This edition contains detailed solutions of selected exercises. Many readers have requested this, because it makes the book more suitable for self-study. At the same time new exercises (without solutions) have beed added. They have all been placed i…
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. In this new ed…
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 to…
Three coherent parts form the material covered in this text, portions of which have not been widely covered in traditional textbooks. In this coverage the reader is quickly introduced to several different topics enriched with 175 exercises which foc…
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 ope…
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. To make for a m…
Requiring no more than a basic knowledge of abstract algebra, this text presents the mathematics of number fields in a straightforward, pedestrian manner. It therefore avoids local methods and presents proofs in a way that highlights the important p…
by Lev Beklemishev, Moscow The ?eld of mathematical logic-evolving around the notions of logical validity, provability, and computation-was created in the ?rst half of the previous century by a cohort of brilliant mathematicians and philosophers suc…
Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapid…
This is a relatively fast paced graduate level introduction to complex algebraic geometry, from the basics to the frontier of the subject. It covers sheaf theory, cohomology, some Hodge theory, as well as some of the more algebraic aspects of algebr…
This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, stron…
At the end of the typical one quarter course on power series the students lack the means to decide 2 whether 1/(1+x ) has an expansion around any point ~ 0, or the tangent has an expansion anywhere and the means to evaluate and predict errors. In us…
Provides a wide range of mathematical models currently used in the life sciencesEach model is thoroughly explained and illustrated by exampleIncludes three appendices to allow for independent reading
The constructive approach to mathematics has enjoyed a renaissance, caused in large part by the appearance of Errett Bishop's book Foundations of constr"uctiue analysis in 1967, and by the subtle influences of the proliferation of powerful computers…
This text is a rigorous treatment of the basic qualitative theory of ordinary differential equations, at the beginning graduate level. Designed as a flexible one-semester course but offering enough material for two semesters, A Short Course covers c…
A book on the subject of normal families more than sixty years after the publication of Montel's treatise Ler;ons sur les familles normales de fonc tions analytiques et leurs applications is certainly long overdue. But, in a sense, it is almost prem…
This textbook provides an accessible introduction to the rich and beautiful area of hyperplane arrangement theory, where discrete mathematics, in the form of combinatorics and arithmetic, meets continuous mathematics, in the form of the topology and…
This book gives an introduction to Linear Functional Analysis, which is a synthesis of algebra, topology, and analysis. In addition to the basic theory it explains operator theory, distributions, Sobolev spaces, and many other things. The text is se…
- < f is increasing. The latter part of the book deals with functions of bounded variation and approximately continuous functions. Finally there is an exhaustive chapter on the generalized Cantor sets and Cantor functions. The bibliography is extens…
This text provides an introduction to some of the best-known fixed-point theorems, with an emphasis on their interactions with topics in analysis. The level of exposition increases gradually throughout the book, building from a basic requirement of…
This self-contained treatment of Morse theory focuses on applications and is intended for a graduate course on differential or algebraic topology, and will also be of interest to researchers. This is the first textbook to include topics such as Mors…
Modern algorithmic techniques for summation, most of which were introduced in the 1990s, are developed here and carefully implemented in the computer algebra system Maple (TM).The algorithms of Fasenmyer, Gosper, Zeilberger, Petkovsek and van Hoeij…
The Motivation. With intensified use of mathematical ideas, the methods and techniques of the various sciences and those for the solution of practical problems demand of the mathematician not only greater readi ness for extra-mathematical applicatio…
The main theme of this book is the theory of heights as they appear in various guises. This includes a large body of results on Mahlers measure of the height of a polynomial. The authors'approach is very down to earth as they cover the rationals, as…
These notes were developed from a course taught at Rice Univ- sity in the spring of 1976 and again at the University of Hawaii in the spring of 1977. It is assumed that the students know some linear algebra and a little about differentiation of vect…
