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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 Goettingen. 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.
It is not often that one gets to write a preface to a collection of
one's own papers. The most urgent task is to thank the people who
made this book possible. That means first of all Hy Bass who, on
behalf of Springer-Verlag, approached me about the idea. The late
Walter Kaufmann-Biihler was very encouraging; Paulo Ribenboim
helped in an important way; and Ina Lindemann saw the project
through with tact and skill that I deeply appreciate. My wishes
have been indulged in two ways. First, I was allowed to follow up
each selected paper with an afterthought. Back in my student days I
became aware of the Gesammelte Mathematische Werke of Dedekind,
edited by Fricke, Noether, and Ore. I was impressed by the editors'
notes that followed most of the papers and found them very usefuL A
more direct model was furnished by the collected papers of Lars
Ahlfors, in which the author himself supplied afterthoughts for
each paper or group of papers. These were tough acts to follow, but
I hope that some readers will find at least some of my
afterthoughts interesting. Second, I was permitted to add eight
previously unpublished items. My model here, to a certain extent,
was the charming little book, A Mathematician's Miscel lany by J.
E. Littlewood. In picking these eight I had quite a selection to
make -from fourteen loose-leaf notebooks of such writings. Here
again I hope that at least some will be found to be of interest.
This book combines in one volume Irving Kaplansky's lecture notes
on the theory of fields, ring theory, and homological dimensions of
rings and modules.
"In all three parts of this book the author lives up to his
reputation as a first-rate mathematical stylist. Throughout the
work the clarity and precision of the presentation is not only a
source of constant pleasure but will enable the neophyte to master
the material here presented with dispatch and ease."--A. Rosenberg,
"Mathematical Reviews"
This volume presents lecture notes based on the author's courses on
Lie algebras and the solution of Hilbert's fifth problem. In
chapter 1, "Lie Algebras," the structure theory of semi-simple Lie
algebras in characteristic zero is presented, following the ideas
of Killing and Cartan. Chapter 2, "The Structure of Locally Compact
Groups," deals with the solution of Hilbert's fifth problem given
by Gleason, Montgomery, and Zipplin in 1952.
A prominent and influential mathematician who was received numerous awards wrote this text to remedy a common failing in teaching algebra: the neglect of related instruction in geometry. Based on his many years of experience as an instructor the University of Chicago, author Irving Kaplansky presents a coherent overview of the correlation between these two branches of mathematics, illustrating his topics with an abundance of examples, exercises, and proofs. Suitable for both undergraduate and graduate courses. Unabridged republication of the edition published by Chelsea Publishing Company, New York, 1974.
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