"In 1824, the Norwegian mathematician N. H. Abel (1802-1829) proved that the general polynomial equation of degree greater than four with real numbers as coefficients is not solvable by radicals. That is, the roots cannot be expressed by a formula involving only rational operations and radicals. This result was unexpected, since formulas are known for the quadratic, cubic, and quartic equations. Another brilliant mathematician, E. Galois (1811-1832), used the concept of a group to penetrate further into the nature of polynomial equations. The object of this paper is to prove the insolvability of the quintic equation. In the process portions of the theory of field extensions and Galois theory are developed. Most of this material can be found in A Survey of Modern Algebra, by G. Birkhoff and S. MacLane. Certain questions, however, are treated in more detail than is found in most textbooks which contain the subject. This is especially true for the proof of the existence of a quintic equation not solvable by radicals"--Introduction. / "May 28, 1952." / Typescript. / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: Nickolas Heerema, Professor Directing Paper. / Includes bibliographical references (leaf 49).
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_257215 |
| Contributors | Replogle, James (authoraut), Heerema, Nickolas (professor directing thesis.), Florida State University (degree granting institution) |
| Publisher | Florida State University, Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text |
| Format | 1 online resource (49 leaves), computer, application/pdf |
| Rights | This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). The copyright in theses and dissertations completed at Florida State University is held by the students who author them. |
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