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Algebraic Geometry
"Surveys and applies fundamental ideas and techniques in the theory of curves, surfaces, and threefolds to a wide variety of subjects. Furnishes all of the basic definitions necessary for understanding and provides interrelated articles that support and refer to one another."
The Richness of the History of Mathematics
This book, a tribute to historian of mathematics Jeremy Gray, offers an overview of the history of mathematics and its inseparable connection to philosophy and other disciplines. Many different approaches to the study of the history of mathematics have been developed. Understanding this diversity is central to learning about these fields, but very few books deal with their richness and concrete suggestions for the “what, why and how” of these domains of inquiry. The editors and authors approach the basic question of what the history of mathematics is by means of concrete examples. For the “how” question, basic methodological issues are addressed, from the different perspectives of mathematicians and historians. Containing essays by leading scholars, this book provides a multitude of perspectives on mathematics, its role in culture and development, and connections with other sciences, making it an important resource for students and academics in the history and philosophy of mathematics.
A Richer Picture of Mathematics
Historian David E. Rowe captures the rich tapestry of mathematical creativity in this collection of essays from the “Years Ago” column of The Mathematical Intelligencer. With topics ranging from ancient Greek mathematics to modern relativistic cosmology, this collection conveys the impetus and spirit of Rowe’s various and many-faceted contributions to the history of mathematics. Centered on the Göttingen mathematical tradition, these stories illuminate important facets of mathematical activity often overlooked in other accounts. Six sections place the essays in chronological and thematic order, beginning with new introductions that contextualize each section. The essays that follow re...
Framing Global Mathematics
This open access book is about the shaping of international relations in mathematics over the last two hundred years. It focusses on institutions and organizations that were created to frame the international dimension of mathematical research. Today, striking evidence of globalized mathematics is provided by countless international meetings and the worldwide repository ArXiv. The text follows the sinuous path that was taken to reach this state, from the long nineteenth century, through the two wars, to the present day. International cooperation in mathematics was well established by 1900, centered in Europe. The first International Mathematical Union, IMU, founded in 1920 and disbanded in 1...
Logic's Lost Genius
Gerhard Gentzen (1909–1945) is the founder of modern structural proof theory. His lasting methods, rules, and structures resulted not only in the technical mathematical discipline called “proof theory” but also in verification programs that are essential in computer science. The appearance, clarity, and elegance of Gentzen's work on natural deduction, the sequent calculus, and ordinal proof theory continue to be impressive even today. The present book gives the first comprehensive, detailed, accurate scientific biography expounding the life and work of Gerhard Gentzen, one of our greatest logicians, until his arrest and death in Prague in 1945. Particular emphasis in the book is put on...
A Historical Dictionary of Mathematical Terms
This unique reference work systematically presents and studies mathematical terms, sourcing literature from antiquity until the 20th century. The book provides detailed and reliable information on the origins and developments of more than 1,000 mathematical terms from all branches of mathematics. The dictionary is based on extensive research of the primary literature, cites from original sources, provides historical illustrations, discusses synonyms and competing terms, and quotes critical or approving comments on newly created terms. Each entry is self-contained and includes a bibliography. All major mathematical fields are represented, ranging from geometry and arithmetic to, for example, calculus, topology, and category theory. This is the first of two volumes, covering terms that begin with the letters A through I.
Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes)
The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
Common Inessential Discriminant Divisors
In mathematics, technical difficulties can spark groundbreaking ideas. This book explores one such challenge: a problem that arose in the formative years of algebraic number theory and played a major role in the early development of the field. When nineteenth-century mathematicians set out to generalize E. E. Kummer's theory of ideal divisors in cyclotomic fields, they discovered that the existence of ?common inessential discriminant divisors? blocked the obvious path. Through extensively annotated translations of key papers, this book traces how Richard Dedekind, Leopold Kronecker, and Kurt Hensel approached these divisors, using them to justify the need for entirely new mathematical ideas and to demonstrate their power. Mathematicians interested in algebraic number theory will enjoy seeing what the field, which is still evolving today, looked like in its very early days. Historians of mathematics will find interesting questions for further study. Engaging and carefully researched, Common Inessential Discriminant Divisors is both a historical study and an invitation to experience mathematics as it was first discovered.
Class Field Theory
This volume is a collection of articles contributed by the speakers at the Mathematical Society of Japan's Seventh International Research Institute entitled, ``Class Field Theory-Its Centenary and Prospect'', held in Tokyo in June 1998. Some of the articles are expository; they discuss important interesting aspects of class field theory and contain full references. Other articles are historical; they vividly explain how leading number theorists in Europe and Japan developed and exchanged their mathematical ideas.
Mathematical Reviews
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