Bücher der Reihe Universitext

This book is based on lectures given at a summer school on motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid, Norway, in August 2002. Vladimir Voevodsky is one of the founders of the theory and received the Fields medal for his work, and the other authors have all done important work in the subject.

The reader is expected to have some familiarity with cohomology theory and differential and integral calculus on smooth manifolds. Some features of the second edition include added applications, such as Morse theory and the curvature of knots, the cohomology of the moduli space of planar polygons, and the Duistermaat-Heckman formula.

This study additionally looks at the concept of corresponding Quantlets, the name given to these program codes and which follow the name scheme SFSxyz123. The book is divided into three main parts, in which option pricing, time series analysis and advanced quantitative statistical techniques in finance is thoroughly discussed.

This book provides an introduction to the theory of stochastic partial differential equations (SPDEs) of evolutionary type. The theory of SPDEs is based both on the theory of deterministic partial differential equations, as well as on modern stochastic analysis.

This volume presents advances that have been made over recent decades in areas of research featuring Hardy's inequality and related topics.

Covering the theory of derivatives pricing and hedging and techniques in mathematical finance, this book starts with basics and moves to applications, presenting theoretical developments alongside exercises, with many practical examples. It includes concepts and mathematical tools that are usually found in separate monographs.

This book provides an introduction to Lebesgue measure and integration as well as the classical results concerning integrals of multivariable functions. It features over 600 examples.

This self-contained, comprehensive book tackles the principal problems and advanced questions of probability theory and random processes in 22 chapters, presented in a logical order but also suitable for dipping into.

It defines the Morse complex and the Morse homology, and develops some of their applications.Morse homology also serves a simple model for Floer homology, which is covered in the second part.

It now begins with a short section on symmetry groups of polygons in the plane, for there is an analogy between polygons and their symmetry groups and polynomials and their Galois groups - an analogy which serves to help readers organise the various field theoretic definitions and constructions.

This comprehensive volume develops all of the standard features of Fourier analysis - Fourier series, Fourier transform, Fourier sine and cosine transforms, and wavelets.

Researchers in this field will find here an account of a theory that is on the one hand known to them but here is "clothed in a different garb" and can be used as a source for seminars on low-dimensional topology, or for preparing independent study projects for students, or again as the basis of a reading course.

Now in its fifth edition, this book offers a detailed yet concise introduction to the growing field of statistical applications in finance. The reader will learn the basic methods for evaluating option contracts, analyzing financial time series, selecting portfolios and managing risks based on realistic assumptions about market behavior. The focus is both on the fundamentals of mathematical finance and financial time series analysis, and on applications to specific problems concerning financial markets, thus making the book the ideal basis for lectures, seminars and crash courses on the topic. All numerical calculations are transparent and reproducible using quantlets.For this new edition the book has been updated and extensively revised and now includes several new aspects such as neural networks, deep learning, and crypto-currencies. Both R and Matlab code, together with the data, can be downloaded from the book's product page and the Quantlet platform.The Quantlet platform quantlet.de, quantlet.com, quantlet.org is an integrated QuantNet environment consisting of different types of statistics-related documents and program codes. Its goal is to promote reproducibility and offer a platform for sharing validated knowledge native to the social web. QuantNet and the corresponding Data-Driven Documents-based visualization allow readers to reproduce the tables, pictures and calculations inside this Springer book."This book provides an excellent introduction to the tools from probability and statistics necessary to analyze financial data. Clearly written and accessible, it will be very useful to students and practitioners alike."Yacine Ait-Sahalia, Otto Hack 1903 Professor of Finance and Economics, Princeton University

Functions in R and C, including the theory of Fourier series, Fourier integrals and part of that of holomorphic functions, form the focal topic of these two volumes.

Easily accessible Includes recent developmentsAssumes very little knowledge of differentiable manifolds and functional analysisParticular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)

They coined the term symbolic dynamics and began to study sequence spaces with the shift transformation as dynamical systems. Since that time symbolic dynamics has been used in ergodic theory, topological dynamics, hyperbolic dynamics, information theory and complex dynamics.

This introduction to modern geometry differs from other books in the field due to its emphasis on applications and its discussion of special relativity as a major example of a non-Euclidean geometry.

Translated from the French, this book is an introduction to first-order model theory. It also introduces logic via the study of the models of arithmetic, and it gives complete but accessible exposition of stability theory.

With an Appendix by P.A. Meyer

Based on courses taught at the University of Dublin, Carnegie Mellon University, and mostly at Simon Fraser University, this book presents the special theory of relativity from a mathematical point of view.

Towards the end of the nineteenth century, Poincare developed methods for the study of global, qualitative properties of solutions of dynamical systems in situations where explicit solution methods had failed: He discovered that the study of the geometry of the space of trajectories of a dynamical system reveals complex phenomena.

The book offers a direct and up-to-date introduction to the theory of one-parameter semigroups of linear operators on Banach spaces. It contains the fundamental results of the theory such as the Hille-Yoshida generation theorem, the bounded perturbation theorem, and the Trotter-Kato approximation theorem.

A one-year course in probability theory and the theory of random processes, taught at Princeton University to undergraduate and graduate students, forms the core of this book. It also includes the theory of stationary random processes, martingales, generalized random processes, and Brownian motion.

This introductory text is the first book about quantum principal bundles and their quantum connections which are natural generalizations to non-commutative geometry of principal bundles and their connections in differential geometry.

Also called Ito calculus, the theory of stochastic integration has applications in virtually every scientific area involving random functions. This introductory textbook provides a concise introduction to the Ito calculus. From the reviews:"Introduction to Stochastic Integration is exactly what the title says.

Based on well-known lectures given at Scuola Normale Superiore in Pisa, this book introduces analysis in a separable Hilbert space of infinite dimension. It starts from the definition of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way.

A set of detailed lecture notes on six topics at the forefront of current research in numerical analysis and applied mathematics. The notes start from a level suitable for first year graduate students in applied mathematics, mathematical analysis or numerical analysis, and proceed to current research topics.

This book is novel in its broad perspective on Riemann surfaces: the text systematically explores the connection with other fields of mathematics.