Digital Commons Network^™

A Compilation Of Published Research In Elementary Arithmetic Since 1931, Alfred C. Birdsell

Master's Theses or Doctor of Nursing Practice

Many articles are published each year pertaining to elementary arithmetic. Some of these may very properly be designated "mere opinion” while others may very properly be classified as "research". Because of the large number of such articles appearing in print pertaining to some aspect of arithmetic, no doubt a service may be rendered to teachers of the subject by evaluating and classifying them as research or otherwise. From this situation grew the problem of this thesis, the title of which may be stated as follows: A Compilation of Published Research in Elementary Arithmetic Since 1931. Such a guide should be …

Fourier Series And Some Applications, Lawrence D. Marcotte

Master's Theses or Doctor of Nursing Practice

The object of the author in writing this thesis was to make a compilation of material necessary to work certain problems in mathematical physics with one use of Fourier series. Although whole books have been written on different aspects of this thesis, all had some intervening material which was too advanced for the average student. Any students interested in mathematics or physics cannot fail to see the importance of Fourier series. To mention a few applications, the series is used in finding the solution to various problems in heat distribution, electrical transmission, and aircraft construction.

A Test Of Richardson's Equation, Gerald J. Pyne

Bachelors’ Theses

The purpose of this work is the verification of the above relationship between saturated emission current and temperature, and especially, the evaluation of the current-temperature relating constants, A and theta.

Additional Equations For The Wigner_Seitz Model Of Solids, Alex Sharley Keene

Bachelors’ Theses

This report consists of an extension of the Wigner-Seitz equations to particular cases and boundary conditions. These equations are tools whereby energy bands and wave functions for a face centered lattice can be determined.

The Darboux Inverse Problem In The Calculus Of Variations, Frank O. Lane

Mathematics & Statistics ETDs

The simplest non-parametric problem of the calculus of variation, the so-called direct problem of the plane, is the problem of finding that arc C_o of a family of admissible arcs y=y (x) joining two fixed pointed (x₁ , y₁ ), (x_1, y₂) in the x,y-plane such that along the C_o the integral takes on a minimum value.

An Analytic Study Of Eight-Grade Pupil Performance As Revealed Through The Stanford Achievement Test In Arithmetic, Dominic J. Brungardt

Master's Theses or Doctor of Nursing Practice

The immediate purpose of the study were: (a) to determine how closely the grade equivalents of two-hundred and sixty pupils follow the normal curve ; (b) to plot the results of the one-step problems on a graph with an analytic explanation of the graph ; (c) to place the results of the two-step problems on a graph with an analytic explanation of the graph; to determine what types of error were most prevalent; to discover apparent causes of error ; (d) to make suggestions helpful to teachers for improving pupil achievement.

Certain Loci Associated With A One Parameter Family Of Conics In Three Dimensions, Raymond Francis Lausmann

Bachelors’ Theses

The conic sections and also the types of traces that might be obtained by the intersection of a plane with the ten real quadric surfaces have always been a source of great interest to me.

Lack of time has always been an obstacle to satisfying this curiosity. However, the opportunity for taking time was presented when the Department granted permission to write this thesis.

On Matrices With Elements In A Principal Ideal Ring, William Leavitt, George Whaples

Department of Mathematics: Faculty Publications

We prove the following theorem.
THEOREM 1. Let D be any commutative principal ideal ring without divisors of zero, and A any matrix with elements in D whose characteristic equation factors into linear factors in D. Then there exists a unimodular matrix T, with elements in D, such that T^-1 AT has zeros below the main diagonal.

The Application Of The Law Of Virtual Work In The Solution Of Civil Engineering Structures, Martin Trester Dyke

University of the Pacific Theses and Dissertations

The purpose of this thesis is to explore the civil engineering application of the law of virtual work to the determination of defelections, shears, bending stresses in truss structures, beams, structures subjected to both direct stress and bending, and indeterminate structures, and further to give examples of their mathematical solutions.

Arithmetical Vocabulary : A Factor In Verbal Problem Solving In Sixth Grade Arithmetic, Ernest A. Hoopes

Master's Theses or Doctor of Nursing Practice

During the writer's experience of teaching in elementary and junior high schools in Kansas he had excellent opportunity through supervision and classroom teaching to note a more-than-ordinary difficulty experienced by most children in the subject of arithmetic. Not only was the dull student baffled by the subject but many times the average and good students were "lost" when certain problems were presented. The exceptional. troublesomeness of this subject led the writer to ponder on the possible cause or causes of incorrect problem solving. One thing was apparent from observation and this was that many children seemed to lack a readiness …

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 or Doctor of Nursing Practice

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.

Torsional Deflection Of Miter-Type Lock Gates And Design Of The Diagonals, Edwin Gustav Hoffmann

Retrospective Theses and Dissertations

No abstract provided.

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 or Doctor of Nursing Practice

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.

A Problem In Reflection Of Light, M. Imogene Palen

Bachelors’ Theses

A circular mirror has a. ray of light from a source at one point on the circumference which is reflected twice. The first ray will by extension, if necessary, intersect the second reflected ray. Increasing the angle of reflection by revolving the source of light so that the first ray falls on all points of the circumference gives a locus, to the successive points made by the intersection of the first ray and the second reflected ray. The problem of this thesis is to picture the locus and find its equation.

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 or Doctor of Nursing Practice

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 …

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.

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. …

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 …