Advanced Courses in Mathematics

Secondary mathematics teachers are frequently required to take a large number of mathematics courses – including advanced mathematics courses such as abstract algebra – as part of their initial teache

This book provides a systematic survey of classical and recent results on hyperbolic cross approximation. Motivated by numerous applications, the last two decades have seen great success in studying m

This book collects the notes of the lectures given at an Advanced Course on Dynamical Systems at the Centre de Recerca Matemàtica (CRM) in Barcelona. The notes consist of four series of lectures.The f

This book contains the notes of the lectures delivered at an Advanced Course on Combinatorial Matrix Theory held at Centre de Recerca Matemàtica (CRM) in Barcelona. These notes correspond to five seri

For briefer traditional courses in elementary differential equations that science, engineering, and mathematics students take following calculus. The Sixth Edition of this widely adopted b

This volume presents an elaborated version of lecture notes for two advanced courses: (Re)Emerging methods in Commutative Algebra and Representation Theory and Building Bridges Between

For one- or two-semester junior or senior level courses in Advanced Calculus, Analysis I, or Real Analysis. This title is part of the Pearson Modern Classics series. Pearson Modern Classics

For courses in discrete mathematics This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/m

For introductory sophomore-level courses in Linear Algebra or Matrix Theory. This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value pr

For a senior undergraduate or first year graduate-level course in Introduction to Topology. Appropriate for a one-semester course on both general and algebraic topology or separate courses treating ea

For sophomore-level courses in Differential Equations and Linear Algebra. This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a valu

For one-semester undergraduate courses in Elementary Number Theory This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price.

For one/two-term courses in Transition to Advanced Mathematics or Introduction to Proofs. Also suitable for courses in Analysis or Discrete Math. This title is part of the Pearson Modern Classics

This text is designed for graduate-level courses in real analysis.This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please

For courses in introductory linear algebra This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhigh

Appropriate for one- or two-semester, junior- to senior-level combinatorics courses. This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles a

This volume is based on four advancedcourses held at the Centre de Recerca Matemàtica (CRM), Barcelona. It presentsboth background information and recent developments on selected topics that areexperi

This volume contains the lecture notes of the two courses given by Davar Khoshnevisan and René Schilling, respectively, at the second edition of the Barcelona Summer School on Stochastic Analysis, hel

This book contains an elaborated version of the lecture notes given at the Advanced Course on Geometry andDynamics of Integrable Systems, held at the CRM in Barcelona.Native to actualproblem-solving p

This volume contains the lecture notes of the two courses given by Vlad Bally and Rama Cont at the Barcelona Summer School on Stochastic Analysis in July 2012.The notes of the course by Vlad Bally are

This book focusses on a large class of objects in moduli theory and provides different perspectives from which compactifications of moduli spaces may be investigated.

The notes of this book originate from three series of lectures given at the Centre de Recerca Matematica (CRM) in Barcelona. The first one is dedicated to the study of periodic solutions of autonomous

This book focuses on a large class of geometric objects in moduli theory and provides explicit computations to investigate their families. Concrete examples are developed that take advantage of the in

This book is the first one that gives a systematic presentation of recent fundamental results on greedy approximation with respect to bases. Greedy approximation is a very fresh area of research where

?This book provides an introduction to h-harmonics and Dunkl transforms. These are extensions of the ordinary spherical harmonics and Fourier transforms, in which the usual Lebesgue measure is replace

This book is an introduction to several active research topics in Foliation Theory and its connections with other areas. It contains expository lectures showing the diversity of ideas and methods conv

In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered

This book targets graduate students and researchers who want to learn about Lebesgue spaces and solutions to hyperbolic equations. It is divided into two parts.Part 1 provides an introduction to the t

This book contains an expanded version of lectures delivered by the authors at the CRM in Spring of 2009. It contains four series of lectures. The first one is an application of harmonic analysis and

The notes in this volume correspond to advanced courses given at the Centre de Recerca Matematica (Bellaterra, Barcelona, Spain) as part of the Research Programme in Arithmetic Geometry in the 2009-20

Prime numbers are the multiplicative building blocks of natural numbers. Understanding their overall influence and especially their distribution gives rise to central questions in mathematics and physics. In particular their finer distribution is closely connected with the Riemann hypothesis, the most important unsolved problem in the mathematical world. Assuming only subjects covered in a standard degree in mathematics, the authors comprehensively cover all the topics met in first courses on multiplicative number theory and the distribution of prime numbers. They bring their extensive and distinguished research expertise to bear in preparing the student for intelligent reading of the more advanced research literature. This 2006 text, which is based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State, is enriched by comprehensive historical notes and references as well as over 500 exercises.

The book covers several topics of current interest in the field of nonlinear partial differential equations and their applications to the physics of continuous media and particle interactions. It trea

A Transition to Advanced Mathematics: A Survey Course promotes the goals of a ``bridge'' course in mathematics, helping to lead students from courses in the calculus sequence (and other courses where

Additive combinatorics is a relatively recent term coined to comprehend the developments of the more classical additive number theory, mainly focussed on problems related to the addition of integers.

This volume offers researchers the opportunity to catch up with important developments in the field of numerical analysis and scientific computing and to get in touch with state-of-the-art numerical t

Prime numbers are the multiplicative building blocks of natural numbers. Understanding their overall influence and especially their distribution gives rise to central questions in mathematics and physics. In particular their finer distribution is closely connected with the Riemann hypothesis, the most important unsolved problem in the mathematical world. Assuming only subjects covered in a standard degree in mathematics, the authors comprehensively cover all the topics met in first courses on multiplicative number theory and the distribution of prime numbers. They bring their extensive and distinguished research expertise to bear in preparing the student for intelligent reading of the more advanced research literature. This 2006 text, which is based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State, is enriched by comprehensive historical notes and references as well as over 500 exercises.

These lecture notes treat polynomial identity rings from both the combinatorial and structural points of view. The greater part of recent research in polynomial identity rings is about combinatorial q