Mathematics Commons^™

Solution To Theory Of Equations For Teachers And Graduate Students, Arthur Lawrence Birkholz

Bachelors’ Theses

This thesis is intended primarily for teachers and graduate students who often find it necessary to review all or part of the basic theorems in the study of equations. Dickson's excellent book on the subject, "First Course in the Theory of Equations", is a recognized authority, so to facilitate a study of this book the writer has worked the problems suggested by Dickson, because these problems, more than any explanation could, illustrate and simplify the theorems on equations.

The user of this work-must bear in mind that there may be several ways of working many of the problems, and hence …

The Construction Of Triangles Having Given Three Elements, Mary Eugene Wolter

Bachelors’ Theses

It is with great pleasure and satisfaction that I dedicate these following pages to those who are especially interested in mathematics, to those who are more geometrically than algebraically inclined, and in particular to my students in mathematics. It is through my students of the past that I have been assisted in bringing forth this work, by applying such knowledge as I have acquired in my teaching experience. To the pupils who in the future will come under my guidance and direction I hope to impart the benefits and fruits that should be the outgrowth of the labor and study …

The Summation Of The Series X+X/4+X/9+...+X/N-+.., William J. Nee

Bachelors’ Theses

The purpose of this thesis is to determine the sum of the series x+4²/4+x³/9+x⁴/16+....xⁿ/n². In order to determine whether or not the series is summable, we must first find out if it is a convergent series and so the first part of this paper will deal with some of the tests of convergence. After this matter is settles, we shall select a value of x, in this case x=1 and determine the ^∞∑/1 1/n2

Graphical Representations Of Singular Solutions Of Differential Equations, Kathryn Lois Pitman

Bachelors’ Theses

The first men to detect singular solutions of differential equations were Leibniz, Brook Taylor and Clairaut. The direct method of attack used by each man in attaining these solutions is not known, but a short history of each man and what he has contributed to mathematics can be given. Gottfried Wilhelm von Leibniz (1646-1716) was born in Leipsic, Germany, and was the son of a professor of law in a nearby university. He was well-educated in law himself, expecting to follow in the profession of his father. But not being under the necessity of earning his living, he enrolled at …

Unicursal Bicircular Quartic Studied By Inversion, William A. Uporsky

Bachelors’ Theses

The quartic equation was studied by Arab scholars after their attention to the results of their study of a cubic had not proved very significant. Abu'l-Faradsh completed the Fihrist (c, 987), and in this he refers to a problem by Abu’l-Wefa (c, 980). The Arabs were Interested in the quartic equation only as they were in the cubic, i.e., from the standpoint of the intersection of two conics.

The Envelope Of A Chord As It Moves Along A Locus, James O'N.B. Kelley

Bachelors’ Theses

What is the curve described by a line of constant length as its end points move along a locus? This locus will be considered as the circle, the perpendicular axes, the ellipse, hyperbola and parabola in that order. Wherever it is possible both an algebraic and graphical solution will be given.

Envelope Curve, Gladys Catherine Apel

Bachelors’ Theses

The theory of motion led three great mathematicians of the seventeenth century into the study of the envelope of a moving line. It was introduced by Christian Huygens, further developed by Ehrenfried Walther von Tschirnhausen, and carefully analyzed by Gottfried Wilhelm Leibniz.

Some Properties And Applications Of Symmetric Functions, Marie C. Kniewel

Bachelors’ Theses

The word symmetry suggests that more fundamental aspect of all being, unity. In mathematics as in all other sciences, there is no going without having glimpsed something of that unity. Given even a glimpse, the wayfarer on the path toward mathematical truth, finds the traveling made, not easy, but more certain.

Marital And Population Composition Of Sheboygan County January 1, 1925 To December 31, 1936, Rhudolph John Ploetz

Bachelors’ Theses

This is a compilation of the marriage and the population figures of Sheboygan County, in the state of Wisconsin. The author has made a survey of both the rural and urban areas. Including the county figures, are the state and federal statistics for an analysis and comparison on the problems relative to the subject. The table of contents giving the title and page of tables, is intended to be of great value to the reader, in that just a particular table wanted is designated and well-outlined. Regarding a lengthy explanation for each or any one of the tables is really …

The Solution Of The Quartic Equation In One Variable, Jack W. Bril

Bachelors’ Theses

The purpose of this thesis is to discuss two of the foremost solutions of the quartic equation---Descartes' method and Ferrari's method. Most of the ideas were garnered from books on the theory of equations. The historical material was obtained from histories of mathematics.

