Digital Commons Network^™

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.

Egyptian Mathematics, Evelyn Williams

Theses & Honors Papers

No abstract provided.

Mathematical Instruments, Marguerite Massey

Theses & Honors Papers

The selection of a subject for my honors work was determined not only by the desire to gain a broader knowledge of mathematics but also to make a study of something that would be of value in teaching in the state. From a variety of possible topics, the one, mathematical instruments seemed most interesting and appealing. This broad subject had to be narrowed down and made more specific. It was decided to limit it mainly to those instruments which might be used in the teaching of mathematics, these falling into two groups, those which can be made and those which …

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.

On The Element Of Decomposition Of A Doubly Periodic Function Of The Second Kind, M. A. Basoco

Department of Mathematics: Faculty Publications

Hermite has shown that a meromorphic function which satisfies periodicity relations of the form (1) F (z + 2ω) = μF (z), F (z + 2ω’) = μ’F (z), where ω’/ω = a+ib, b>0, and μ, μ' are independent of z, maybe expressed in terms of the function v{z + X) (2) G(z) = σ(z + λ) ÷ σ(z) + σ(λ) eρz, and its derivatives, in which λ, ρ are suitably determined constants and σ(u) is the …

On The Summability And Generalized Sum Of A Series Of Legendre Polynomials, W. C. Brenke

Department of Mathematics: Faculty Publications

The results obtained in this paper are as follows. (A) The series of Legendre polynomials Σn^pX_n(x), where p is a positive integer, is summable (H, p) for -1< x < 1, and summable (H, p +1) for - 1 ≤ x < 1 .

A Dictionary Of Mathematical Terms For High School Students, Matilda O. Iverson

University of the Pacific Theses and Dissertations

In compiling and writing this dictionary the needs of the high school student and teacher interested in mathematics have been kept constantly in mind. The mathematics of the high school is perhaps the simplest of its kind and yet very few textbooks carefully define all technical terms as they are introduced. The thoughtful student may turn to an abridged or unabridged dictionary but will find in most cases that the definitions of the terms are vague, often misleading, and in some cases not given.

The words in the vocabulary have been arranged in alphabetical order so that the reference to …

On The Trigonometric Developments Of Certain Doubly Periodic Functions Of The Second Kind, M. A. Basoco

Department of Mathematics: Faculty Publications

The class of meromorphic functions which satisfy periodicity relations of the form (1) ƒ(z + 2ω_l) = c₁f(z), f(z + 2ω₂) = c₂f{z), where the multipliers c₁ and c₂ are independent of z, and ω_l/ω₂ is a complex number with non-vanishing imaginary part, has been named by Hermite doubly periodic of the second kind. It is possible to make the study of these functions depend on others of the same type, but such that one of the multipliers, say c_l, is unity. In what follows …

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 …

Hyperbolic Functions, Dolores Fitzgerald

Bachelors’ Theses

No abstract provided.

Development Of Geometry And Its Assistance In Promoting Society, Nelson Jean

Electronic Theses and Dissertations

This bachelor’s thesis, presented to Xavier University in 1932, traces the history of geometry and argues that the subject has contributed to the development of society. Jean begins with geometry’s origins in practical needs in ancient Egypt, such as land division and taxation after the flooding of the Nile. He then follows its development through the Greeks, giving particular attention to Thales, Pythagoras, and the third-century mathematicians Euclid, Archimedes, and Apollonius.

Jean also discusses the educational and cultural value of geometry and its practical uses in physics, mechanics, architecture, and astronomy. He concludes that geometry is indispensable to society and …

The Practical Evaluation Of Resultants, T. A. Pierce

Department of Mathematics: Faculty Publications

The purpose of the present note is to give a practical method of evaluating the resultant of two equations. The method is particularly effective when the degree of one of the equations is high while that of the other is low. Use will be made of certain results in the theory of matrices.

General Steps In The Evolution Of The Calculus From The Time Of The Ancients To The Present, Sister Mary Virginia Ssf

Electronic Theses and Dissertations

This thesis, submitted to Xavier University in partial fulfillment of requirements for a Bachelor of Science degree in 1931, traces the historical development of the calculus from ancient Greek mathematics through the early twentieth century. The study is organized chronologically across eight sections. The introduction defines key mathematical terms including calculus, variable, and limit, and situates the calculus as the most powerful instrument of mathematical investigation. The thesis then examines the Method of Exhaustion developed by Greek mathematicians including Antiphon (430 B.C.), Eudoxus (370 B.C.), and Archimedes (225 B.C.), whose summation of infinite series represents the nearest ancient approach to …

The Theory Of Exponents, Olive Marie Lass

Bachelors’ Theses

When one speaks of Algebra, with its laws and operations, one asks the question - Is it an ancient subject, and how old is it? In answer to this question I find it is necessary to go back to the years before Christ.

