Kategoria BISAC: Mathematics >> Algebra - General

In this book, the author writes freely and often humorously about his life, beginning with his earliest childhood days. He describes his survival of American bombing raids when he was a teenager in Japan, his emergence as a researcher in a post-war university system that was seriously deficient, and his life as a mature mathematician in Princeton and in the international academic community. Every page of this memoir contains personal observations and striking stories. Such luminaries as Chevalley, Oppenheimer, Siegel, and Weil figure prominently in its anecdotes.

Goro Shimura...

Graduated Algebra has been written to serve both as a ready reference book and a revision guide. Drawing on his extensive teaching experience the author has structured the book so that the students could self educate themselves with the all important Algebra skills.

Features of the book include:

1. Concise and clear explanation of each topic with

appropriate examples

2. Graded exercises with answers below each exercise

3. Avoidance of long and time consuming exercises

From a Geometrical Point of View explores historical and philosophical aspects of category theory, trying therewith to expose its significance in the mathematical landscape. The main thesis is that Klein s Erlangen program in geometry is in fact a particular instance of a general and broad phenomenon revealed by category theory. The volume starts with Eilenberg and Mac Lane s work in the early 1940 s and follows the major developments of the theory from this perspective. Particular attention is paid to the philosophical elements involved in this development. The book ends with a...

For many years, algebraic topology rests on three legs: "ordinary" cohomology, K-theory, and cobordism. This book is the first guide on the subject of cobordism since R. Stong's encyclopaedic and influential notes of a generation ago. It concentrates on Thom spaces (spectra), orientability theory and (co)bordism theory (including (co)bordism with singularities and, in particular, Morava K-theories), framed by (co)homology theories and spectra.

From the Foreword by Haynes Miller

The author has also performed a service to the history of science in this book, giving detailed...

Since its publication, C.F. Gauss's Disquisitiones Arithmeticae (1801) has acquired an almost mythical reputation, standing as an ideal of exposition in notation, problems and methods; as a model of organisation and theory building; and as a source of mathematical inspiration. Eighteen authors - mathematicians, historians, philosophers - have collaborated in this volume to assess the impact of the Disquisitiones, in the two centuries since its publication.

The worthy purpose of this text is to provide a complete, self-contained development of the trace formula and theta inversion formula for SL(2, Z i])SL(2, C). Unlike other treatments of the theory, the approach taken here is to begin with the heat kernel on SL(2, C) associated to the invariant Laplacian, which is derived using spherical inversion. The heat kernel on the quotient space SL(2, Z i])SL(2, C) is arrived at through periodization, and further expanded in an eigenfunction expansion. A theta inversion formula is obtained by studying the trace of the heat kernel. Following the...