Introduction to Modern Mathematics (Second Edition) (Photo-reproduction Edition)

Author: Yu.I.Manin
Publisher:
Publish Date: 2006-01-17
Features: This book provides a unified perspective on the current state of number theory and the development trends of its various branches, starting from fundamental questions and revealing the central ideas of modern number theory. The main topics include the non-Abelian generalization of class field theory, recursive computation, Diophantine equations, Zeta-functions, and L-functions. The new edition of this book has been extensively revised and expanded in content, adding several new chapters such as Wiles' proof of Fermat's Last Theorem and the techniques in modern number theory derived from the integration of different theories. Additionally, the author has included a dedicated chapter on arithmetic homology and noncommutative geometry, a report on counting points in varieties with multiple rational points, polynomial-time algorithms for primality testing, and other topics.