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.

Algebra

Saunders MacLane

Garrett D. Birkhoff

An introductory algebra text covering commutative, non-commutative, and Boolean algebra and the lattice and Galois theories

A Survey of Modern Algebra

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.

Richard S. Varga

Reactor Criticality and Non-negative Matrices

Rudolph Ernest Langer

Orbit Theory

Gian-Carlo Rota

Lecture Notes on Ordinary Differential Equations

Like its elder sister group theory, lattice theory is a fruitful source of abstract concepts, common to traditionally unrelated branches of mathematics. Both subjects are based on postulates of an extremely simple and general nature. Lattice theory has become a recognized branch of modern algebra, with a steady flow of contributions to it from numerous mathematicians. This revised edition takes these contributions into account.

Lattice Theory

Since its original publication in 1940, this book has been revised and modernized several times, most notably in 1948 (second edition) and in 1967 (third edition). The material is organized into four main parts: general notions and concepts of lattice theory (Chapters I-V), universal algebra (Chapters VI-VII), applications of lattice theory to various areas of mathematics (Chapters VIII-XII), and mathematical structures that can be developed using lattices (Chapters XIII-XVII). At the end of the book there is a list of 166 unsolved problems in lattice theory, many of which still remain open. It is excellent reading, and ... the best place to start when one wishes to explore some portion of lattice theory or to appreciate the general flavor of the field. --Bulletin of the AMS

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.

Garrett Birkhoff

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