Bücher von Jeremy Gray

This book is a compact clinical introduction to Lyme borreliosis for physicians of all specialties who care for patients with suspected B. burgdorferi infection, whether in hospital or general practice. The book provides a great deal of practice-oriented information on symptomatology, diagnosis, treatment, and prophylaxis with a special emphasis on the situation in Europe. At the same time, it describes contemporary scientific knowledge in as much detail as is required in order to understand the pathogenetic relationships and their relevance to medical care. The authors are members of an interdisciplinary expert group of epidemiologists, biologists, microbiologists, and clinicians who have been working in the area of tick-borne diseases for many years. The personal experience of each of the authors, accumulated through their daily work with patients in special clinics or by confrontation with complicated questions in basic research, epidemiology, and laboratory diagnostics of Lyme borreliosis, represents an important mainstay of the book. Written from the perspective of clinical management and practical problem-solving, this topical monograph will assist clinicians in meeting diagnostic challenges and providing appropriate medical aid to patients with Lyme borreliosis.

This book details the history of complex function theory. It examines the rise of elliptic function theory, differential equations in the complex domain, geometric function theory, and the early years of complex function theory in several variables.

This textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in the seventeenth and eighteenth centuries, and exploring the impact of ideas on the development of the subject.Beginning with Gauss's theory of numbers and Galois's ideas, the book progresses to Dedekind and Kronecker, Jordan and Klein, Steinitz, Hilbert, and Emmy Noether. Approaching mathematical topics from a historical perspective, the author explores quadratic forms, quadratic reciprocity, Fermat's Last Theorem, cyclotomy, quintic equations, Galois theory, commutative rings, abstract fields, ideal theory, invariant theory, and group theory. Readers will learn what Galois accomplished, how difficult the proofs of his theorems were, and how important Camille Jordan and Felix Klein were in the eventual acceptance of Galois's approach to the solution of equations. The book also describes the relationship between Kummer's ideal numbers and Dedekind's ideals, and discusses why Dedekind felt his solution to the divisor problem was better than Kummer's. Designed for a course in the history of modern algebra, this book is aimed at undergraduate students with an introductory background in algebra but will also appeal to researchers with a general interest in the topic. With exercises at the end of each chapter and appendices providing material difficult to find elsewhere, this book is self-contained and therefore suitable for self-study.

This book contains a history of real and complex analysis in the nineteenth century, from the work of Lagrange and Fourier to the origins of set theory and the modern foundations of analysis.

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.