Heinrich Weber

This book is the first English translation of the classic long paper Theorie der algebraischen Functionen einer Veranderlichen (Theory of algebraic functions of one variable), published by Dedekind and Weber in 1882. The translation has been enriched by a Translator's Introduction that provides historical background, and extensive commentary embedded in the translation itself. The translation, introduction, and commentary provide the first easy access to this important paper for a wide mathematical audience: students, historians of mathematics, and professional mathematicians. Why is the Dedekind-Weber paper important? In the 1850s, Riemann initiated a revolution in algebraic geometry by interpreting algebraic curves as surfaces covering the sphere. He obtained deep and striking results in pure algebra by intuitive arguments about surfaces and their topology. However, Riemann's arguments were not rigorous, and they remained in limbo until 1882, when Dedekind and Weber put them on a sound foundation. The key to this breakthrough was to develop the theory of algebraic functions in analogy with Dedekind's theory of algebraic numbers, where the concept of ideal plays a central role. By introducing such concepts into the theory of algebraic curves, Dedekind and Weber paved the way for modern algebraic geometry.

Estimates show that there are around 20,000 Ultra High Net Worth individuals in existence today, each with bankable assets in excess of $50 million. Between them they possess a wealth of $5,000 billion, 10 per cent of the world's estimated total wealth. The UHNW wealth management business is therefore a critically important as well as complex part of modern finance. It exists within a 'client-banker-bank' triangle and is influenced by serious exogenous factors in political, economic and fiscal environments, as well as by numerous emotional, familial and personal dimensions. In this book, the authors address these complex relationships, serving as guides and advisors for UHNW bankers, banks and clients alike. The authors' clients have taught them that the three major frustrations for private banking clients are bad performance, bad communication with the banker, and confusion in the face of poorly explained financial processes. In the first part of the book, the authors offer their expert solutions to these problems and, in the second, help to eliminate confusion by explaining UHNW financial processes as clearly and simply as possible. The authors mix authoritative advice, gained from long careers in wealth management, with anecdotes and narrative, to make the book approachable as well as informative. The book also contains five major case studies that help to exemplify certain elements involved in UHNW banking across the world, including the importance and impact of: family values and governance; client confidence and connections; cultural and religious considerations; philanthropy; market crises and volatility; and, portfolio diversity and enterprise management. This book is for private bankers who work or aim to work in the Ultra High Net Worth field, the most sought-after and secluded high-end client segment of private banking and wealth management. For UHNW clients, this book is a guide on how to deal with your bankers and what you can expect from them, depicting the view from the other side of the table. And for the management of a private bank or private banking division of a financial institution, this book will serve as an essential introduction on how to improve performance. Expert, in-depth and accessible, "The Ultra High Net Worth Banker's Handbook" is the ultimate guide to this area of modern finance.