Bøger i Universitext serien

The authors present introductory material in algebraic topology from a novel point of view in using a homotopy-theoretic approach. This carefully written book can be read by any student who knows some topology, providing a useful method to quickly learn this novel homotopy-theoretic point of view of algebraic topology.

This is a very basic and accessible introduction to option pricing, invoking a minimum of stochastic analysis and requiring only basic mathematical skills.

Focuses on the application of functional analysis and operator theory to some concrete asymptotic problems of linear algebra. This text is useful for graduate students, teachers, and researchers for those who have to deal with infinite matrices and their large truncations.

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.

Suitable for advanced undergraduate and graduate students of mathematics, physics, or engineering, this introduction to the calculus of variations focuses on variational problems involving one independent variable. It also discusses more advanced topics such as the inverse problem, eigenvalue problems, and Noether's theorem.

This second volume of a comprehensive tour through mathematical core subjects for computer scientists completes the ?rst volume in two - gards: Part III ?rst adds topology, di?erential, and integral calculus to the t- ics of sets, graphs, algebra, formal logic, machines, and linear geometry, of volume 1.

"The text can serve as an introduction to fundamentals in the respective areas from a residuated-maps perspective and with an eye on coordinatization.

Contains all the mathematics that computer scientists need to know in one place.

A study of the functional analytic properties of Weyl transforms as bounded linear operators on $ L2u(aBbb Runu) $ in terms of the symbols of the transforms.

This book presents fundamentals from the theory of algebraic surfaces, including areas such as rational singularities of surfaces and their relation with Grothendieck duality theory, numerical criteria for contractibility of curves on an algebraic surface, and the problem of minimal models of surfaces.

Providing readers with the very basic knowledge necessary to begin research on differential equations with professional ability, the selection of topics here covers the methods and results that are applicable in a variety of different fields.

Topology is a relatively young and very important branch of mathematics, which studies the properties of objects that are preserved through deformations, twistings, and stretchings.

This book is based on two series of lectures given at a summer school on algebraic combinatorics at the Sophus Lie Centre in Nordfjordeid, Norway, in June 2003, one by Peter Orlik on hyperplane arrangements, and the other one by Volkmar Welker on free resolutions.

Vitushkin's conjecture, a special case of Painleve's problem, states that a compact subset of the complex plane with finite linear Hausdorff measure is removable for bounded analytic functions if and only if it intersects every rectifiable curve in a set of zero arclength measure.

The treatment is thoroughly mathematical and prepares students to branch out in several areas of mathematics related to foundations and computability, such as logic, axiomatic set theory, model theory, recursion theory, and computability.

The classical geometries of points and lines include not only the projective and polar spaces, but similar truncations of geometries naturally arising from the groups of Lie type. Simple point-line characterizations of Lie incidence geometries allow one to recognize Lie incidence geometries and their automorphism groups.

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.