Abels Proof
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Author | : Peter Pesic |
Publisher | : MIT Press |
Total Pages | : 242 |
Release | : 2004-02-27 |
Genre | : Technology & Engineering |
ISBN | : 9780262661829 |
The intellectual and human story of a mathematical proof that transformed our ideas about mathematics. In 1824 a young Norwegian named Niels Henrik Abel proved conclusively that algebraic equations of the fifth order are not solvable in radicals. In this book Peter Pesic shows what an important event this was in the history of thought. He also presents it as a remarkable human story. Abel was twenty-one when he self-published his proof, and he died five years later, poor and depressed, just before the proof started to receive wide acclaim. Abel's attempts to reach out to the mathematical elite of the day had been spurned, and he was unable to find a position that would allow him to work in peace and marry his fiancé. But Pesic's story begins long before Abel and continues to the present day, for Abel's proof changed how we think about mathematics and its relation to the "real" world. Starting with the Greeks, who invented the idea of mathematical proof, Pesic shows how mathematics found its sources in the real world (the shapes of things, the accounting needs of merchants) and then reached beyond those sources toward something more universal. The Pythagoreans' attempts to deal with irrational numbers foreshadowed the slow emergence of abstract mathematics. Pesic focuses on the contested development of algebra—which even Newton resisted—and the gradual acceptance of the usefulness and perhaps even beauty of abstractions that seem to invoke realities with dimensions outside human experience. Pesic tells this story as a history of ideas, with mathematical details incorporated in boxes. The book also includes a new annotated translation of Abel's original proof.
Author | : Peter Pesic |
Publisher | : MIT Press |
Total Pages | : 222 |
Release | : 2016-06-17 |
Genre | : Technology & Engineering |
ISBN | : 0262338955 |
The intellectual and human story of a mathematical proof that transformed our ideas about mathematics. In 1824 a young Norwegian named Niels Henrik Abel proved conclusively that algebraic equations of the fifth order are not solvable in radicals. In this book Peter Pesic shows what an important event this was in the history of thought. He also presents it as a remarkable human story. Abel was twenty-one when he self-published his proof, and he died five years later, poor and depressed, just before the proof started to receive wide acclaim. Abel's attempts to reach out to the mathematical elite of the day had been spurned, and he was unable to find a position that would allow him to work in peace and marry his fiancé. But Pesic's story begins long before Abel and continues to the present day, for Abel's proof changed how we think about mathematics and its relation to the "real" world. Starting with the Greeks, who invented the idea of mathematical proof, Pesic shows how mathematics found its sources in the real world (the shapes of things, the accounting needs of merchants) and then reached beyond those sources toward something more universal. The Pythagoreans' attempts to deal with irrational numbers foreshadowed the slow emergence of abstract mathematics. Pesic focuses on the contested development of algebra—which even Newton resisted—and the gradual acceptance of the usefulness and perhaps even beauty of abstractions that seem to invoke realities with dimensions outside human experience. Pesic tells this story as a history of ideas, with mathematical details incorporated in boxes. The book also includes a new annotated translation of Abel's original proof.
Author | : V.B. Alekseev |
Publisher | : Springer Science & Business Media |
Total Pages | : 278 |
Release | : 2007-05-08 |
Genre | : Mathematics |
ISBN | : 1402021879 |
Do formulas exist for the solution to algebraical equations in one variable of any degree like the formulas for quadratic equations? The main aim of this book is to give new geometrical proof of Abel's theorem, as proposed by Professor V.I. Arnold. The theorem states that for general algebraical equations of a degree higher than 4, there are no formulas representing roots of these equations in terms of coefficients with only arithmetic operations and radicals. A secondary, and more important aim of this book, is to acquaint the reader with two very important branches of modern mathematics: group theory and theory of functions of a complex variable. This book also has the added bonus of an extensive appendix devoted to the differential Galois theory, written by Professor A.G. Khovanskii. As this text has been written assuming no specialist prior knowledge and is composed of definitions, examples, problems and solutions, it is suitable for self-study or teaching students of mathematics, from high school to graduate.
