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A Remedial Program In The Four Fundamental Operations In Decimal Fractions, Hallie Ruth Weber

Master's Theses or Doctor of Nursing Practice

Can the results of the teaching of the four fundamental operations in arithmetic be improved? This is an important question that confronts most teachers of arithmetic. How can the teacher eliminate the difficulties which interfere with pupil progress, and reduce the number of failures in arithmetic? A group diagnostic test will show not only the level of ability of pupils in the various operations, but will point out weaknesses so that the teacher may organize her work in such a way as to give time to those who are below the standard and omit deadening drill for those who are …

Variation Of Moments With Distributions Of Masses And Areas, Mayo Glenwood Shults

Master's Theses or Doctor of Nursing Practice

The purpose of this investigation has been to determine the variations of the first, second, third and fourth moments as functions of distributions of masses and areas. These moments were found about a line or plane perpendicular to the horizontal axes of the figures, and at various distances along the axes. For a complete understanding of the problem, an explanation of various terms will be made in relation to mechanics statistics.

Gauss' Hypergeometric Equation, William R. Smith

Master's Theses

As early as the seventeenth century the English mathematician, john Wallis (1616-1703), used the term "hypergeometric" to describe a series which he was studying. This series, ∑(a)(a+b)(a+2b)…(a+n-1b), is quite different from the usual geometric series, hence the term, "hyper" (=above) plus "geometric," was used to signify that the series was of greater complexity than the geometric series. Wallis did not consider his series a power series or a function of x.

In 1769 this series received a remarkable development at the hands of Loonhard Euler who, following the example of Wallis, applied the word "hypergeometric" to it. He observed that …

Upon The Asymptotic Representation Of Entire Functions Where The General Coefficient Is The Product Of Two Gamma Functions, James R. Ellis

Mathematics & Statistics ETDs

The essential purpose of this paper is to obtain further information in regard to the asymptotic representation of a power series.

The Segregation Of Real Roots Of Lower Orders, Ross W. Bland

Master's Theses or Doctor of Nursing Practice

The purpose of this thesis is the presentation of the better algebraic methods of the segregation of real roots of equations of lower orders and a brief historical sketch of the advance made in the development of algebra. Mention is also made of a few of the men who have made notable contributions to this field of mathematics and the time, as nearly as it is possible to determine it, when new ideas were discovered.

Linearity In Factor Analysis, Opal Emmons

Master's Theses or Doctor of Nursing Practice

The uniqueness of mathematics in that it is a science complete in itself makes it possible to apply mathematical tools to sciences which, in themselves vary widely in content. There is, however, a particular difficulty which must be surmounted. A given mathematical procedure may be valid in the science of mathematics but invalid in another science, such as psychology. The reason for this is that sometimes there is a discrepancy between the implicit assumptions in the field of mathematics and those implicit in the field of application. The purpose of this investigation is twofold: (1) To point out that linearity …

Asymptotic Series, Bernard Martin

Master's Theses or Doctor of Nursing Practice

The purpose of this thesis is to follow the development of the asymptotic series from the beginning made by Euler, in his solution of problems, to the modern applications of asymptotic series, also to present a definition and an analysis of asymptotic series, explain some different theories of their use, and show the ways in which they find common usage. The use of asymptotic series is a comparative new development in the field of applied mathematics. The divergent series were not used as a method of calculation until Euler showed that they gave close approximations in the solution of problems. …

Some Applications Of The Principles Of Isomorphism And Variation To The Teaching Of Geometry, Ralph Mock

Mathematics & Statistics ETDs

In summary, it should be stressed that the numerous examples of this paper are important only in so much as they illustrate the use of the devices and concepts emphasized in the study. It is our premise that plane geometry, as usually taught, does not possess the value which it might have. Certain changes in content as well as in presentation would materially improve the course. This study, then, presents suggestions for improving the ordinary course in two directions. First, by presenting logical propositions from the students' experiences which are partially isomorphic to the theorems of plane geometry, it is …

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 Efficiency Of Approximation Formulae For Determining The Rate Of Interest In Amortization Schedules, Wade Ellis

Mathematics & Statistics ETDs

The problem of this study is to determine the relative efficiency of the more important formulae for approximating the rate of interest involved in an amortization plan when the amount of the debt, the amount of the periodic payment, and the number of periods are known. By efficiency this meant the degree of accuracy obtainable, and the time required for solution.

