Thesis (doctoral)--Universität Bern, 1910.

Thesis--Kaiserl. Alexanders-Universität in Finnland, 1916. / Includes bibliographical references.

Inaug.-dis.--Strassburg. / Lebenslauf.

Thesis--Catholic University of America, 1940. / Bibliography: p. 35.

Inaug.-diss.--Friedrichs Universität. / Lebenslauf.

Inaug.-diss.--Halle. / Lebenslauf.

"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).

In this research the Bring-Jerrard quintic polynomial equation is investigated for a formula. Firstly, an explanation given as to why finding a formula and the equation being unsolvable by radicals may appear contradictory when read out of context. Secondly, the reason why some mathematical software programs may fail to render a conclusive test of the formula, and how that can be corrected is explained. As an application, this formula is used to determine another formula that expresses the gravitational constant in terms of other known physical constants. It is also explained why up to now it has been impossible to determine this expression using the current underlying theoretical basis. / M. Sc. (Applied Mathematics)

In this research the Bring-Jerrard quintic polynomial equation is investigated for a formula. Firstly, an explanation given as to why finding a formula and the equation being unsolvable by radicals may appear contradictory when read out of context. Secondly, the reason why some mathematical software programs may fail to render a conclusive test of the formula, and how that can be corrected is explained. As an application, this formula is used to determine another formula that expresses the gravitational constant in terms of other known physical constants. It is also explained why up to now it has been impossible to determine this expression using the current underlying theoretical basis. / M. Sc. (Applied Mathematics)

Thesis (Ph. D.)--Ohio State University, 2008. / Title from first page of PDF file. Includes bibliographical references (p. 44).