surfaces. Cartan to study the local differential geometry of immersed surfaces in R3 as well as the intrinsic geometry of surfaces.

Sheaves also appear in logic as carriers for models of set theory. Beginning with several examples, it explains the underlying ideas of topology and sheaf theory as well as the general theory of elementary toposes and geometric morphisms and their relation to logic.

Based on lectures given by Professor Hlawka, this book covers diophantine approximation, uniform distribution of numbers, geometry of numbers and analytic numbers theory.

Proofs or sketches are given for many important results.From the reviews:"An excellent introduction to current research in the geometry of Calabi-Yau manifolds, hyper-Kahler manifolds, exceptional holonomy and mirror symmetry....This is an excellent and useful book."

(January 2006)This richly illustrated text covers the Cauchy and Neumann problems for the classical linear equations of mathematical physics. A large number of problems are sprinkled throughout the book, and a full set of problems from examinations given in Moscow are included at the end.

This book provides an easily accessible, computationally-oriented introduction into the numerical solution of stochastic differential equations using computer experiments. It develops in the reader an ability to apply numerical methods solving stochastic differential equations.

This textbook provides a rigorous analytical treatment of the theory of Maass wave forms. Other topics include Maass wave forms of real weight, Maass cusp forms, and weak harmonic Maass wave forms.