Sinopsis
Explore the math behind polynomials, solvability, and the surprising limits of what equations can reveal.
This accessible guide traces how mathematicians uncover why some polynomial equations can be solved with formulas and others cannot. It introduces ideas like resolvents, Galois theory, and the role of symmetry in equations, using concrete examples from cubic to quintic problems. The book blends historical insight with clear, intuitive explanations to show how abstract concepts connect to solvability.
- Learn how roots of equations relate to permutations and symmetry
- See why certain degrees of equations resist algebraic solutions
- Discover the idea of natural irrationalities and auxiliary equations
- Follow a coherent path from simple cases to the general theory of solvability
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Reseña del editor
Excerpt from Algebraic Equations
College of North Wales, for helping me by verifying some long cal culations which had to be made in connexion with Art. 52.
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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Reseña del editor
Galois. The conspicuous merit of this method is that it analyses, so far as exact algebraical processes permit, the set of roots possessed by any given numerical equation. To appreciate it properly it is necessary to bear constantly in mind the difference between equalities in value and identities or equivalences in form; I hope that this has been made sufficiently clear in the text. The method of A bel has not been discussed, because it is neither so clear nor so precise as that of Galois, and the space thus gained has been filled up with examples and illustrations. More than to any other treatise, I feel indebted toP rofessor H. Weber sinvaluable A lgebra, where students who are interested in the arithmetical branch of the subject will find a discussion of various types of equations, which, for lack of space, I have been compelled to omit. I am obliged toM rM orris Owen, a student of the University College of North Wales, for helping me by verifying some long calculations which had to be made in connexion with A rt. 52. G. B. M. Bangor, A ugust, 1907.
(Typographical errors above are due to OCR software and don't occur in the book.)
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Forgotten Books is a publisher of historical writings, such as: Philosophy, Classics, Science, Religion, History, Folklore and Mythology.
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Algebraic Equations (Classic Reprint)
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Paperback. Condición: New. Print on Demand. This book takes a scholarly approach to solving mathematical equations. It builds upon and expands a crucial method known as Galois theory, originally developed by Ãvariste Galois in the 19th century. Galois theory provides a framework for understanding the solvability of polynomial equations and explores properties of their roots. The method involves studying symmetries and structures within these equations, providing insights into their behavior and potential solutions. The author delves deep into the theoretical underpinnings of Galois theory, offering a comprehensive analysis of its concepts and applications. They guide readers through constructing equations and determining their solvability based on the Galois group associated with each equation. The book also examines the implications of adjoining irrational quantities to extend the field of rationality and simplify the Galois group, making it a valuable resource for mathematicians seeking to expand their knowledge of equation theory and the Galois theory that underpins it. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Nº de ref. del artículo: 9781440069826_0
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Algebraic Equations Classic Reprint
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PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781440069826
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PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781440069826
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Algebraic Equations (Classic Reprint)
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Paperback. Condición: Brand New. 76 pages. 9.00x6.00x0.18 inches. This item is printed on demand. Nº de ref. del artículo: zk1440069824
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