James Joseph Sylvester

This book brings together for the first time 140 letters from Sylvester's correspondence in an attempt to separate the fact from the many myths surrounding his life and work --

Features a paper 'On the Theory of the Syzygetic Relations of Two Rational Integral Functions, comprising an application to the Theory of Sturm's Functions'. This title also contains Sylvester's Constructive Theory of Partitions, papers on Binary Matrices, and the Lectures on the Theory of Reciprocants.

Comprehensive and elegantly composed, this biography makes clear the scope of Arthur Cayley's prodigious achievements, firmly enshrining him as the Mathematician Laureate of the Victorian Age.

Features a paper 'On the Theory of the Syzygetic Relations of Two Rational Integral Functions, comprising an application to the Theory of Sturm's Functions'. This title also contains Sylvester's Constructive Theory of Partitions, papers on Binary Matrices, and the Lectures on the Theory of Reciprocants.

Cover -- Title page -- Contents -- Preface -- Acknowledgments -- Photograph and Figure Credits -- Chapter 1. An overview of American mathematics: 1776-1876 -- Chapter 2. A new departmental prototype: J.J. Sylvester and the Johns Hopkins University -- Chapter 3. Mathematics at Sylvester's Hopkins -- Chapter 4. German mathematics and the early mathematical career of Felix Klein -- Chapter 5. America's wanderlust generation -- Chapter 6. Changes on the horizon -- Chapter 7. The World's Columbian exposition of 1893 and the Chicago mathematical congress -- Chapter 8. Surveying mathematical landscapes: The Evanston colloquium lectures -- Chapter 9. Meeting the challenge: The University of Chicago and the American mathematical research community -- Chapter 10. Epilogue: Beyond the threshold: The American mathematical research community, 1900-1933 -- Bibliography -- Subject Index -- Back Cover

How a new mathematical field grew and matured in America Graph Theory in America focuses on the development of graph theory in North America from 1876 to 1976. At the beginning of this period, James Joseph Sylvester, perhaps the finest mathematician in the English-speaking world, took up his appointment as the first professor of mathematics at the Johns Hopkins University, where his inaugural lecture outlined connections between graph theory, algebra, and chemistry—shortly after, he introduced the word graph in our modern sense. A hundred years later, in 1976, graph theory witnessed the solution of the long-standing four color problem by Kenneth Appel and Wolfgang Haken of the University of Illinois. Tracing graph theory’s trajectory across its first century, this book looks at influential figures in the field, both familiar and less known. Whereas many of the featured mathematicians spent their entire careers working on problems in graph theory, a few such as Hassler Whitney started there and then moved to work in other areas. Others, such as C. S. Peirce, Oswald Veblen, and George Birkhoff, made excursions into graph theory while continuing their focus elsewhere. Between the main chapters, the book provides short contextual interludes, describing how the American university system developed and how graph theory was progressing in Europe. Brief summaries of specific publications that influenced the subject’s development are also included. Graph Theory in America tells how a remarkable area of mathematics landed on American soil, took root, and flourished.