The Hyperbola, Mary Aquin Miller

Bachelors’ Theses

This thesis is by no means an exhaustive presentation of the subject "The Hyperbola" or of the many and varied properties connected with this conic section and its associated parts. The aim in writing this paper has been to give a general outline of the history of the development of the hyperbola, to show the various constructions of it, and, with this as a basis, to show the relation between the hyperbola and its connected parts.

A Short Study Of Laplace's Equation, Sidney Teweles Jr.

Bachelors’ Theses

Perhaps if I set forth my original inspiration for this thesis, the reader will be better able to understand the reason for the apparent limitations of treatment. In my study of differential equations, I had the task set before me of presenting a discussion of Laplace's equation to the class. A seemingly easy matter turned out to be quite difficult for the reason that most texts make but brief use of Laplace's equation. Thus in a mathematics book reference will be made to Laplace's equation simply as example of a mathematical process. Some of these processes are the change of …

The Conchoid, James J. Blask

Bachelors’ Theses

The purpose of this thesis is to present 1n a simple and compact manner the conchoid, and to show its use in solving certain mathematical problems. Some of the better known curves related to the conchoid will also be discussed.

Solution Of The Equation: Y1 = (Ax2 + Bx + C)N (Kx + L), Edith Florence Mayer

Bachelors’ Theses

The general solution of an ordinary differential equation of the n^th order is one that involves n arbitrary constants* Although the general solution may assume a variety of forms. all of these give the same relation among the variables, so that actually there is only one general solution.

The Brocard Points Of A Triangle, Mary Geraldine Stamm

Bachelors’ Theses

The Brocard points, two remarkable points related to a triangle, were first noticed in 1816 by August Leopold Crelle. In a paper published in Berlin, he showed how to determine a point inside a triangle, so that the angles (taken in the same order) formed by the lines joining it to the vertices are equal. Investigations were also made by Karl Friedrich Andreas Jacobi (1795-1855) of Pforta, and by some of his pupils. However, interest in these researches died out, and the matter was soon forgotten.

Parabolic Curves, M.J. Berchmans Gentinetta

Bachelors’ Theses

No abstract provided.

The Important Lines In A Triangle, Jane Bogiel

Bachelors’ Theses

Geometry, as one of the fields of Mathematics, has been the object of extensive studies in ancient, Greek times, as well as in modern times, times of revival of scientific interests and researches. Analytical, descriptive, and projective geometry has been introduced as means of symplifying the study of the relations of different geometrical elements. Consequently, pure geometrical methods have been almost altogether abandonned, and, it is only in introducing basic geometrical concepts that they are now used. --This, however, seems to be the only reasonable course as long as the new methods do not change the basic structure of the …

The Sine-Function, Audrey Siehr

Bachelors’ Theses

Since the sine function is one of the most important elements of that phase of mathematics known as Trigonometry, it is only proper that we pause a moment for a short explanation of that subject. Trigonometry originated with the Greeks as the name itself implies. It was derived from the two Greek words trlgonon, meaning triangle; and metria, meaning measure. Trigonometry, then, dealt with problems related to measuring triangles.

Groups Of Order Eight, Ludwig Eugene Loos

Bachelors’ Theses

The problem of this thesis is to show that there can be only five groups of order eight. Its basis is Kronecker's Theorem, and it demonstrates that, regardless of the number of generators used in composing the groups, the result will always be limited to four groups of order eight. The fifth and last group is a cyclic group formed on eight letters.

Pedal Curves, Walter V.S. Budny

Bachelors’ Theses

The Pedal Curve may be defined as the locus of the intersection of the tangent at any point on a base curve with a perpendicular from a fixed point P to that tangent.