The aim of this book is to offer, in a concise, rigorous, and largely self-contained manner, a rapid introduction to the theory of distributions and its applications to partial differential equations and harmonic analysis. The book is written in a f…
Designed for intermediate graduate studies, this text will broaden students' core knowledge of differential geometry providing foundational material to relevant topics in classical differential geometry. The method of moving frames, a natural means…
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. They include both classical and…
This is an introduction to probabilistic and statistical concepts necessary to understand the basic ideas and methods of stochastic differential equations. Based on measure theory, which is introduced as smoothly as possible, it provides practical s…
Based on a graduate course by the celebrated analyst Nigel Kalton, this well-balanced introduction to functional analysis makes clear not only how, but why, the field developed. All major topics belonging to a first course in functional analysis are…
The main theorem of Linear Programming Duality, relating a "pri- mal" Linear Programming problem to its "dual" and vice versa, can be seen as a statement about sign patterns of vectors in complemen- tary subspaces of Rn. This observation, first made…
This text aims to provide graduate students with a self-contained introduction to topics that are at the forefront of modern algebra, namely, coalgebras, bialgebras and Hopf algebras. The last chapter (Chapter 4) discusses several applications of Ho…
Eugene Charles Catalan made his famous conjecture - that 8 and 9 are the only two consecutive perfect powers of natural numbers - in 1844 in a letter to the editor of Crelle's mathematical journal. One hundred and fifty-eight years later, Preda Miha…
Class field theory brings together the quadratic and higher reciprocity laws of Gauss, Legendre, and others, and vastly generalizes them. This book provides an accessible introduction to class field theory. It takes a traditional approach in that it…
This is a very basic and accessible introduction to option pricing, invoking a minimum of stochastic analysis and requiring only basic mathematical skills. It covers the theory essential to the statistical modeling of stocks, pricing of derivatives…
The book contains a complete self-contained introduction to highlights of classical complex analysis. New proofs and some new results are included. All needed notions are developed within the book: with the exception of some basic facts which can be…
This book gives a systematic introduction to the basic theory of financial mathematics, with an emphasis on applications of martingale methods in pricing and hedging of contingent claims, interest rate term structure models, and expected utility max…
Few books on Ordinary Differential Equations (ODEs) have the elegant geometric insight of this one, which puts emphasis on the qualitative and geometric properties of ODEs and their solutions, rather than on routine presentation of algorithms. From…
An application of differential forms for the study of some local and global aspects of the differential geometry of surfaces. Differential forms are introduced in a simple way that will make them attractive to "users" of mathematics. A brief and ele…
This textbook on combinatorial commutative algebra focuses on properties of monomial ideals in polynomial rings and their connections with other areas of mathematics such as combinatorics, electrical engineering, topology, geometry, and homological…
This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangl…
This book provides the mathematical foundations of networks of linear control systems, developed from an algebraic systems theory perspective. This includes a thorough treatment of questions of controllability, observability, realization theory, as…
The famous problems of squaring the circle, doubling the cube and trisecting an angle captured the imagination of both professional and amateur mathematicians for over two thousand years. Despite the enormous effort and ingenious attempts by these m…
This volume presents advances that have been made over recent decades in areas of research featuring Hardy's inequality and related topics. The inequality and its extensions and refinements are not only of intrinsic interest but are indispensable to…
This book offers a modern introduction to Nevanlinna theory and its intricate relation to the theory of normal families, algebraic functions, asymptotic series, and algebraic differential equations. Following a comprehensive treatment of Nevanlinna'…
Many mathematics books suffer from schizophrenia, and this is yet another. On the one hand it tries to be a reference for the basic results on flat riemannian manifolds. On the other hand it attempts to be a textbook which can be used for a second y…
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 l…
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. Additionally, it covers the two important areas o…
Mori's Program is a fusion of the so-called Minimal Model Program and the IItaka Program toward the biregular and/or birational classification of higher dimensional algebraic varieties. The author presents this theory in an easy and understandable w…