Physical Sciences and Mathematics Commons^™

An Investigation Of The Meaning Of Α3 As A Measure Of Skewness, John W. Coy

Mathematics & Statistics ETDs

The purpose of this study is the interpretation of α₃ by means of a relatively simple formula which will predict the amount of shift in the effective limits of the Type III curve for a given change in the skewness. The methods used are chiefly empirical.

A Study Of Retention Of Percentage, Fred Dellett

Master's Theses

The problem of this thesis was to determine by means of a test the retention of the fundamentals of percentage as shown by beginning eighth grade pupils, who were taught percentage the previous year in the seventh grade. The fundamentals of percentage are here considered as the changing of percents to decimal fractions or common fractions, the reverse procedures, and the three types of problems arising from the relation, base times rate equals part. These quantities, base, rate, and part, are represented in the example, 300 X 12% = 36, respectively. Because of the inherent relationship of decimal fractions and …

An Investigation Of The Nature Of The Coefficients Of Entire Function, Marie Ann Philips

Mathematics & Statistics ETDs

The purpose of this study is to investigate the nature of the coefficients of certain power series. In particular, it is desired to know what characteristics the coefficients must possess in order that the series shall represent an entire function.

A Theorem On The Unit Groups Of Simple Algebras, Ralph Hull

Department of Mathematics: Faculty Publications

Let k be an algebraic number field of finite degree m and let A be a normal simple algebra of degree n, order n², over k. Our object is to prove the following theorem.
THEOREM. If A is an R-algebra, that is, if n>2 or at least one infinite prime place of k is unramified in A when n=2, then any two distinct maximal orders of A have distinct groups of units.

On Certain Arithmetical Functions Due To G. Humbert, M. A. Basoco

Department of Mathematics: Faculty Publications

G. Humbert has discussed, in a series of brief notes, a certain class of entire functions with interesting arithmetical properties. These functions are defined, in an essentially unique manner, by certain functional equations. The Fourier series representations of the solutions of these equations are similar in form to those for the elliptic functions snu, cnu, dnu, and so on. They differ from these, however, in that their domain of validity extends throughout the entire complex plane (Z_∞ excluded) and moreover, in that their arithmetized forms involve incomplete numerical functions of the divisors of an integer.
In the …

A Study Of Certain Substitution Groups, Merle Mitchell

Mathematics & Statistics ETDs

This thesis purposes to study a certain group of movements which can be expressed as substitutions. The groups of movements which send a square into itself is to be studied as a group of eight substitutions on the vertices for the purpose of leading up to the real problem of this paper. From the octic group, it is natural to proceed to a study of the movements which send a cube into itself. In particular, it is the aim of this thesis to discover the group of the cube and to analyze some of its properties. There are twenty-eight rotations …

On The Fourier Developments Of A Certain Class Of Theta Quotients, M. A. Basoco

Department of Mathematics: Faculty Publications

In this paper we shall be concerned with the functions φ^k_a(z) defined by the relation
(1) φ^k_a(z) ≡{d/(dz)logℓ_α (z,q)}^k = {[ℓά(z,q)] ÷ [ℓα(z,q)]^k, α + 0, 1, 2, 3,
where ℓ_α(z, q) is a Jacobi theta function and k is a positive integer. In the first place, we shall derive the Fourier developments which represent these functions in a certain strip of the complex plane; it …

A Research In Sixth Grade Children's Solution Of Verbal Arithmetic Problems, Herbert Schroder

Master's Theses

The purpose of this research in sixth grade children's solution of verbal problems in arithmetic is to investigate the mental processes that lie back of pupils' answers in arithmetic. That is, how do pupils solve verbal problems in arithmetic? The investigation involves several related problems such as; to what extent is the pupils' method of solution influenced by irrelevant data, cues, details, and numbers used in a problem?

The Basic Analogue Of Kummer’S Theorem, J. A. Daum

Department of Mathematics: Faculty Publications

About one hundred years ago, E. E. Kummer proved the formula
(1) ₂F₁ [_{1 + a – b} ^{a, b; -1}] = [Γ(1 + a - b)Γ(1 + a/2) ÷ Γ(1+a)Γ(1+a/2 - b)
which has since been known as Kummer's theorem. This appears to be the simplest relation involving a hypergeometric function with argument ( - 1).
All the relations in the theory of hypergeometric series _rF₈ which have analogues in the theory of basic serie3 are those in which the argument is ( + 1 ) …

Studies Arising From A Problem In The Calculus Of Variations, John Gonzalez

Mathematics & Statistics ETDs

In mathematics, generalization is progress; so much so that oftentimes one loses sight of the fact that generalization is the result of arduous work in the consideration of the particular. In no other branch of mathematics is this better exemplified than in the Calculus of Variations. The beginning of a systematic development of the theory of the Calculus of Variations really started with the two Bernoulli brothers (1654-1748) in their discussion of the brachistochrone problem in 1696. The method devised by them were sufficiently powerful in the attack of a large number of problems. Euler (1707-85) further elaborated the geometrical …

Families Of Circles, Mary Olive Norman

Bachelors’ Theses

No abstract provided.

