Beyond the Quartic Equation (Modern Birkhäuser Classics) 1st Edition by R. Bruce King (PDF)

Description

The objective of this book is to present for the first time the complete algorithm for roots of the general quintic equation with enough background information to make the key ideas accessible to non-specialists and even to mathematically oriented readers who are not professional mathematicians. The book includes an initial introductory chapter on group theory and symmetry, Galois theory and Tschirnhausen transformations, and some elementary properties of elliptic function in order to make some of the key ideas more accessible to less sophisticated readers. The book also includes a discussion of the much simpler algorithms for roots of the general quadratic, cubic, and quartic equations before discussing the algorithm for the roots of the general quintic equation. A brief discussion of algorithms for roots of general equations of degrees higher than five is also included.”If you want something truly unusual, try [this book] by R. Bruce King, which revives some fascinating, long-lost ideas relating elliptic functions to polynomial equations.”–New Scientist

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The problem considered in the book is of great interest and is rarely exposed in modern literature.The book has pleasing elementary expositions on geometry of groups and galios theory. The description of the use of special functions(theta etc) is good. My only complaint is that I would have liked to see more about equations beyond the quintic. Also it might be fun to see how his code works

⭐King’s text is primarily concerned with the theory of finding the roots of a quintic polynomial. He masterfully sets forth a series of transformations based on icosahedral groups, Galois, Tschirnhausen, and other theories. King fails to include a single, practical example, however.

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