The Solution Of The Quartic Equation In One Variable, Beatrice Dwyer

Bachelors’ Theses

The purpose of this thesis has been to give a brief account of the history of the quartic equation, to develop and illustrate the particular solutions of the quartic and the more important solutions of equations in general.

Three types of solutions have been considered the particular algebraic solutions for biquadratic, the graphical solution, and methods of approximation A brief discussion has been given concerning the nature of the roots and the discriminant of the quartic.

The Function Concept, Anton J. Skowronski

Bachelors’ Theses

The purpose of this thesis is to present a general discussion of mathematical functions.

Most of the ideas are deduced from books on the Calculus and Mathematical Analysis. The Historical sketch was taken from books on the History of Mathematics.

Mathematical Short Cuts And Checks, Leon Schram

Bachelors’ Theses

A computer naturally should be the master of short cuts and methods for checking his work. The latter is perhaps of more importance than the former because one must be able to show his employer that he knows that his work is correct.

Sylvester’S Method Of Elimination, John D. Gardner

Bachelors’ Theses

To understand and appreciate Sylvester's method of elimination, it is necessary to review the most important points in the general field of algebraic elimination. As the information from which this thesis was written was derived from no particular text, specific references will, for the most part, be omitted. The titles of the books referred to are to be found in a bibliography placed at the back of the thesis.

A Study Of The Groups Of The Regular Solids, Lawrence J. Stanton

Bachelors’ Theses

Groups of movements are special groups in general group theory. Particular groups of movements are those obtained by rotating the regular solids. Before we take up the study of these groups of the regular solids, we shall first discuss subjects related to this work, namely, inversion in a sphere, stereographic projection, and rotations in a sphere.

Problem-Solving In Arithmetic, Eva M. Acker

Bachelors’ Theses

For a century arithmetic has been a popular subject in the elementary schools, and has consumed more time than any other subject. The war had an effect in reducing this time on arithmetic, largely due to the war-time emphasis on health, food production, back-of-the-line morale, and kindred subjects. More recently, school activities and playground work have come in for a reasonable share of the school time. The Twenty-ninth Yearbook recognizes the child as the center of interest, and the final criterion of all values being the effect any technique of teaching or any content of instruction has on the child. …

Arithmetical Progressions, Frances Agnes Scherkenbach

Bachelors’ Theses

Of the origin and the methods of treatment very little is known. The arithmetic and geometric progression first attracted attention after the Greeks had brought into prominence the harmonic series. The term ’series’ is derived from the Greek, while the term’ progression’ is derived from the Latin. The latter term was used most prominently until the seventeenth century, during which period the writers seemed to prefer the term "series" which is now mosy [sic] generally used.

The Problem Of The Trisection Of The Angle, Ruth O'Brien

Bachelors’ Theses

The great problem of the trisection of the angle dates back to the rise of the Sophist School about 480 B.C. The Sophist School was one of six Greek mathematical schools which included the Iconic, Pythagorean, Platonic, First Alexandrian and Second Alexandrian Schools. The periods of their existence overlapped considerably. thus, for example, Pythagorean activity continued during the time of the Sophists until the opening of the Platonic School. The rise of the Sophists to prominence came as a result of certain social and political conditions of the time.

The History Of The Parallel Postulate And Non-Euclidean Geometry, Clare Switalski

Bachelors’ Theses

After approximately two thousand years mathematicians have ventured to dispute the geometry of Euclid. Euclid's axioms were regarded as indisputable laws of space, the sole source from which his theorems were deduced. One needs only to survey the history of the controversies concerning his parallel postulate to be convinced that his assumptions are only metaphysical, since these assumptions can be changed when a space different from Euclid's is considered.

Thomas William Robertson, The Mid-Victorian Dramatist, James A. Fitzpatrick

Bachelors’ Theses

It is the purpose of this thesis to determine the position of Thomas William Robertson in the dramatic history of the nineteenth century, and to discover what contributions, if any, he made to the drama of this period. In addition to making a careful analysis of Robertson's more important dramas, I have read all the outstanding dramatic histories of the middle of the last century and some of its popular dramatic works. In my investigation of this problem I have explained the dramatic conditions of the early and mid-nineteenth century, revealed the characteristic tendencies of its popular plays, set forth …