Author | : V.B. Alekseev |
Publisher | : Springer Science & Business Media |
Total Pages | : 278 |
Release | : 2004-05-31 |
Genre | : Mathematics |
ISBN | : 1402021860 |
Do formulas exist for the solution to algebraical equations in one variable of any degree like the formulas for quadratic equations? The main aim of this book is to give new geometrical proof of Abel's theorem, as proposed by Professor V.I. Arnold. The theorem states that for general algebraical equations of a degree higher than 4, there are no formulas representing roots of these equations in terms of coefficients with only arithmetic operations and radicals. A secondary, and more important aim of this book, is to acquaint the reader with two very important branches of modern mathematics: group theory and theory of functions of a complex variable. This book also has the added bonus of an extensive appendix devoted to the differential Galois theory, written by Professor A.G. Khovanskii. As this text has been written assuming no specialist prior knowledge and is composed of definitions, examples, problems and solutions, it is suitable for self-study or teaching students of mathematics, from high school to graduate.
Author | : Jörg Bewersdorff |
Publisher | : American Mathematical Soc. |
Total Pages | : 202 |
Release | : 2006 |
Genre | : Mathematics |
ISBN | : 0821838172 |
Galois theory is the culmination of a centuries-long search for a solution to the classical problem of solving algebraic equations by radicals. This book follows the historical development of the theory, emphasizing concrete examples along the way. It is suitable for undergraduates and beginning graduate students.
Author | : Henry Frederick Baker |
Publisher | : |
Total Pages | : 834 |
Release | : 1897 |
Genre | : Functions, Abelian |
ISBN | : |
Author | : John Edward Maxfield |
Publisher | : Courier Corporation |
Total Pages | : 228 |
Release | : 2010-03-01 |
Genre | : Mathematics |
ISBN | : 0486477231 |
The American Mathematical Monthly recommended this advanced undergraduate-level text for teacher education. It starts with groups, rings, fields, and polynomials and advances to Galois theory, radicals and roots of unity, and solution by radicals. Numerous examples, illustrations, commentaries, and exercises enhance the text, along with 13 appendices. 1971 edition.
Author | : |
Publisher | : |
Total Pages | : 636 |
Release | : 1911 |
Genre | : Photography |
ISBN | : |
Author | : Øystein Ore |
Publisher | : U of Minnesota Press |
Total Pages | : 306 |
Release | : 1957 |
Genre | : Biography & Autobiography |
ISBN | : 0816660247 |
Niels Henrik Abel was first published in 1957. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. Few men are more famous in the world of modern mathematics than Niels Henrik Abel, whose concepts and results are familiar to all present-day mathematicians. This volume, the first biography of Abel published in English, presents the story of the brilliant young Norwegian whose scientific achievements were not fully recognized until after his untimely death. It is also a case history of our perennial problem of how to detect genius and ease its path. Abel was born in 1802 in Finnoy, a little island on the coast of Norway. His father was a minister and politician of national importance, but his family descended from prominence to moral dissolution. Abel's studies were financed by his professors, aware of his extraordinary abilities. He was granted a fellowship to travel and study on the continent, and the year and a half which he then spent in Germany, Italy, and France was a most happy period in his life. When Abel returned to Norway, he could only obtain a temporary position, and in his last years he was harassed by grave difficulties. He managed, however, to write inspired mathematical articles which made a reputation for him among the mathematicians of Europe. Just as the security he longed for seemed within his grasp, he died of tuberculosis at the age of twenty-six. Abel's life has been the subject of several books, published in the Scandinavian countries, France, and Germany, but, in preparing this biography, Mr. Ore made use of much new material obtained from private letters, official documents, and newspaper files in various European sources.
Author | : Ivor Grattan-Guinness |
Publisher | : Elsevier |
Total Pages | : 1042 |
Release | : 2005-02-11 |
Genre | : Mathematics |
ISBN | : 0080457444 |
This book contains around 80 articles on major writings in mathematics published between 1640 and 1940. All aspects of mathematics are covered: pure and applied, probability and statistics, foundations and philosophy. Sometimes two writings from the same period and the same subject are taken together. The biography of the author(s) is recorded, and the circumstances of the preparation of the writing are given. When the writing is of some lengths an analytical table of its contents is supplied. The contents of the writing is reviewed, and its impact described, at least for the immediate decades. Each article ends with a bibliography of primary and secondary items. First book of its kind Covers the period 1640-1940 of massive development in mathematics Describes many of the main writings of mathematics Articles written by specialists in their field