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 Books in the series:
Graduate Texts in Mathematics
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The Arithmetic of Hyperbolic 3-Manifolds
Colin MacLachlan,
Alan W. Reid
Recently there has been considerable interest in developing techniques based on number theory to attack problems of 3-manifolds; Contains many examples and lots of problems; Brings together much of the existing literature of Kleinian groups in a clear and concise...
Format: Paperback - Released: 29/07/2011
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Introduction to Topological Manifolds
John M. Lee
Extensively revised and updated, this volume provides an introduction to manifolds at the beginning graduate level. It contains the essential topological ideas involved with further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields.
Format: Hardback - Released: 30/12/2010
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A Course in Commutative Algebra
Gregor Kemper
This text offers a thorough, modern introduction to commutative algebra. It concentrates on concepts and results at the center of the field while keeping a constant view on the natural geometrical context. It includes many examples and exercises.
Format: Hardback - Released: 09/12/2010
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A Course in Computational Algebraic Number Theory
Henri Cohen
A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number...
Format: Paperback - Released: 08/12/2010
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Mathematical Methods of Classical Mechanics
V. I. Arnold
This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and...
Format: Paperback - Released: 05/12/2010
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Model Theory: An Introduction
David Marker
Assumes only a familiarity with algebra at the beginning graduate level; Stresses applications to algebra; Illustrates several of the ways Model Theory can be a useful tool in analyzing classical mathematical structures
Format: Paperback - Released: 05/12/2010
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A Classical Introduction to Modern Number Theory
Kenneth F. Ireland,
Michael Rosen
This well-developed, accessible text details the historical development of the subject throughout. It also provides wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. This second edition contains two new chapters that provide a complete proof...
Format: Paperback - Released: 05/12/2010
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Classical Topics in Complex Function Theory
Reinhold Remmert
Ideal for advanced courses in the theory of complex functions, this book leads readers to personally experience function theory and to participate in the work of creative mathematicians. Offers many glimpses of the function theory of several complex variables.
Format: Paperback - Released: 05/12/2010
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Foundations of Differentiable Manifolds and Lie Groups
Frank W. Warner
Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. Coverage includes differentiable manifolds, tensors and differentiable forms, Lie groups and homogenous spaces, and integration on...
Format: Paperback - Released: 04/12/2010
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Algebraic Geometry
Robin Hartshorne
An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised...
Format: Paperback - Released: 04/12/2010
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The Symmetric Group
Bruce E. Sagan
This book brings together many of the important results in this field. From the reviews: A classic gets even better...The edition has new material including the Novelli-Pak-Stoyanovskii bijective proof of the hook formula, Stanley's proof of the sum of squares...
Format: Paperback - Released: 04/12/2010
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Algebraic Functions and Projective Curves
David M. Goldschmidt
This book gives an introduction to algebraic functions and projective curves. It covers a wide range of material by dispensing with the machinery of algebraic geometry and proceeding directly via valuation theory to the main results on function fields. It...
Format: Paperback - Released: 04/12/2010
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From Holomorphic Functions to Complex Manifolds
Klaus Fritzsche,
Hans Grauert
This introduction to the theory of complex manifolds covers the most important branches and methods in complex analysis of several variables while completely avoiding abstract concepts involving sheaves, coherence, and higher-dimensional cohomology. Only elementary methods such as power series, holomorphic...
Format: Paperback - Released: 03/12/2010
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Harmonic Function Theory
Sheldon Axler,
Paul Bourdon,
Ramey Wade
This book is about harmonic functions in Euclidean space. This new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bochers Theorem, new exercises and proofs, as well as revisions throughout to improve the...
Format: Paperback - Released: 03/12/2010
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Number Theory in Function Fields
Michael Rosen
Early in the development of number theory, it was noticed that the ring of integers has many properties in common with the ring of polynomials over a finite field. The first part of this book illustrates this relationship by presenting...
Format: Paperback - Released: 03/12/2010
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Smooth Manifolds and Observables
Jet Nestruev
This book gives an introduction to fiber spaces and differential operators on smooth manifolds. Over the last 20 years, the authors developed an algebraic approach to the subject and they explain in this book why differential calculus on manifolds can...
Format: Paperback - Released: 03/12/2010
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Optima and Equilibria
Jean-Pierre Aubin
This book offers a self-contained, rigorous and concise review of the mathematical tools needed to study optima and equilibria, as solutions to problems in economics, management sciences, operations research, cooperative and non-cooperative games and more.
