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Universitext

Universitext
359 Volumes | 1980 - 2020

Description

Universitext

is a series of textbooks that presents material from a wide variety of mathematical disciplines at master’s level and beyond. The books, often well class-tested by their author, may have an informal, personal even experimental approach to their subject matter. Some of the most successful and established books in the series have evolved through several editions, always following the evolution of teaching curricula, into very polished texts.

Thus as research topics trickle down into graduate-level teaching, first textbooks written for new, cutting-edge courses may make their way into Universitext.

All books of the series Universitext

2020 | Book

Probability Theory and Stochastic Processes

The ultimate objective of this book is to present a panoramic view of the main stochastic processes which have an impact on applications, with complete proofs and exercises. Random processes play a central role in the applied sciences, including …

2020 | Book

On the Theory of Maass Wave Forms

This textbook provides a rigorous analytical treatment of the theory of Maass wave forms. Readers will find this unified presentation invaluable, as it treats Maass wave forms as the central area of interest. Subjects at the cutting edge of …

2020 | Book

A Course on Rough Paths

With an Introduction to Regularity Structures

With many updates and additional exercises, the second edition of this book continues to provide readers with a gentle introduction to rough path analysis and regularity structures, theories that have yielded many new insights into the analysis of …

2020 | Book

A Course on Tug-of-War Games with Random Noise

Introduction and Basic Constructions

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 …

2020 | Book

p-adic Numbers

An Introduction

There are numbers of all kinds: rational, real, complex, p-adic, and more. The p-adic numbers are not as well known as the others, but they play a fundamental role in number theory and in other parts of mathematics, capturing information related …

2020 | Book

Galois Cohomology and Class Field Theory

This graduate textbook offers an introduction to modern methods in number theory. It gives a complete account of the main results of class field theory as well as the Poitou-Tate duality theorems, considered crowning achievements of modern number …

2020 | Book

Notes on Geometry and Arithmetic

This English translation of Daniel Coray’s original French textbook Notes de géométrie et d’arithmétique introduces students to Diophantine geometry. It engages the reader with concrete and interesting problems using the language of classical …

2019 | Book

Applied Stochastic Control of Jump Diffusions

The main purpose of the book is to give a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and their applications. Both the dynamic programming method and …

2019 | Book

Convex and Stochastic Optimization

This textbook provides an introduction to convex duality for optimization problems in Banach spaces, integration theory, and their application to stochastic programming problems in a static or dynamic setting. It introduces and analyses the main …

2019 | Book

Statistics of Financial Markets

An Introduction

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 …

2019 | Book

Submanifold Theory

Beyond an Introduction

This book provides a comprehensive introduction to Submanifold theory, focusing on general properties of isometric and conformal immersions of Riemannian manifolds into space forms. One main theme is the isometric and conformal deformation problem …

2019 | Book

Jump SDEs and the Study of Their Densities

A Self-Study Book

The present book deals with a streamlined presentation of Lévy processes and their densities. It is directed at advanced undergraduates who have already completed a basic probability course. Poisson random variables, exponential random variables …

2019 | Book

Mathematical Foundations of Game Theory

This book gives a concise presentation of the mathematical foundations of Game Theory, with an emphasis on strategic analysis linked to information and dynamics. It is largely self-contained, with all of the key tools and concepts defined in the …

2019 | Book

Algebraic Curves, the Brill and Noether Way

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. It includes Puiseux series, branches, intersection multiplicity …

2019 | Book

Functional Analysis for the Applied Sciences

This advanced graduate textbook presents main results and techniques in Functional Analysis and uses them to explore other areas of mathematics and applications. Special attention is paid to creating appropriate frameworks towards solving …

2018 | Book

Discrete Stochastic Processes and Applications

This unique text for beginning graduate students gives a self-contained introduction to the mathematical properties of stochastics and presents their applications to Markov processes, coding theory, population dynamics, and search engine design.

2018 | Book

Nonlinear Elliptic Partial Differential Equations

An Introduction

This textbook presents the essential parts of the modern theory of nonlinear partial differential equations, including the calculus of variations.

After a short review of results in real and functional analysis, the author introduces the main …

2018 | Book

Functional Analysis

An Introductory Course

This concise text provides a gentle introduction to functional analysis. Chapters cover essential topics such as special spaces, normed spaces, linear functionals, and Hilbert spaces. Numerous examples and counterexamples aid in the understanding …


2018 | Book

Calculus of Variations

This textbook provides a comprehensive introduction to the classical and modern calculus of variations, serving as a useful reference to advanced undergraduate and graduate students as well as researchers in the field.

Starting from ten …

2018 | Book

Number Fields

Requiring no more than a basic knowledge of abstract algebra, this textbook presents the basics of algebraic number theory in a straightforward, "down-to-earth" manner. It thus avoids local methods, for example, and presents proofs in a way that …