Saunders Mac Lane - Böcker

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.

***preliminary version -- do not use for promotional material*** 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 expoitation of Kan extensions. This second edition includes a number of revisions and additions, including two new chapters on topics of active interest. 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. The bibliography has also been expanded to cover some of the many other recent advances concerning categories.

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. One is onsymmetric monoidal categories and braided monoidal categories and the coherence theorems for them.

J. Richard Biichi is well known for his work in mathematical logic and theoretical computer science. (He himself would have sharply objected to the qualifier "theoretical," because he more or less identified science and theory, using "theory" in a broader sense and "science" in a narrower sense than usual.) We are happy to present here this collection of his papers. I (DS)1 worked with Biichi for many years, on and off, ever since I did my Ph.D. thesis on his Sequential Calculus. His way was to travel locally, not globally: When we met we would try some specific problem, but rarely dis­ cussed research we had done or might do. After he died in April 1984 I sifted through the manuscripts and notes left behind and was dumbfounded to see what areas he had been in. Essentially I knew about his work in finite au­ tomata, monadic second-order theories, and computability. But here were at least four layers on his writing desk, and evidently he had been working on them all in parallel. I am sure that many people who knew Biichi would tell an analogous story.

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.

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.

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.

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 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.