Format: Paperback - Released: 01/12/2010
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Algebraic Geometry
Joe Harris
This book succeeds brilliantly by concentrating on a number of core topics...and by treating them in a hugely rich and varied way. The author ensures that the reader will learn a large amount of classical material and perhaps more importantly,...
Format: Paperback - Released: 01/12/2010
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A Course in Functional Analysis
John B. Conway
This book is an introductory text in functional analysis. Unlike many modern treatments, it begins with the particular and works its way to the more general. From the reviews: This book is an excellent text for a first graduate course...
Format: Paperback - Released: 01/12/2010
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Analysis for Applied Mathematics
Ward Cheney
This well-written book contains the analytical tools, concepts, and viewpoints needed for modern applied mathematics. It treats various practical methods for solving problems such as differential equations, boundary value problems, and integral equations. Pragmatic approaches to difficult equations are presented,...
Format: Paperback - Released: 01/12/2010
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Metric Structures in Differential Geometry
Gerard Walschap
This book offers an introduction to the theory of differentiable manifolds and fiber bundles. It examines bundles from the point of view of metric differential geometry: Euclidean bundles, Riemannian connections, curvature, and Chern-Weil theory are discussed, including the Pontrjagin, Euler,...
Format: Paperback - Released: 30/11/2010
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Partial Differential Equations
Jurgen Jost
This book develops the important approaches to the existence and regularity of partial differential equations, in particular of elliptic (and parabolic) type, particularly those aspects and methods that are relevant not only for linear, but also for nonlinear equations.
Format: Paperback - Released: 30/11/2010
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A Course in Enumeration
Martin Aigner
Combinatorial enumeration is a readily accessible subject full of easily stated, but sometimes tantalizingly difficult problems. This book leads the reader in a leisurely way from basic notions of combinatorial enumeration to advanced topics, ranging from algebra to statistical physics.
Format: Paperback - Released: 30/11/2010
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Fourier Analysis and Its Applications
Anders Vretblad
A carefully prepared account of the basic ideas in Fourier analysis and its applications to the study of partial differential equations. The author succeeds to make his exposition accessible to readers with a limited background, for example, those not acquainted...
Format: Paperback - Released: 30/11/2010
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Foundations of Hyperbolic Manifolds
John Ratcliffe
This book is an exposition of the theoretical foundations of hyperbolic manifolds. It is intended to be used both as a textbook and as a reference. This book has been heavily class-tested and each chapter contains exercises and a section...
Format: Paperback - Released: 25/11/2010
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Topics in Banach Space Theory
Fenando Albiac,
Nigel J. Kalton
This book emphasizes the isomorphic theory of Banach spaces and techniques using the unifying viewpoint of basic sequences. Its aim is to provide the reader with the necessary technical tools and background to reach the frontiers of research without the...
Format: Paperback - Released: 19/11/2010
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Algebraic Function Fields and Codes
Henning Stichtenoth
This is an expanded edition of a popular textbook that provides a purely algebraic, self-contained and in-depth exposition of the theory of function fields. It contains numerous exercises, some fairly simple, some quite difficult.
Format: Paperback - Released: 18/11/2010
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Matrices
Denis Serre
Offers an introduction to the basic theory of matrices. This title contains many applications of matrices to different aspects of mathematics and also other areas of science and engineering. It mixes together algebra, analysis, complexity theory and numerical analysis.
Format: Hardback - Released: 03/11/2010
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The Arithmetic of Dynamical Systems
J.H. Silverman
This book provides an introduction to the relatively new discipline of arithmetic dynamics. Whereas classical discrete dynamics is the study of iteration of self-maps of the complex plane or real line, arithmetic dynamics is the study of the number-theoretic properties...
Format: Paperback - Released: 19/10/2010
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Symmetry, Representations, and Invariants
Roe W. Goodman,
Nolan R. Wallach
This book is a significant reworking of an earlier work by the authors. It offers a comprehensive introduction to Lie theory, representation theory, invariant theory, and algebraic groups, in a new presentation that includes a broader range of applications.
Format: Paperback - Released: 19/10/2010
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Buildings
Peter Abramenko,
Kenneth S. Brown
Covering all three approaches to Jacques Tits's beautiful theory of buildings, this accessible volume is suitable as a textbook introduction to the subject as well as a self-study text for researchers. It contains numerous exercises.
Format: Paperback - Released: 19/10/2010
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Classical Fourier Analysis
Loukas Grafakos
The primary goal of this text is to present the theoretical foundation of the field of Fourier analysis. There are historical notes at the end of each chapter, and examples illustrate the definitions and ideas.