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

Orthogonal Polynomials With Orthogonal Derivatives, M. S. Webster

Department of Mathematics: Faculty Publications

We are concerned with the following assertion:
THEOREM. If {φ_n(x)} and { φ_n’(x)} are orthogonal systems of polynomials, then {φ_n(x)} may be reduced to the classical polynomials of Jacobi, Laguerre, or Hermite by means of a linear transformation on x.

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 …

A Brief Consideration Of The Different Methods Of Integration, Donald Golden

Master's Theses or Doctor of Nursing Practice

Any student of mathematics is familiar with the importance of the process of integration. Integration is as fundamental to analysis as the basic principles of the number theory are to arithmetical calculation. Some of the common applications of integration are, finding the distance a falling body has travelled during a particular interval of time; to determine the equation of a curve, given different conditions (such as slope of the curve equal numerically to one-half the abscissa, or some similar problem); motion of a projectile; motion in a resisting medium; finding areas and volumes of revolution; length of a curve; areas …

The Asymptotic Development Of A Special Type Of Power Series, David A. Lawson

Mathematics & Statistics ETDs

It is the purpose of this study to consider certain aspects of the theorem due to Walter B. Ford, may be considered as a function g(w) of the complex variable w=x+iy and as such satisfies two conditions chosen by the author.

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 Theory Of Determinants: Some Special Forms And Applications, William Ralph Eikelberger

Master's Theses or Doctor of Nursing Practice

The theory of determinants is a relatively new branch of mathematics; it was not firmly established until a brief 200 years ago. It was not until the middle of the 18th century that Cramer, one of the independent discoverers of the fundamental idea, was fortunate enough to attract attention to the theory of determinants. Much of the literature is written on the assumption that its reader has a good background in the subject. Then other authors just give the fundamental properties of determinants without proof of their statements. These latter authors are not interested in the mathematical theory of determinants, …

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.

Singular Solutions Of Differential Equations, John E. Klest

Master's Theses

No abstract provided.

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 …

A Method Of Changing Certain Infinite Series To New But Equivalent Series, Moneta Gunilla Johnson

Mathematics & Statistics ETDs

The purpose of this investigation is to prove that the sum of a series of variable terms of a certain type is equal to a constant plus the sum of another series of variable terms. As a result of this proof it may be hoped that certain series, which so far have not been summed, may be shown equal to a constant plus another series for which the sum is known.

Some Studies Upon Boolean-Schröder Algebra, Madge Childre

Mathematics & Statistics ETDs

As a basis of reference the assumptions and theorems of the Boole-Schröder system are given in full below. In general, the proofs of the theorems are not included, as they may be found in the treatise on the subject by these two men. However, in the case of a few of the theorems, new and original proofs were deemed to be of sufficient interest to be included here.

In the proofs which are included the following form has been used throughout. The page is divided into two columns, the logical steps of the proof appearing in the left column, and …

Note On The Greatest Integer Function, M. A. Basoco

Department of Mathematics: Faculty Publications

In this note we wish to record certain finite sums involving the greatest integer function E(x), which seem to be of some interest. Hermite* has shown that the generating function for E(x) has the simple form, (1) x^b ÷(1 -x)(1 -x^a) = Σ_(n)E[(n + a - b) ÷ a]xⁿ, where a, b are positive integers. To him is due, likewise, the development (2) ) x^b ÷(1 -x)(1 + x^a) =Σ_(n)E₁[( …

The Solution Of Ordinary & Partial Differential Equations In Series, Kenneth Wood

Masters Theses & Specialist Projects

The purpose of this thesis is to compile and discuss some of the methods of solution of both ordinary and partial differential equations, whose solutions are expressible in the form of a series. An exhaustive study is not attempted. A few of the methods of most common occurrence for finding solutions in series are discussed and examples illustrating these methods are presented.