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› Find signed collectible books: 'Algebra. Second Edition'
Book by Saunders Mac Lane, Garrett Birkhoff
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› Find signed collectible books: 'Algebra (AMS Chelsea Publishing)'
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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› Find signed collectible books: 'Categories for the Working Mathematician'
Book by Saunders Mac Lane
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› Find signed collectible books: 'Categories for the Working Mathematician (Graduate Texts in Mathematics)'
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. It 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 characterised 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 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.
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› Find signed collectible books: 'Saunders Mac Lane: A Mathematical Autobiography'
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.
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› Find signed collectible books: 'Sheaves in Geometry and Logic: A First Introduction to Topos Theory (Universitext)'
This introduction to the theory of toposes (developed by Grothendieck and followed up by Lawvere and Tierney) begins with illustrative examples and goes on to explain the underlying ideas of topology and sheaf theory as well as the general theory of elementary toposes and geometric morphisms and their relation to logic.
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› Find signed collectible books: 'Spectral Sequences And Homotopy: Lectures, Notes'
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› Find signed collectible books: 'A Survey of Modern Algebra (Akp Classics)'
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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