Format: Paperback - Released: 19/10/2010
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A Course in Commutative Banach Algebras
Eberhard Kaniuth
This book is a thorough introduction to the subject, aimed at students with knowledge of functional and complex analysis, topology, measure theory, and group theory. At the core of this text are chapters on Gelfand's theory, regularity and spectral synthesis.
Format: Paperback - Released: 19/10/2010
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Modern Fourier Analysis
Loukas Grafakos
The primary goal of this text is to present the theoretical foundation of the field of Fourier analysis. There are historical notes at the end of each chapter, and examples illustrate the definitions and ideas.
Format: Paperback - Released: 19/10/2010
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Monomial Ideals
Jurgen Herzog,
Takayuki Hibi
This book demonstrates current trends in research on combinatorial and computational commutative algebra with a primary emphasis on topics related to monomial ideals. In the text, theory is complemented by a number of examples and exercises.
Format: Hardback - Released: 07/10/2010
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Graph Theory
Reinhard (University of Hamburg,
Germany) Diestel
The fourth edition of this standard textbook of modern graph theory has been revised, updated, and substantially extended. Covering all major recent developments, it can be used both as a reliable textbook for an introductory course and as a graduate...
Format: Paperback - Released: 19/07/2010
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Analysis and Probability Wavelets, Signals, Fractals
Palle E.T. Jorgensen,
B. Treadway
Combines analysis and tools from probability, harmonic analysis, operator theory, and engineering (signal/image processing) Interdisciplinary focus with hands-on approach, generous motivation and new pedagogical techniques Numerous exercises reinforce fundamental concepts and hone computational skills Separate sections explain engineering terms to...
Format: Paperback - Released: 12/02/2010
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Complex Analysis
Jane P. Gilman,
Irwin Kra,
Rubi E. Rodriguez
Organizing the basic material of complex analysis in a unique manner, the authors of this versatile book aim is to present a precise and concise treatment of those parts of complex analysis that should be familiar to every research mathematician.
Format: Paperback - Released: 12/02/2010
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Number Theory
Henri Cohen
This book deals with several aspects of what is now called explicit number theory. The central theme is the solution of Diophantine equations. This unique collection of topics contains more than 350 exercises and its text is largely self-contained.
Format: Paperback - Released: 12/02/2010
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Braid Groups
Christian Kassel,
Vladimir Turaev,
O. Dodane
The authors introduce the basic theory of braid groups, highlighting several definitions showing their equivalence. This is followed by a treatment of the relationship between braids, knots and links. Important results then look at linearity and orderability.
Format: Paperback - Released: 12/02/2010
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Number Theory
Henri Cohen
The central theme of this book is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers.
Format: Paperback - Released: 12/02/2010
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Bounded Analytic Functions
John Garnett
This book is an account of the theory of Hardy spaces in one dimension, with emphasis on some of the exciting developments of the past two decades or so. The book covers a wide range of topics in analysis and...
Format: Paperback - Released: 12/02/2010
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Abstract Algebra
Pierre Antoine Grillet
This key textbook covers, with proofs, the usual major branches of abstract algebra, with its inclusive approach meaning that all of the necessary areas are explored. This new edition has been completed reworked and revised.
Format: Paperback - Released: 12/02/2010
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Compact Lie Groups
Mark R. Sepanski
Blending algebra, analysis, and topology, the study of compact Lie groups is one of the most beautiful areas of mathematics and a key stepping stone to the theory of general Lie groups. Assuming no prior knowledge of Lie groups, this...
Format: Paperback - Released: 12/02/2010
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Distributions and Operators
Gerd Grubb
This book gives an introduction to distribution theory, based on the work of Schwartz and of many other people. It is the first book to present distribution theory as a standard text. Each chapter has been enhanced with many exercises...
Format: Paperback - Released: 12/02/2010
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Elementary Functional Analysis
Barbara D. MacCluer
This concise text on functional analysis is gently written and covers a unique set of topics. It includes numerous high-quality exercises and interesting historical tidbits scattered throughout.
Format: Paperback - Released: 12/02/2010
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Advanced Linear Algebra
Steven Roman
This graduate level textbook provides encyclopedic treatment of linear algebra theory, both classical and modern. This new edition has been revised and expanded with many new chapters.
Format: Paperback - Released: 12/02/2010
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The Finite Simple Groups
Robert Wilson,
Christopher W. Parker
Here, a thorough grounding in the theory of alternating and classical groups is followed by discussion of exceptional groups (classed as automorphism groups of multilinear forms), sporadic and Chevalley groups, as well as the theory of Lie algebras.
