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Saunders Mac Lane was an extraordinary mathematician, a dedicated teacher, and a good citizen who cared deeply about the values of science and education. In his autobiography, he gives us a glimpse of his "life and times," mixing the highly personal with professional observations. His recollections bring to life a century of extraordinary accomplishments and tragedies that inspire and educate. Saunders Mac Lane's life covers nearly a century of mathematical developments. During the earlier part of the twentieth century, he participated in the exciting happenings in Göttingen---the Mecca of mathematics. He studied under David Hilbert, Hermann Weyl, and Paul Bernays and witnessed the collapse of a great tradition under the political pressure of a brutal dictatorship. Later, he contributed to the more abstract and general mathematical viewpoints developed in the twentieth century. Perhaps the most outstanding accomplishment during his long and extraordinary career was the development of the concept of categories, together with Samuel Eilenberg, and the creation of a theory that has broad applications in different areas of mathematics, in particular topology and foundations. He was also a keen observer and active participant in the social and political events. As a member and vice president of the National Academy of Science and an advisor to the Administration, he exerted considerable influence on science and education policies in the post-war period. Mac Lane's autobiography takes the reader on a journey through the most important milestones of the mathematical world in the twentieth century.

Saunders Mac Lane was an extraordinary mathematician, a dedicated teacher, and a good citizen who cared deeply about the values of science and education. In his autobiography, he gives us a glimpse of his "life and times," mixing the highly personal with professional observations. His recollections bring to life a century of extraordinary accomplishments and tragedies that inspire and educate. Saunders Mac Lane's life covers nearly a century of mathematical developments. During the earlier part of the twentieth century, he participated in the exciting happenings in Göttingen---the Mecca of mathematics. He studied under David Hilbert, Hermann Weyl, and Paul Bernays and witnessed the collapse of a great tradition under the political pressure of a brutal dictatorship. Later, he contributed to the more abstract and general mathematical viewpoints developed in the twentieth century. Perhaps the most outstanding accomplishment during his long and extraordinary career was the development of the concept of categories, together with Samuel Eilenberg, and the creation of a theory that has broad applications in different areas of mathematics, in particular topology and foundations. He was also a keen observer and active participant in the social and political events. As a member and vice president of the National Academy of Science and an advisor to the Administration, he exerted considerable influence on science and education policies in the post-war period. Mac Lane's autobiography takes the reader on a journey through the most important milestones of the mathematical world in the twentieth century.

This new edition includes a number of revisions and additions. One is on symmetric monoidal categories and braided monoidal categories and the coherence theorems for them. The second describes 2-categories and the higher dimensional categories which have recently come into prominence.

Categories for the Working Mathematician provides an array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. The book then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterized by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including two new chapters on topics of active interest. One is onsymmetric monoidal categories and braided monoidal categories and the coherence theorems for them. The second describes 2-categories and the higher dimensional categories which have recently come into prominence. The bibliography has also been expanded to cover some of the many other recent advances concerning categories.

Covering a period up to 1971, this selection of Saunders Mac Lane’s most distinguished papers takes the reader on a journey through the most important milestones of the mathematical world in the twentieth century. Mac Lane was an extraordinary mathematician and a dedicated teacher who cared earnestly about the values of science and education. His life spanned nearly a century of mathematical progress. In his earlier years, he participated in the exciting developments in Göttingen. He studied under David Hilbert, Hermann Weyl, and Paul Bernays. Later, he contributed to the more abstract and general mathematical viewpoints which emerged in the twentieth century. Perhaps the most outstanding accomplishment during his long and extraordinary career was the development of the concept and theory of categories, together with Samuel Eilenberg, which has broad applications in different areas, in particular in topology and the foundations of mathematics.

""Spectral Sequences And Homotopy: Lectures, Notes by Mac Lane, Saunders"" is a book that provides a comprehensive introduction to the theory of spectral sequences and homotopy. The book is based on lectures and notes by the renowned mathematician Saunders Mac Lane, and is aimed at graduate students and researchers in the field of algebraic topology.The book begins with an introduction to homotopy theory, including the fundamental group and higher homotopy groups. It then goes on to cover the basics of spectral sequences, including their construction and use in algebraic topology. The book also includes a detailed discussion of the relationship between spectral sequences and homotopy theory, including the use of spectral sequences to compute homotopy groups and homology groups.Throughout the book, Mac Lane provides clear and concise explanations of key concepts, making it accessible to readers with a basic knowledge of algebraic topology. The book also includes numerous examples and exercises to help readers develop their understanding of the material.Overall, ""Spectral Sequences And Homotopy: Lectures, Notes by Mac Lane, Saunders"" is an essential resource for anyone interested in the theory of spectral sequences and homotopy, and is sure to be a valuable addition to any mathematics library.Department Of Mathematics, University Of Chicago, Autumn 1953. Prepared With The Assistance Of A Grant By The Research Corporation.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.

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.

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.

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.