Series: Modern Birkhauser Classics
Originally published as a monograph
1st ed. 1999. 2nd printing, 2008, Approx. 380 p. 40 illus., Softcover
ISBN: 978-0-8176-4776-6
Due: February 2008
About this book
Presents the work of Bernhard Riemann from a historical perspective
Discusses the impact of Riemann's work on later math, physics, and philosophy
Examines the philosophy of Riemannian thought
The name of Bernard Riemann is well known to mathematicians and physicists around the world. College students encounter the Riemann integral early in their studies. Real and complex function theories are founded on Riemannfs work. Einsteinfs theory of gravitation would be unthinkable without Riemannian geometry. In number theory, Riemannfs famous conjecture stands as one of the classic challenges to the best mathematical minds and continues to stimulate deep mathematical research. The name is indelibly stamped on the literature of mathematics and physics.
This book, originally written in German and presented here in an English-language translation, examines Riemannfs scientific work from a single unifying perspective. Laugwitz describes Riemannfs development of a conceptual approach to mathematics at a time when conventional algorithmic thinking dictated that formulas and figures, rigid constructs, and transformations of terms were the only legitimate means of studying mathematical objects. David Hilbert gave prominence to the Riemannian principle of utilizing thought, not calculation, to achieve proofs. Hermann Weyl interpreted the Riemann principle ? for mathematics and physics alike ? to be a matter of "understanding the world through its behavior in the infinitely small."
This remarkable work, rich in insight and scholarship, is addressed to mathematicians, physicists, and philosophers interested in mathematics. It seeks to draw those readers closer to the underlying ideas of Riemannfs work and to the development of them in their historical context. This illuminating English-language version of the original German edition will be an important contribution to the literature of the history of mathematics.
Table of contents
Preface.- Note to the Reader.- List of Illustrations.- Translator's Remarks.- Introduction.- Complex Analysis.- Real Analysis.- Geometry; Physics; Philosophy.- Turning Points in the Conception of Mathematics.- Bibliography.- Name Index
Series: Modern Birkhauser Classics
Originally published as a monograph
2nd ed. 2000. 2nd printing, 2008, Approx. 360 p. 30 illus., Softcover
ISBN: 978-0-8176-4772-8
Due: February 2008
About this textbook
This book is a study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century. The central focus is on the convergence of three mathematical topics: the hypergeometric and related linear differential equations, group theory, and on-Euclidean geometry.
The text for this second edition has been greatly expanded and revised, and the existing appendices enriched with historical accounts of the Riemann?Hilbert problem, the uniformization theorem, Picard?Vessiot theory, and the hypergeometric equation in higher dimensions. The exercises have been retained, making it possible to use the book as a companion to mathematics courses at the graduate level.
Table of contents
Introduction to the Second Edition.- Introduction to the First Edition.- Hypergeometric Equations and Modular Equations.- Lazarus Fuchs.- Algebraic Solutions to a Differential Equation.- Modular Equations.- Some Algebraic Curves.- Automorphic Functions.- Appendices.- Notes.- Bibliography.- Historical.- Index.
Series: Modern Birkhauser Classics
Originally published as a monograph
Reprint of the 1997 ed., 2008, XXII, 280 p. 1 illus., Softcover
ISBN: 978-0-8176-4780-3
A Birkhauser book
Due: February 2008
About this book
Beautifully written perspectives on the nature of mathematics
Provides an excellent starting point for discussion and debate
Creates a source of supplemental reading for any course in the foundations or history of mathematics
Indiscrete Thoughts gives a glimpse into a world that has seldom been described, that of science and technology as seen through the eyes of a mathematician. The era covered by this book, 1950 to 1990, was surely one of the golden ages of science as well as of the American university.
Cherished myths are debunked along the way as Gian-Carlo Rota takes pleasure in portraying, warts and all, some of the great scientific personalities of the period ?Stanislav Ulam (who, together with Edward Teller, signed the patent application for the hydrogen bomb), Solomon Lefschetz (Chairman in the 1950s of the Princeton mathematics department), William Feller (one of the founders of modern probability theory), Jack Schwartz (one of the founders of computer science), and many others.
