Unraveling The Enigma Of Riemann S Zeta Function A Journey Through The Realm Of Analytic Number Theory
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Unraveling the Enigma of Riemann's Zeta-Function: A Journey Through the Realm of Analytic Number Theory
Author: Pasquale De Marco
language: en
Publisher: Pasquale De Marco
Release Date: 2025-07-10
In the vast expanse of mathematical inquiry, few concepts have captured the imagination and ignited the curiosity of scholars like the Riemann zeta-function. Introduced by Bernhard Riemann in the 19th century, this enigmatic function has stood as a towering enigma, challenging mathematicians and inspiring generations of exploration. This comprehensive and engaging book invites you on an intellectual journey through the captivating world of the Riemann zeta-function, unveiling its intricate properties, profound applications, and historical significance. Delve into the depths of analytic number theory as we navigate concepts like Dirichlet's theorem, the prime number theorem, and the Riemann zeta-function's relationship with other mathematical functions. Unravel the mysteries surrounding the Riemann hypothesis, a conjecture that has captivated mathematicians for over a century. Discover the profound implications of this hypothesis, its potential to unlock the secrets of prime numbers, and its role in shaping our understanding of the fundamental nature of mathematics. Witness the Riemann zeta-function's remarkable applications in diverse fields, ranging from physics and computer science to finance and engineering. Explore its contributions to quantum field theory, string theory, coding theory, and cryptography, gaining insights into the function's versatility and far-reaching impact. Trace the Riemann zeta-function's historical significance, from its introduction by Riemann to its enduring legacy in modern mathematics. Learn about the brilliant minds who have dedicated their lives to studying this function, their contributions to the field, and the ongoing pursuit of knowledge that continues to drive research in this captivating area. Join us on this intellectual odyssey as we unravel the enigma of the Riemann zeta-function, embarking on an exploration that promises to expand your horizons, deepen your understanding of mathematics, and ignite your passion for discovery. Prepare to be captivated by the beauty, elegance, and profound implications of this mathematical marvel. If you like this book, write a review!
Mind and Nature
Author: Hermann Weyl
language: en
Publisher: Princeton University Press
Release Date: 2009-03-31
Hermann Weyl (1885-1955) was one of the twentieth century's most important mathematicians, as well as a seminal figure in the development of quantum physics and general relativity. He was also an eloquent writer with a lifelong interest in the philosophical implications of the startling new scientific developments with which he was so involved. Mind and Nature is a collection of Weyl's most important general writings on philosophy, mathematics, and physics, including pieces that have never before been published in any language or translated into English, or that have long been out of print. Complete with Peter Pesic's introduction, notes, and bibliography, these writings reveal an unjustly neglected dimension of a complex and fascinating thinker. In addition, the book includes more than twenty photographs of Weyl and his family and colleagues, many of which are previously unpublished. Included here are Weyl's exposition of his important synthesis of electromagnetism and gravitation, which Einstein at first hailed as "a first-class stroke of genius"; two little-known letters by Weyl and Einstein from 1922 that give their contrasting views on the philosophical implications of modern physics; and an essay on time that contains Weyl's argument that the past is never completed and the present is not a point. Also included are two book-length series of lectures, The Open World (1932) and Mind and Nature (1934), each a masterly exposition of Weyl's views on a range of topics from modern physics and mathematics. Finally, four retrospective essays from Weyl's last decade give his final thoughts on the interrelations among mathematics, philosophy, and physics, intertwined with reflections on the course of his rich life.
The Topological Classification of Stratified Spaces
Author: Shmuel Weinberger
language: en
Publisher: University of Chicago Press
Release Date: 1994
This book provides the theory for stratified spaces, along with important examples and applications, that is analogous to the surgery theory for manifolds. In the first expository account of this field, Weinberger provides topologists with a new way of looking at the classification theory of singular spaces with his original results. Divided into three parts, the book begins with an overview of modern high-dimensional manifold theory. Rather than including complete proofs of all theorems, Weinberger demonstrates key constructions, gives convenient formulations, and shows the usefulness of the technology. Part II offers the parallel theory for stratified spaces. Here, the topological category is most completely developed using the methods of "controlled topology." Many examples illustrating the topological invariance and noninvariance of obstructions and characteristic classes are provided. Applications for embeddings and immersions of manifolds, for the geometry of group actions, for algebraic varieties, and for rigidity theorems are found in Part III. This volume will be of interest to topologists, as well as mathematicians in other fields such as differential geometry, operator theory, and algebraic geometry.