This book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem.

This second edition contains two new chapters that provide a complete proof of the Mordel-Weil theorem for elliptic curves over the rational numbers and an overview of recent progress on the arithmetic of elliptic curves.

... 0072-5285 ; 86 ) Includes bibliographical references and index . ISBN 978-3-642-63653-0 ISBN 978-3-642-58575-3 ( eBook ) DOI 10.1007 / 978-3-642-58575-3 1. Coding theory . I. Title . II . Series . QA268 .L57 1998 003'.54 -- dc21 98 ...

This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism.

By the year 1950 the defini tion of fibre bundle had been clearly formulated, the homotopy classifica tion of fibre bundles achieved, and the theory of characteristic classes of fibre bundles developed by several mathematicians, Chern, ...

This volume is geared toward a second-year graduate course, but it leads naturally to the study of more advanced books listed in the bibliography.

Based on a graduate course at the Technische Universität, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes.

"This book succeeds brilliantly by concentrating on a number of core topics...and by treating them in a hugely rich and varied way.

But because the text is intended for beginning graduate students, it does not require graduate algebra, and in particular, does not assume that the reader is familiar with modules.

Review of the first edition: This is an excellent book.