Download or read book Beyond the Quartic Equation written by R. Bruce King and published by Springer Science & Business Media. This book was released on 2009-01-16 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Geometry of the Quintic written by Jerry Michael Shurman and published by John Wiley & Sons. This book was released on 1997-01-31 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book helps students at the advanced undergraduate and beginning graduate levels to develop connections between the algebra, geometry, and analysis that they know, and to better appreciate the totality of what they have learned. The text demonstrates the use of general concepts by applying theorems from various areas in the context of one problem - solving the quintic. The problem is approached from two directions: the first is Felix Klein's nineteenth-century approach, using the icosahedron. The second approach presents recent works of Peter Doyle and Curt McMullen, which update Klein's use of transcendental functions to a solution through pure iteration.
Download or read book Solvable Quintic Equations With Commensurable Coefficients microform written by George Paxton 1819-1889 Young and published by Legare Street Press. This book was released on 2021-09-09 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Download or read book Topological Galois Theory written by Askold Khovanskii and published by Springer. This book was released on 2014-10-10 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed and largely self-contained description of various classical and new results on solvability and unsolvability of equations in explicit form. In particular, it offers a complete exposition of the relatively new area of topological Galois theory, initiated by the author. Applications of Galois theory to solvability of algebraic equations by radicals, basics of Picard–Vessiot theory, and Liouville's results on the class of functions representable by quadratures are also discussed. A unique feature of this book is that recent results are presented in the same elementary manner as classical Galois theory, which will make the book useful and interesting to readers with varied backgrounds in mathematics, from undergraduate students to researchers. In this English-language edition, extra material has been added (Appendices A–D), the last two of which were written jointly with Yura Burda.
Download or read book Solvable Quintic Equations with Commensurable Coefficients written by George Paxton Young and published by . This book was released on 1887 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Beyond the Quadratic Formula written by Ron Irving and published by American Mathematical Soc.. This book was released on 2020-01-29 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The quadratic formula for the solution of quadratic equations was discovered independently by scholars in many ancient cultures and is familiar to everyone. Less well known are formulas for solutions of cubic and quartic equations whose discovery was the high point of 16th century mathematics. Their study forms the heart of this book, as part of the broader theme that a polynomial's coefficients can be used to obtain detailed information on its roots. The book is designed for self-study, with many results presented as exercises and some supplemented by outlines for solution. The intended audience includes in-service and prospective secondary mathematics teachers, high school students eager to go beyond the standard curriculum, undergraduates who desire an in-depth look at a topic they may have unwittingly skipped over, and the mathematically curious who wish to do some work to unlock the mysteries of this beautiful subject.
Download or read book Associate Equations of Linear Differential Equations written by Daniel Alexander Murray and published by . This book was released on 1894 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Essentials of Mathematics written by Margie Hale and published by MAA. This book was released on 2003-12-24 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: Textbook and self-study guide for students beginning to study mathematics requiring proof.
Download or read book Library of Congress Subject Headings written by Library of Congress and published by . This book was released on 1995 with total page 1408 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The History of Mathematics A Source Based Approach Volume 2 written by June Barrow-Green and published by American Mathematical Society. This book was released on 2022-05-26 with total page 703 pages. Available in PDF, EPUB and Kindle. Book excerpt: The History of Mathematics: A Source-Based Approach is a comprehensive history of the development of mathematics. This, the second volume of a two-volume set, takes the reader from the invention of the calculus to the beginning of the twentieth century. The initial discoverers of calculus are given thorough investigation, and special attention is also paid to Newton's Principia. The eighteenth century is presented as primarily a period of the development of calculus, particularly in differential equations and applications of mathematics. Mathematics blossomed in the nineteenth century and the book explores progress in geometry, analysis, foundations, algebra, and applied mathematics, especially celestial mechanics. The approach throughout is markedly historiographic: How do we know what we know? How do we read the original documents? What are the institutions supporting mathematics? Who are the people of mathematics? The reader learns not only the history of mathematics, but also how to think like a historian. The two-volume set was designed as a textbook for the authors' acclaimed year-long course at the Open University. It is, in addition to being an innovative and insightful textbook, an invaluable resource for students and scholars of the history of mathematics. The authors, each among the most distinguished mathematical historians in the world, have produced over fifty books and earned scholarly and expository prizes from the major mathematical societies of the English-speaking world.
Download or read book Annals of Mathematics written by and published by . This book was released on 1928 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: Founded in 1884, Annals of Mathematics publishes research papers in pure mathematics.
Download or read book Library of Congress Subject Headings written by Library of Congress. Office for Subject Cataloging Policy and published by . This book was released on 1991 with total page 1580 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book American Journal of Mathematics written by and published by . This book was released on 1886 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ramanujan s Place in the World of Mathematics written by Krishnaswami Alladi and published by Springer Science & Business Media. This book was released on 2012-10-30 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of articles, all by the author, on the Indian mathematical genius Srinivasa Ramanujan as well as on some of the greatest mathematicians throughout the history whose life and works have things in common with Ramanujan. It presents a unique comparative study of Ramanujan’s spectacular discoveries and remarkable life and of the monumental contributions of various mathematical luminaries, some of whom, like Ramanujan, overcame great difficulties in life. In the book, some aspects of Ramanujan’s contributions, such as his remarkable formulae for the number pi, his pathbreaking work in the theory of partitions, and his fundamental observations on quadratic forms, are discussed. Finally, the book describes various current efforts to ensure that the legacy of Ramanujan will be preserved and continue to thrive in the future. Thus the book is an enlightening study of Ramanujan as a mathematician and a human being.
Download or read book Library of Congress Subject Headings written by Library of Congress. Subject Cataloging Division and published by Washington, D.C. : Cataloging Distribution Service, Library of Congress. This book was released on 1988 with total page 1348 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Library of Congress Subject Headings written by Library of Congress. Cataloging Policy and Support Office and published by . This book was released on 2009 with total page 1688 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Abel s Proof written by Peter Pesic and published by MIT Press. This book was released on 2004-02-27 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
