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More information about this seller Contact this seller 1. Published by Moskva: Nauka, About this Item: Moskva: Nauka, Condition: Gut. Still Good.
Cover slightly used creased. Inside clean. More information about this seller Contact this seller 2. Condition: New. Language: English. Brand new Book. 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.
Abel's Theorem in Problems and Solutions. Based on the lectures of Professor V.I. Arnold by. V.B. Alekseev. Moscow State University,. Moscow. Abel's Theorem in Problems and Solutions. Based on the lectures of Professor V.I. Arnold. Authors: Alekseev, V.B.. Free Preview.
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.
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. Seller Inventory LHB More information about this seller Contact this seller 3. Published by Springer, Netherlands About this Item: Springer, Netherlands, Softcover reprint of the original 1st ed.
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Seller Inventory n. Condition: Used: Good. Softcover reprint of hardcover 1. Published by MGSU Thus our algebraists have cut out most of the course, but stick to the dogma that a group is a set with a binary operation satisfying various axioms. Groups can be taught as symmetry groups geometric transformation groups , and the abstract definition of groups held back until the student knows enough examples and methods of calculation to motivate all the definitions, and to see the point of isomorphism of groups. MR Nikulin, V. Geometries and groups. Translated from the Russian by M.
Springer-Verlag, Berlin, MR Alekseev, V. Abel's theorem in problems and solutions. Based on the lectures of Professor V. With a preface and an appendix by Arnold and an appendix by A. Kluwer Academic Publishers, Dordrecht, It is worth to read the first book on Group Theory -- W. Burnside, Theory of Groups of Finite Order -- to understand that abstract theory is usefull. By the way, sometime in the 19th century infinite groups were also considered as useless.
When I give lectures on the theory of groups for students, I end with Polya theory a simplified version. In it the same group acts on different sets, and therefore it is difficult to manage without abstract groups.
I suggest to take a look at the first chapter of the book "Algebra. A graduate course" by M. This may not be exactly what you wanted, since it assumes a little prior background in group theory, but Permutation Groups by Dixon and Mortimer certainly focuses on the perspective of permutation groups :.
While not? Cohen, R. Ushirobira and J. Draisma might offer some helpful ideas. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Ask Question. Asked 6 years ago. Active 2 years, 5 months ago.
Viewed 1k times. Some quotes to motivate the question: from V. Arnold, ' On Teaching Mathematics ': What is a group? Marius Kempe. Perhaps I'm biased from all my exposure to the 3-manifolds literature but my impression is that almost all modern group theory texts use this perspective as the primary perspective. He also said, if I remember correctly, that most graduates from ENS in France cannot add fractions because they are too busy studying schemes.