Rota is not afraid of controversy. Some readers may even consider these essays indiscreet. After the publication of the essay "The Pernicious Influence of Mathematics upon Philosophy" (reprinted six times in five languages) the author was blacklisted in analytical philosophy circles. Indiscrete Thoughts should become an instant classic and the subject of debate for decades to come.
Table of contents
Foreward by Reuben Hersh.- Foreward by Robert Sokolowski.- Introduction by Gian-Carlo Rota.- Fine Hall in its Golden Age Remembrances of Princeton in the Early Fifties.- Light Shadows Yale in the Early Fifties.- Combinatorics, Representation Theory and Invariant Theory The Story of a Menage a Trois.- The Barrier of Meaning.- Stan Ulam.- The Lost Cafe.- The Pernicious Influence of Mathematics Upon Philosophy.- Philosophy and Computer Science.- The Phenomenology of Mathematical Truth.- The Phenomenology of Mathematical Beauty.- The Phenomenology of Mathematical Proof.- Syntax, Semantics, and the Problem of the Identity of Mathematical Items.- The Barber of Seville or the Useless Precaution.- Kant and Husserl.- Fundierung as a Logical Concept.- The Primacy of Identity.- Three Senses of "A is B" in Heidegger.- Ten Lessons I Wish I Had Been Taught.- Ten Lessons for the Survival of a Mathematics Department.- A Mathematicianfs Gossip.- Book Reviews.- End Notes.- Epilogue by Fabrizion Palombi.- Index
Series: Trends in Mathematics
2008, Approx. 300 p., Hardcover
ISBN: 978-3-7643-8741-9
Due: April 2008
About this book
The 23 articles in this volume encompass the proceedings of the International Conference on Modules and Comodules held in Porto (Portugal) in 2006 and dedicated to Robert Wisbauer on the occasion of his 65th birthday. These articles reflect Professor Wisbauer's wide interests and give an overview of different fields related to module theory, some of which have a long tradition whereas others have emerged in recent years. They include topics in the formal theory of modules bordering on category theory, in ring theory, in Hopf algebras and quantum groups, and in corings and comodules.
Written for:
Postgraduates and researchers in module and ring theory and related areas like Hopf algebras and the theory of comodules and corings
Table of contents
Preface.- Injective Morita Contexts (Revisited).- A Categorical Proof of a Useful Result.- On Nichols algebras with generic braiding.- Dual algebras of some semisimple finite dimensional Hopf algebras.- Balanced Bilinear Forms for Corings.- Ring hulls of semiprime homomorphic images.- Notes on formal smoothness.- Certain Chain Conditions in Modules over Dedekind Domains and Related Rings.- Tau-Injective Modules.- A note on polynomial rings over nil rings.- QI-modules.- Corings with exact rational functors and injective objects.- Preradicals of associative algebras and their connections with preradicals of modules.- On the construction of separable modules.- Essential Extensions of a Direct Sum of Simple Modules-II.- Pseudo-Galois Extensions and Hopf Algebroids.- Cohereditary modules in sigma [M].- When maximal linearly independent subsets of a free module have the same cardinality?- Embedding group algebras into finite von Neumann regular rings.- The Local Multiplier Algebra: Blending Noncommutative Ring Theory and Functional Analysis.- On Some Injective Modules In sigma [M].- Biproducts and Two-Cocycle Twists of Hopf Algebras.
Series: Operator Theory: Advances and Applications , Vol. 185
2008, Approx. 300 p., Hardcover
ISBN: 978-3-7643-8754-9
Due: July 2008
About this book
The volume contains the proceedings of the OTAMP 2006 (Operator Theory, Analysis and Mathematical Physics) conference held at Lund University in June 2006. The conference was devoted to the methods of analysis and operator theory in modern mathematical physics. The following special sessions were organized during the conference: Spectral analysis of Schrodinger operators; Jacobi and CMV matrices and orthogonal polynomials; Quasi-periodic and random Schrodinger operators; Quantum graphs.
Written for:
Specialists in mathematical physics and operator theory
Keywords:
mathematical physics
operator theory
spectral theory