On Certain Basic Series, John Daum

Department of Mathematics: Faculty Publications

The identity
(1) Σ_n=1^∞ (qⁿ)/[(1-qⁿ)²] {(1÷(1-q)) + (1÷(1-q²)) + … + (1 ÷ (1 -qⁿ))} = Σ_n=1^∞ [(n²qⁿ)
was deduced from arithmetical considerations by E. T. Bell. About five years ago, W. N. Bailey proved the relation
(2) Σ_n=0^∞ [(1-q)(1-q²)…(1-qⁿ] ÷ [(1-z)(1-qz)…(1-qⁿz)] x [(zⁿ + 1) ÷ (1 - q^{n …}

The Unit Plan Versus The Textbook Plan Of Teaching Arithmetic To Seventh And Eighth Grade Pupils, Arthur P. Harvey

Master's Theses

The present day trends in education seem to indicate the desirability of its becoming more and more a socialized education. This trend will no doubt have a more significant bearing on some subjects or studies in the school curriculum than on other subjects. The Kansas public elementary schools have recently adopted a Unit Program in School Studies, which includes history, civics, geography, science, and hygiene in an attempt to contribute better to the socialized idea. This Unit Program, however, does not make direct provision for English, spelling, arithmetic, and penmanship .Naturally, perhaps, comes the question to many teachers of why …

A Reorganization In The Continuity Of Subject Matter In Mathematics, Beryl E. Warner

Electronic Theses and Dissertations

This thesis considers a reorganization in the order of arrangement of certain topics in elementary and undergraduate mathematics; i.e. , arithmetic, algebra, plane geometry, solid geometry, trigonometry, analytic geometry, and calculus. Two terms important in the discussion are reorganization, the process of changing the relative position of topics or proofs in mathematics to an earlier or later place in the development of subject matter, and continuity, the logical order of topics arranged according to the need of one to explain the other.

The purpose of the thesis is two-fold; First, to show what arrangement of topics may be desirable; and, …

The Evolution Of The Concept Of Axiom, William Fred Jones

Mathematics & Statistics ETDs

The field of knowledge known as mathematics is composed of the totality of mathematical systems. A mathematical system consists of a body of propositions known as the axioms. The concern of this paper is with the axioms; in fact, with the change which has taken place during the centuries in the ideas of mathematicians about the axioms.

New Formulae For The Determination Of The Yield Of A Bond, Marvin Roberts

Mathematics & Statistics ETDs

A written contract to pay a certain amount of money on a specified redemption date, and to pay equal periodical dividends, is called a bond from a mathematical standpoint. The principal mentioned in the contract is its face value, or par value. The amount redeemed, or the redemption value, is denoted by C, the dividends by D, and the principal by F. A bond is redeemed at a par if C and F are the same, and at a premium if C is greater than F. The divided rate, or bond rate, is the interest rate named in the bond. …

Upon The Asymptotic Representation Of Certain Entire Functions In Distant Portions Of The Plane, Abraham Franck

Mathematics & Statistics ETDs

The purpose of this paper is to study two particular entire functions which satisfy the conditions set up in a theorem due to Newsom. It is to be hoped that this report may be preliminary to the invention of a method which will lend itself toward the solution of certain general problems.

A Study Of Fermat's Last Theorem., Jerome L. Krumpelman

Electronic Theses and Dissertations

This work is intended primarily for the student of mathematics who may not necessarily wish to delve into the complete theory of the problem. but who may wish to get a picture of the work necessary to study and understand it. For a complete history of the problem until 1919, refer to Chapter XXVI of Dickson's History of the Theory of Numbers, II, and for the work primarily connected with Irregular Cyclotomic Fields and Fermat's Last Theorem through part of 1927, refer to Algebraic Numbers, II, National Research Council Bulletin, # 62. For a Short presentation of the problem refer …

The Existence Theorem Of Ordinary Differential Equations, Harris J. Dark

Master's Theses

There are a great many devices for solving differential equations of certain special forms. But there is a large number of classes of differential equations that are not included in these special forms and cannot be integrated by quadratures or other purely elementary methods. When mathematicians were forced to abandon their cherished hope of finding a method for expressing the solution of every differential equation in terms of a finite number of known functions or their integrals they turned their attention to the question of whether a differential equation in general had a solution at all, and, if so, of …

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

Master's Theses

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

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

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

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

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 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