Bøger af Saunders Mac Lane

""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.

Department Of Mathematics, University Of Chicago, Autumn 1953. Prepared With The Assistance Of A Grant By The Research Corporation.

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 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.

This autobiography of Saunders Mac Lane, an extraordinary mathematician, takes the reader on a journey through the most important milestones of the mathematical world in the twentieth century.

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. Later, he contributed to the more abstract and general mathematical viewpoints which emerged in the twentieth century.

This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.

MacLane's autobiography takes the reader on a journey through the most important milestones of the mathematical world in the 20th century. Early in the century he participated in the exciting happenings at Gottingen.