Format: Hardback - Released: 14/12/2009
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Deformation Theory
Robin Hartshorne
This first textbook on deformation theory begins by studying what happens over small infinitesimal deformations, and then gradually builds up to more global situations. The author provides plenty of motivation, including numerous exercises and examples.
Format: Hardback - Released: 01/12/2009
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A Course in Mathematical Logic for Mathematicians
Yu. I. Manin,
Boris Zilber
This fresh edition of the straightforward introduction to modern mathematical logic retains its appeal to the intuition of working mathematicians, yet along with the material from the first edition, it has fresh chapters, one of which deals with Model Theory.
Format: Hardback - Released: 30/10/2009
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The Arithmetic of Elliptic Curves
Joseph H. Silverman
The theory of elliptic curves is distinguished by the diversity of the methods used in its study. This book treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic...
Format: Hardback - Released: 23/06/2009
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Symmetry, Representations, and Invariants
Roe W. Goodman,
Nolan R. Wallach
This book is a significant reworking of an earlier work by the authors. It offers a comprehensive introduction to Lie theory, representation theory, invariant theory, and algebraic groups, in a new presentation that includes a broader range of applications.
Format: Hardback - Released: 01/06/2009
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Elementary Functional Analysis
Barbara D. MacCluer
This concise text on functional analysis is gently written and covers a unique set of topics. It includes numerous high-quality exercises and interesting historical tidbits scattered throughout.
Format: Hardback - Released: 01/02/2009
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Probability
Albert N. Shiryaev
Contains a systematic treatment of probability from the ground up, starting with intuitive ideas and gradually developing more sophisticated subjects, such as random walks, martingales, Markov chains, ergodic theory, weak convergence of probability measures, stationary stochastic processes, and the Kalman-Bucy...
Format: Hardback - Released: 01/01/2009
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Probability and Stochastics
E. Cinlar
Probability and Stochastics provides an introduction to the field, and begins by describing the fundamentals and basic principles of probability theory. Later chapters discuss more advanced topics, such as Martingales, Poisson Random Measures, Levy Processes and Brownian Motion.
Format: Hardback - Released: 01/01/2009
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Probability
Albert N. Shiryaev
Contains a systematic treatment of probability from the ground up, starting with intuitive ideas and gradually developing more sophisticated subjects, such as random walks, martingales, Markov chains, ergodic theory, weak convergence of probability measures, stationary stochastic processes, and the Kalman-Bucy...
Format: Hardback - Released: 00/01/2009
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Modern Fourier Analysis Preliminary Entry 250
Loukas Grafakos
The primary goal of this text is to present the theoretical foundation of the field of Fourier analysis. There are historical notes at the end of each chapter, and examples illustrate the definitions and ideas.
Format: Hardback - Released: 16/12/2008
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Algebraic Function Fields and Codes
Henning Stichtenoth
This is an expanded edition of a popular textbook that provides a purely algebraic, self-contained and in-depth exposition of the theory of function fields. It contains numerous exercises, some fairly simple, some quite difficult.
Format: Hardback - Released: 20/11/2008
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Classical Fourier Analysis Prelimianry Entry 249
Loukas Grafakos
The primary goal of this text is to present the theoretical foundation of the field of Fourier analysis. There are historical notes at the end of each chapter, and examples illustrate the definitions and ideas.
Format: Hardback - Released: 24/10/2008
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Distributions and Operators
Gerd Grubb
This book gives an introduction to distribution theory, based on the work of Schwartz and of many other people. It is the first book to present distribution theory as a standard text. Each chapter has been enhanced with many exercises...
Format: Hardback - Released: 23/10/2008
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Buildings Theory and Applications
Peter Abramenko,
Ken Brown
Covering all three approaches to Jacques Tits's beautiful theory of buildings, this accessible volume is suitable as a textbook introduction to the subject as well as a self-study text for researchers. It contains numerous exercises.
Format: Hardback - Released: 01/09/2008
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Lectures on Polytopes
Gunter M. Ziegler
Based on a graduate course at the Technische Universitat, Berlin, this book presents a wealth of material on the modern theory of convex polytopes. With linear algebra as a prerequisite, the text moves quickly from the basics to topics of...
Format: Paperback - Released: 07/04/2008
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Problems in Analytic Number Theory
U.S.R. Murty
Offers a problem-solving approach to the subject of analytic number theory. This book describes the ways in which analytic methods are used to study the distribution of prime numbers. It includes an introduction to p-adic analytic methods. It is suitable...
Format: Hardback - Released: 10/03/2008
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Advanced Linear Algebra
Steven Roman
This graduate level textbook provides encyclopedic treatment of linear algebra theory, both classical and modern. This new edition has been revised and expanded with many new chapters.
