Abel’s Theorem in Problems and Solutions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Abel’s Theorem in Problems and Solutions write by V.B. Alekseev. This book was released on 2007-05-08. Abel’s Theorem in Problems and Solutions available in PDF, EPUB and Kindle. 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.
Abel’s Theorem in Problems and Solutions
Abel’s Theorem in Problems and Solutions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Abel’s Theorem in Problems and Solutions write by V.B. Alekseev. This book was released on 2004-05-31. Abel’s Theorem in Problems and Solutions available in PDF, EPUB and Kindle. 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.
Abel's Theorem in Problems and Solutions
Abel's Theorem in Problems and Solutions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Abel's Theorem in Problems and Solutions write by V. B. Alekseev. This book was released on 2014-01-15. Abel's Theorem in Problems and Solutions available in PDF, EPUB and Kindle.
Abel's Proof
Abel's Proof - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Abel's Proof write by Peter Pesic. This book was released on 2004-02-27. Abel's Proof available in PDF, EPUB and Kindle. 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.
ARNOLD: Swimming Against the Tide
ARNOLD: Swimming Against the Tide - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook ARNOLD: Swimming Against the Tide write by Boris A. Khesin. This book was released on 2014-09-10. ARNOLD: Swimming Against the Tide available in PDF, EPUB and Kindle. Vladimir Arnold, an eminent mathematician of our time, is known both for his mathematical results, which are many and prominent, and for his strong opinions, often expressed in an uncompromising and provoking manner. His dictum that "Mathematics is a part of physics where experiments are cheap" is well known. This book consists of two parts: selected articles by and an interview with Vladimir Arnold, and a collection of articles about him written by his friends, colleagues, and students. The book is generously illustrated by a large collection of photographs, some never before published. The book presents many a facet of this extraordinary mathematician and man, from his mathematical discoveries to his daredevil outdoor adventures.
