Garrett Birkhoff's Books

Numerical Solution of Elliptic Problems

By: Garrett Birkhoff,Robert E. Lynch

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Numerical Solution of Elliptic Problems

By: Garrett Birkhoff,Robert E. Lynch

A study of the art and science of solving elliptic problems numerically, with an emphasis on problems that have important scientific and engineering applications, and that are solvable at moderate cost on computing machines.

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Page Count

326

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SIAM

Published Date

ISBN 10

0898714761

ISBN 13

9780898714760

A Survey of Modern Algebra

By: Garrett Birkhoff,Saunders Mac Lane

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A Survey of Modern Algebra

By: Garrett Birkhoff,Saunders Mac Lane

This classic, written by two young instructors who became giants in their field, has shaped the understanding of modern algebra for generations of mathematicians and remains a valuable reference and text for self study and college courses.

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Page Count

393

Publisher

CRC Press

Published Date

ISBN 10

1351991736

ISBN 13

9781351991735

Algebra

Third Edition

By: Saunders Mac Lane,Garrett Birkhoff

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Algebra

Third Edition

By: Saunders Mac Lane,Garrett Birkhoff

This book presents modern algebra from first principles and is accessible to undergraduates or graduates. It combines standard materials and necessary algebraic manipulations with general concepts that clarify meaning and importance. This conceptual approach to algebra starts with a description of algebraic structures by means of axioms chosen to suit the examples, for instance, axioms for groups, rings, fields, lattices, and vector spaces. This axiomatic approach—emphasized by Hilbert and developed in Germany by Noether, Artin, Van der Waerden, et al., in the 1920s—was popularized for the graduate level in the 1940s and 1950s to some degree by the authors' publication of A Survey of Modern Algebra. The present book presents the developments from that time to the first printing of this book. This third edition includes corrections made by the authors.

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Page Count

650

Publisher

American Mathematical Society

Published Date

ISBN 10

147047476X

ISBN 13

9781470474768

Selected Papers on Algebra and Topology by Garrett Birkhoff

By: J.S. Oliveira,G.-C. Rota

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Selected Papers on Algebra and Topology by Garrett Birkhoff

By: J.S. Oliveira,G.-C. Rota

The present volume of reprints are what I consider to be my most interesting and influential papers on algebra and topology. To tie them together, and to place them in context, I have supplemented them by a series of brief essays sketching their historieal background (as I see it). In addition to these I have listed some subsequent papers by others which have further developed some of my key ideas. The papers on universal algebra, lattice theory, and general topology collected in the present volume concern ideas which have become familiar to all working mathematicians. It may be helpful to make them readily accessible in one volume. I have tried in the introduction to each part to state the most significant features of ea ch paper reprinted there, and to indieate later developments. The background that shaped and stimulated my early work on universal algebra, lattice theory, and topology may be of some interest. As a Harvard undergraduate in 1928-32, I was encouraged to do independent reading and to write an original thesis. My tutorial reading included de la Vallee-Poussin's beautiful Cours d'Analyse Infinitesimale, Hausdorff's Grundzüge der Mengenlehre, and Frechet's Espaces Abstraits. In addition, I discovered Caratheodory's 1912 paper "Vber das lineare Mass von Punktmengen" and Hausdorff's 1919 paper on "Dimension und Ausseres Mass," and derived much inspiration from them. A fragment of my thesis, analyzing axiom systems for separable metrizable spaces, was later published [2]. * This background led to the work summarized in Part IV.

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648

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817631143

ISBN 13

9780817631147

Introduction to Dynamical Systems

By: Michael Brin,Garrett Stuck

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Introduction to Dynamical Systems

By: Michael Brin,Garrett Stuck

This book provides a broad introduction to the subject of dynamical systems, suitable for a one- or two-semester graduate course. In the first chapter, the authors introduce over a dozen examples, and then use these examples throughout the book to motivate and clarify the development of the theory. Topics include topological dynamics, symbolic dynamics, ergodic theory, hyperbolic dynamics, one-dimensional dynamics, complex dynamics, and measure-theoretic entropy. The authors top off the presentation with some beautiful and remarkable applications of dynamical systems to such areas as number theory, data storage, and Internet search engines. This book grew out of lecture notes from the graduate dynamical systems course at the University of Maryland, College Park, and reflects not only the tastes of the authors, but also to some extent the collective opinion of the Dynamics Group at the University of Maryland, which includes experts in virtually every major area of dynamical systems.

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Page Count

254

Publisher

Cambridge University Press

Published Date

ISBN 10

1139433970

ISBN 13

9781139433976

Modern Analysis of Automorphic Forms By Example: Volume 2

By: Paul Garrett

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Modern Analysis of Automorphic Forms By Example: Volume 2

By: Paul Garrett

This is Volume 2 of a two-volume book that provides a self-contained introduction to the theory and application of automorphic forms, using examples to illustrate several critical analytical concepts surrounding and supporting the theory of automorphic forms. The two-volume book treats three instances, starting with some small unimodular examples, followed by adelic GL2, and finally GLn. Volume 2 features critical results, which are proven carefully and in detail, including automorphic Green's functions, metrics and topologies on natural function spaces, unbounded operators, vector-valued integrals, vector-valued holomorphic functions, and asymptotics. Volume 1 features discrete decomposition of cuspforms, meromorphic continuation of Eisenstein series, spectral decomposition of pseudo-Eisenstein series, and automorphic Plancherel theorem. With numerous proofs and extensive examples, this classroom-tested introductory text is meant for a second-year or advanced graduate course in automorphic forms, and also as a resource for researchers working in automorphic forms, analytic number theory, and related fields.