Format: Hardback - Released: 09/11/2007
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Graph Theory An Advanced Course
Adrian Bondy,
J.A. Bondy,
U.S.R. Murty
Graph theory is a flourishing discipline containing a body of beautiful and powerful theorems of wide applicability. This book provides a systematic treatment of the theory of graphs. It describes and illustrates commonly used proof techniques, and presents exercises -...
Format: Hardback - Released: 00/10/2007
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Abstract Algebra
Pierre Antoine Grillet
This key textbook covers, with proofs, the usual major branches of abstract algebra, with its inclusive approach meaning that all of the necessary areas are explored. This new edition has been completed reworked and revised.
Format: Hardback - Released: 28/08/2007
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Number Theory Analytic and Modern Tools
Henri Cohen
This book deals with several aspects of what is now called explicit number theory. The central theme is the solution of Diophantine equations. This unique collection of topics contains more than 350 exercises and its text is largely self-contained.
Format: Hardback - Released: 19/06/2007
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Number Theory Tools and Diophantine Equations
Henri Cohen
The central theme of this book is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers.
Format: Hardback - Released: 18/06/2007
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A First Course in Modular Forms
Fred Diamond,
Jerry Shurman
This book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem. The Theorem is stated in various forms, related to each other and to their applications to number theory.
Format: Hardback - Released: 21/05/2007
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Braid Groups
Christian Kassel,
Vladimir Turaev,
O. Dodane
The authors introduce the basic theory of braid groups, highlighting several definitions showing their equivalence. This is followed by a treatment of the relationship between braids, knots and links. Important results then look at linearity and orderability.
Format: Hardback - Released: 00/04/2007
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Partial Differential Equations
Jurgen Jost
This book develops the important approaches to the existence and regularity of partial differential equations, in particular of elliptic (and parabolic) type, particularly those aspects and methods that are relevant not only for linear, but also for nonlinear equations.
Format: Hardback - Released: 06/02/2007
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Compact Lie Groups
Mark R. Sepanski
Blending algebra, analysis, and topology, the study of compact Lie groups is one of the most beautiful areas of mathematics and a key stepping stone to the theory of general Lie groups. Assuming no prior knowledge of Lie groups, this...
Format: Hardback - Released: 24/01/2007
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Bounded Analytic Functions
John Garnett
This book is an account of the theory of Hardy spaces in one dimension, with emphasis on some of the exciting developments of the past two decades or so. The book covers a wide range of topics in analysis and...
Format: Hardback - Released: 15/10/2006
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Foundations of Optimization
Osman Guler
This book covers the fundamental principles of optimization in finite dimensions. It develops the necessary material in multivariable calculus both with coordinates and coordinate-free, so recent developments such as semidefinite programming can be dealt with.
Format: Hardback - Released: 00/10/2006
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Foundations of Hyperbolic Manifolds
John Ratcliffe
This book is an exposition of the theoretical foundations of hyperbolic manifolds. It is intended to be used both as a textbook and as a reference. This book has been heavily class-tested and each chapter contains exercises and a section...
Format: Hardback - Released: 26/09/2006
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Riemannian Geometry
Peter Petersen
This comprehensive introduction to Riemannian Geometry offers a detailed and engaging account of the topic, plus numerous exercises and examples. It combines both the geometric parts of Riemannian geometry and the analytic aspects of the theory, and reviews the latest...
Format: Hardback - Released: 22/09/2006
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Topics in Banach Space Theory
Fenando Albiac,
N.J. Kalton
Emphasizes the isomorphic theory of Banach spaces and techniques using the unifying viewpoint of basic sequences. This book intends to provide the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of...
Format: Hardback - Released: 15/02/2006
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Field Theory
Steven Roman
Offers an expository account of field theory, a very exciting area in mathematics.
Format: Hardback - Released: 15/12/2005
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Algebra
Serge Lang
A basic text for a one year course in algebra at the graduate level or as a useful reference for mathematicians and professionals who use higher-level algebra. It addresses the basic concepts of algebra.
Format: Hardback - Released: 19/09/2005
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Combinatorial Commutative Algebra
Ezra Miller,
Bernd Sturmfels
Provides an introduction to combinatorial commutative algebra with emphasis on combinatorial techniques for multigraded polynomial rings, semigroup algebras, and determined rings. This book covers topics ranging from homological invariants of monomial ideals and their polyhedral resolutions, to hands-on tools for...
Format: Paperback - Released: 30/06/2005
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