History Algebraic Geometry PDF Download

Author: Suzanne C. Dieudonne
Publisher: CRC Press
ISBN: 9780412993718
Category : Mathematics
Languages : en
Pages : 202

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Book Description
This book contains several fundamental ideas that are revived time after time in different guises, providing a better understanding of algebraic geometric phenomena. It shows how the field is enriched with loans from analysis and topology and from commutative algebra and homological algebra.

Author: Carl B. Boyer
Publisher: Courier Corporation
ISBN: 0486154513
Category : Mathematics
Languages : en
Pages : 306

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Book Description
This study presents the concepts and contributions from before the Alexandrian Age through to Fermat and Descartes, and on through Newton and Euler to the "Golden Age," from 1789 to 1850. 1956 edition. Analytical bibliography. Index.

Author: Jean Dieudonné
Publisher: Springer Science & Business Media
ISBN: 0817649077
Category : Mathematics
Languages : en
Pages : 648

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Book Description
This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincaré and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results.... Within its chosen boundaries the coverage of this book is superb. Read it! —MathSciNet

Author: Suzanne C. Dieudonne
Publisher: CRC Press
ISBN: 1351440543
Category : Mathematics
Languages : en
Pages : 186

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Book Description
This book contains several fundamental ideas that are revived time after time in different guises, providing a better understanding of algebraic geometric phenomena. It shows how the field is enriched with loans from analysis and topology and from commutative algebra and homological algebra.

Author: Bartel L. van der Waerden
Publisher: Springer Science & Business Media
ISBN: 3642617794
Category : Mathematics
Languages : en
Pages : 236

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Book Description
Originally, my intention was to write a "History of Algebra", in two or three volumes. In preparing the first volume I saw that in ancient civiliza tions geometry and algebra cannot well be separated: more and more sec tions on ancient geometry were added. Hence the new title of the book: "Geometry and Algebra in Ancient Civilizations". A subsequent volume on the history of modem algebra is in preparation. It will deal mainly with field theory, Galois theory and theory of groups. I want to express my deeply felt gratitude to all those who helped me in shaping this volume. In particular, I want to thank Donald Blackmore Wagner (Berkeley) who put at my disposal his English translation of the most interesting parts of the Chinese "Nine Chapters of the Art of Arith metic" and of Liu Hui's commentary to this classic, and also Jacques Se siano (Geneva), who kindly allowed me to use his translation of the re cently discovered Arabic text of four books of Diophantos not extant in Greek. Warm thanks are also due to Wyllis Bandler (Colchester, England) who read my English text very carefully and suggested several improve ments, and to Annemarie Fellmann (Frankfurt) and Erwin Neuenschwan der (Zurich) who helped me in correcting the proof sheets. Miss Fellmann also typed the manuscript and drew the figures. I also want to thank the editorial staff and production department of Springer-Verlag for their nice cooperation.

Author: Igor V. Dolgachev
Publisher: Cambridge University Press
ISBN: 1139560786
Category : Mathematics
Languages : en
Pages : 653

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Book Description
Algebraic geometry has benefited enormously from the powerful general machinery developed in the latter half of the twentieth century. The cost has been that much of the research of previous generations is in a language unintelligible to modern workers, in particular, the rich legacy of classical algebraic geometry, such as plane algebraic curves of low degree, special algebraic surfaces, theta functions, Cremona transformations, the theory of apolarity and the geometry of lines in projective spaces. The author's contemporary approach makes this legacy accessible to modern algebraic geometers and to others who are interested in applying classical results. The vast bibliography of over 600 references is complemented by an array of exercises that extend or exemplify results given in the book.

Author: John Derbyshire
Publisher: Penguin
ISBN: 0452288533
Category : Mathematics
Languages : en
Pages : 393

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Book Description
Perfect for history buffs and armchair algebra experts, Unknown Quantity tells the story of the development of abstract mathematical thought. John Derbyshire discovers the story behind the formulae, roots, and radicals. As he did so masterfully in Prime Obsession, Derbyshire brings the evolution of mathematical thinking to dramatic life by focusing on the key historical players. Unknown Quantity begins in the time of Abraham and Isaac and moves from Abel's proof to the higher levels of abstraction developed by Galois through modern-day advances. Derbyshire explains how a simple turn of thought from "this plus this equals this" to "this plus what equals this?" gave birth to a whole new way of perceiving the world. With a historian's narrative authority and a beloved teacher's clarity and passion, Derbyshire leads readers on an intellectually satisfying and pleasantly challenging historical and mathematical journey.

Author: Ciro Ciliberto
Publisher: Springer Nature
ISBN: 3030710211
Category : Mathematics
Languages : en
Pages : 327

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Book Description
This book consists of two parts. The first is devoted to an introduction to basic concepts in algebraic geometry: affine and projective varieties, some of their main attributes and examples. The second part is devoted to the theory of curves: local properties, affine and projective plane curves, resolution of singularities, linear equivalence of divisors and linear series, Riemann–Roch and Riemann–Hurwitz Theorems. The approach in this book is purely algebraic. The main tool is commutative algebra, from which the needed results are recalled, in most cases with proofs. The prerequisites consist of the knowledge of basics in affine and projective geometry, basic algebraic concepts regarding rings, modules, fields, linear algebra, basic notions in the theory of categories, and some elementary point–set topology. This book can be used as a textbook for an undergraduate course in algebraic geometry. The users of the book are not necessarily intended to become algebraic geometers but may be interested students or researchers who want to have a first smattering in the topic. The book contains several exercises, in which there are more examples and parts of the theory that are not fully developed in the text. Of some exercises, there are solutions at the end of each chapter.

Author: S. G. Dani
Publisher: Springer Nature
ISBN: 3030136094
Category : Mathematics
Languages : en
Pages : 759

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Book Description
This is a collection of surveys on important mathematical ideas, their origin, their evolution and their impact in current research. The authors are mathematicians who are leading experts in their fields. The book is addressed to all mathematicians, from undergraduate students to senior researchers, regardless of the specialty.

Author: Jeremy J. Gray
Publisher: American Mathematical Soc.
ISBN: 0821869043
Category : Mathematics
Languages : en
Pages : 346

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Book Description
Algebra, as a subdiscipline of mathematics, arguably has a history going back some 4000 years to ancient Mesopotamia. The history, however, of what is recognized today as high school algebra is much shorter, extending back to the sixteenth century, while the history of what practicing mathematicians call "modern algebra" is even shorter still. The present volume provides a glimpse into the complicated and often convoluted history of this latter conception of algebra by juxtaposing twelve episodes in the evolution of modern algebra from the early nineteenth-century work of Charles Babbage on functional equations to Alexandre Grothendieck's mid-twentieth-century metaphor of a ``rising sea'' in his categorical approach to algebraic geometry. In addition to considering the technical development of various aspects of algebraic thought, the historians of modern algebra whose work is united in this volume explore such themes as the changing aims and organization of the subject as well as the often complex lines of mathematical communication within and across national boundaries. Among the specific algebraic ideas considered are the concept of divisibility and the introduction of non-commutative algebras into the study of number theory and the emergence of algebraic geometry in the twentieth century. The resulting volume is essential reading for anyone interested in the history of modern mathematics in general and modern algebra in particular. It will be of particular interest to mathematicians and historians of mathematics.