#### Date of Award

8-1945

#### Document Type

Thesis

#### Degree Name

Master of Science

#### Degree Discipline

Mathematics

#### Abstract

Origin and History of the Problem: The science of algebra arose In its effort to solve equations. Since the main objects in algebra have been the discussion of equalities and the transformation of forms into simpler equivalent ones, that science may well be called the Science of Equations. The solution of an equation containing one unknown quantity consists in the determination of Its value or values, these being called roots. An algebraic equation of degree n has n roots, while transcendental equations have an infinite number of roots. There has existed for years the problem of finding values, as exact as possible, or as close as one wishes of these roots. This problem still has not been satisfactorily solved. It is the object of researchers to continue work to the end of calculating all of the real and complex roots of algebraic and transcendental equations simultaneously by a single method. Thus, Lagrange, at the beginning of his manuscript on "The Solution of Numerical Equations" (1767), published his first memoirs which were followed by works of Harriot, Ougtred, Pell, and others. Descartes has assisted in these findings by his rule of signs, which though fundamentally important, lacks sufficient accuracy. The greatest analysis initiated by Newton and terminated by Lagrange made a decisive step from Descartes' theory by using "the squares of the differences." This method was simple in theory but necessitated tiring and sometimes indefinite conclusions. Fourier attained approximately the same conclusions in his efforts. In 1820, he published a rule which he had formulated and used for several years. Though his rule lacked satisfactory proof, his findings at least aided Sturm with his theories advanced several years later. This theorem concerns only a derivative and the function itself which is somewhat similar to the highest common factor.

#### Committee Chair/Advisor

A. W. Randall

#### Committee Member

C. P. Stephens

#### Committee Member

C. P. Stephens

#### Committee Member

J. S. Flipper

#### Publisher

Prairie View State University

#### Rights

© 2021 Prairie View A & M UniversityThis work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

#### Date of Digitization

11/10/2021

#### Contributing Institution

John B Coleman Library

#### City of Publication

Prairie View

#### MIME Type

Application/PDF

#### Recommended Citation

Stubblefield, B. (1945). Computation Of The Real And Complex Roots Of Algebraic And Transcendental Equations. Retrieved from https://digitalcommons.pvamu.edu/pvamu-theses/703