The Fundamental Theorem Of Algebra, John D. Fitzpatrick

Bachelors’ Theses

Algebra is indeed an interesting and intriguing field of knowledge. Many people fear and dread it, and­ yet what do they fear? Is not algebra a logical se­quence of simple facts based perhaps on a few self-evident truths? If people saw the value of algebra, they would strive more enthusiastically to understand its principles. John Locke has a fitting commentary on those who are unfamiliar with algebra.

Probability, The Historical Development Of The Theory And Its Application To Games Of Chance, Rose M. Brandt

Bachelors’ Theses

The theory of probability had its origin in isolated mathematical problems taken from games of chance. The beginnings of many of our modern theories and concepts can be traced back to Chinese origin. So too can the theory of probability. With the exception of the Chinese problem, dating from the beginning of the Christian era, no reference seems to have again been made to the theory prior to the latter part of the fifteenth century. In 1494 an Italian monk, Pacioli, was one of the first to introduce the "Problem of Points" into a treatise on mathematics. By the solution …

Remedial Work In Subtraction, Multiplication And Division, Margaret A. Fleming

Bachelors’ Theses

The subject matter of this thesis is Remedial Work in Subtraction, Multiplication and Division of Whole Numbers. A class or 39 pupils, 15 girls and 24 boys were given the Compass Diagnostic Tests in Arithmetic in each or these three fundamentals.

Oval Curves, Leona G. Harner

Bachelors’ Theses

It has been the aim of the writer to present in this thesis a discussion of the most commonly known oval curves and their chief properties.

Continued Fractions, Alma Holmgren

Bachelors’ Theses

The aim of this thesis is to give the reader a general idea of the two types of continued fractions -- the simple continued fractions and the general continued fractions. Some properties of each type are also included.

A Certain Multiple-Parameter Expansion, H. P. Doole

Department of Mathematics: Faculty Publications

C. C. Camp has shown the convergence of the expansion of an arbitrary function in terms of the solutions of the systems of equations
X_1’ (λa₁ - Σ_i=2ⁿμ_i)X₁ = 0,
X_1’ (λa_i + μ_i)X_i = 0, (j = 2, 3, …, n),
where the a_i’s are functions of x, with the boundary conditions
X_i(-π) = X_i(π), (j = 1, 2, …, n).
In this paper it is intended to use a …

Parametric Solutions Of Certain Diophantine Equations, T. A. Pierce

Department of Mathematics: Faculty Publications

In this note parametric solutions of certain diophantine equations are given. The method of obtaining the solutions is derived from an equation involving the determinants of certain matrices. It will be recognized that the method is a generalization of the method of Euler and Lagrange which depends on forms which repeat under multiplication. The matrices used in this paper must be such that their forms are retained under matric multiplication and addition. When integer values are assigned to the parameters of our solutions we obtain integer solutions of the particular equation under consideration; however not all integer solutions are necessarily …

The Spinning Top, Aaron Jefferson Miles

Masters Theses

"Several mathematicians have solved the problems of motion of the top and gyroscope most completely, but none of them have considered in their solutions the effects of the supporting gimbal rings upon the motion or the effects of a variable rotor speed. It is the purpose of this paper to investigate the top equations by two well known methods; namely, by the method of Lagrange and by the method of Jacobi; considering in both the dynamics of the gimbal rings and varying rotor speed"--Introduction, page 3.

The Construction Of Conic Sections By Means Of Pascal's And Brianchon's Theorems, Benjamin Lee Welker Jr.

University of the Pacific Theses and Dissertations

The discovery of conic sections was made by Menaechmus (375-325 B.C.) an associate of Plato and a pupil of Eudoxus. This discovery, in the course of only a century, raised geometry to the loftiest height which it was destined to reach during antiquity.

On The Trigonometric Expansion Of Elliptic Functions, M. A. Basoco

Department of Mathematics: Faculty Publications

The problem of expressing an elliptic function in terms of infinite sums of trigonometric functions has been treated by Hermite, Briot and Bouquet, A. C. Dixon and others. In the present paper we treat the same problem from the point of view of Cauchy's residue theorem in function theory, which is also Briot and Bouquet's starting point, but we differ from these authors in that the integrand we use leads to an expansion for an elliptic function which is valid in an arbitrarily wide, but finite, strip of the complex plane, and which contains certain classical results as special cases. …

A Determination Of The Solubility Curves Of Several Liquid Ternary Systems And The Effect Of Change Of Temperature On These Curves, Samuel Klieger

Bachelors’ Theses

The following paper treats of the solubility relations found in ternary systems. The components of the system are, the lower alcohols, Benzene or toluene and water. The work consists of a determination of the solubility curve of the three components in various proportions. The influence of temperature on the solubility is so studied.

Symmetric Functions, Mildred L. Roth

Bachelors’ Theses

If function of two or more quantities is not altered when any two of the quantities are interchanged, it is called a symmetric function. For example, the trinomial a²+ b²+ c² is a symmetric function of a, b, c, because if any two quantities, say a and b are interchanged, the expression is unaltered in value.