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Page Count

367

Publisher

Cambridge University Press

Published Date

ISBN 10

1108669212

ISBN 13

9781108669214

Modern Analysis of Automorphic Forms By Example

By: Paul Garrett

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Modern Analysis of Automorphic Forms By Example

By: Paul Garrett

Volume 2 of a two-volume introduction to the analytical aspects of automorphic forms, featuring proofs of critical results with examples.

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367

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Cambridge University Press

Published Date

ISBN 10

1108473849

ISBN 13

9781108473842

Modern Analysis of Automorphic Forms By Example: Volume 1

By: Paul Garrett

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Modern Analysis of Automorphic Forms By Example: Volume 1

By: Paul Garrett

This is Volume 1 of a two-volume book that provides a self-contained introduction to the theory and application of automorphic forms, using examples to illustrate several critical analytical concepts surrounding and supporting the theory of automorphic forms. The two-volume book treats three instances, starting with some small unimodular examples, followed by adelic GL2, and finally GLn. Volume 1 features critical results, which are proven carefully and in detail, including discrete decomposition of cuspforms, meromorphic continuation of Eisenstein series, spectral decomposition of pseudo-Eisenstein series, and automorphic Plancherel theorem. Volume 2 features automorphic Green's functions, metrics and topologies on natural function spaces, unbounded operators, vector-valued integrals, vector-valued holomorphic functions, and asymptotics. With numerous proofs and extensive examples, this classroom-tested introductory text is meant for a second-year or advanced graduate course in automorphic forms, and also as a resource for researchers working in automorphic forms, analytic number theory, and related fields.

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Page Count

407

Publisher

Cambridge University Press

Published Date

ISBN 10

1108228240

ISBN 13

9781108228244

Abstract Algebra

By: Paul B. Garrett

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Abstract Algebra

By: Paul B. Garrett

Designed for an advanced undergraduate- or graduate-level course, Abstract Algebra provides an example-oriented, less heavily symbolic approach to abstract algebra. The text emphasizes specifics such as basic number theory, polynomials, finite fields, as well as linear and multilinear algebra. This classroom-tested, how-to manual takes a more narra

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Page Count

460

Publisher

CRC Press

Published Date

ISBN 10

1584886900

ISBN 13

9781584886907

Hydrodynamics

By: Garrett Birkhoff

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Hydrodynamics

By: Garrett Birkhoff

A complete revision of the first edition this book. The author has added a chapter on turbulence, and has expanded the work on paradoxes and modeling. W.M. Elsasser said of the first edition, "A book such as this, concentrating as it does on the boundaries of fundamental progress, should be indispensable to all those engaged in hydrodynamical research who are concerned with the type of generalization that so often in the past has led to fundamental progress." Originally published in 1960. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

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201

Publisher

Princeton University Press

Published Date

ISBN 10

1400877776

ISBN 13

9781400877775

The Numerical Solution of Elliptic Equations

By: Garrett Birkhoff

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The Numerical Solution of Elliptic Equations

By: Garrett Birkhoff

A concise survey of the current state of knowledge in 1972 about solving elliptic boundary-value eigenvalue problems with the help of a computer. This volume provides a case study in scientific computing?the art of utilizing physical intuition, mathematical theorems and algorithms, and modern computer technology to construct and explore realistic models of problems arising in the natural sciences and engineering.

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Page Count

100

Publisher

SIAM

Published Date

ISBN 10

0898710014

ISBN 13

9780898710014

A Survey of Modern Algebra

By: Garrett Birkhoff,Saunders Mac Lane

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A Survey of Modern Algebra

By: Garrett Birkhoff,Saunders Mac Lane

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Page Count

393

Publisher

CRC Press

Published Date

ISBN 10

1351991736

ISBN 13

9781351991735

Numerical Solution of Elliptic Problems

By: Garrett Birkhoff,Robert E. Lynch

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Numerical Solution of Elliptic Problems

By: Garrett Birkhoff,Robert E. Lynch

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326

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SIAM

Published Date

ISBN 10

0898714761

ISBN 13

9780898714760

Algebra

By: Serge Lang

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Algebra

By: Serge Lang

This book is intended as 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. This book successfully addresses all of the basic concepts of algebra. For the new edition, the author has added exercises and made numerous corrections to the text. From MathSciNet's review of the first edition: "The author has an impressive knack for presenting the important and interesting ideas of algebra in just the "right" way, and he never gets bogged down in the dry formalism which pervades some parts of algebra.

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Page Count

914

Publisher

Springer

Published Date

ISBN 10

038795385X

ISBN 13

9780387953854

Book's by Garrett Birkhoff

Numerical Solution of Elliptic Problems

Numerical Solution of Elliptic Problems

A Survey of Modern Algebra

A Survey of Modern Algebra

Algebra

Algebra

Selected Papers on Algebra and Topology by Garrett Birkhoff

Selected Papers on Algebra and Topology by Garrett Birkhoff

Introduction to Dynamical Systems

Introduction to Dynamical Systems

Modern Analysis of Automorphic Forms By Example: Volume 2

Modern Analysis of Automorphic Forms By Example: Volume 2

Modern Analysis of Automorphic Forms By Example

Modern Analysis of Automorphic Forms By Example

Modern Analysis of Automorphic Forms By Example: Volume 1

Modern Analysis of Automorphic Forms By Example: Volume 1

Abstract Algebra

Abstract Algebra

Hydrodynamics

Hydrodynamics

The Numerical Solution of Elliptic Equations

The Numerical Solution of Elliptic Equations

A Survey of Modern Algebra

A Survey of Modern Algebra

Numerical Solution of Elliptic Problems

Numerical Solution of Elliptic Problems

Algebra

Algebra

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