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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 …

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[( …

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 …

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.

Analysis Of Errors Made By 717 Collge Students In Arithmetic, O.D. Barnes

Masters Theses & Specialist Projects

During the greater part of the elementary-school training of the average American child he receives a large amount of instruction and drill in arithmetic. In the high school he suddenly drops arithmetic except as he maintains practices in courses of science or high school mathematics and except as the transactions of every day life involve arithmetic. In college the individual may suddenly find that the amount of arithmetical knowledge required is not small as in physics, chemistry or certain commercial courses. Evidence exists to indicate that students doing poor work in these courses are often found deficient in arithmetic.

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.

E, Doyle K. Brooks

Master's Theses or Doctor of Nursing Practice

The meteoric splendor of the transcendental constant e is an intriguing mystery. It rises unexpectedly from nowhere, brilliantly illuminates some obscure mathematical concept, points to its solution, and abruptly fades into oblivion. Its unheralded visitation leaves the student wiser but wondering, tantalized by its omnipotence in apparently unrelated fields. Ever since his first introduction to e in elementary logarithms it has seemed to the writer that all the authors of textbooks are in a conspiracy to defeat any real knowledge of e. They say "2.71828… , called e, is the base of Naperian logarithms." Why? "The derivative of eX is …

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.

An Application Of A Theorem Of Borel On Natural Boundaries To The Theta-Zero Functions And Analogous Functions, Louis William Tordella

Master's Theses

No abstract provided.

Parabolic Curves, M.J. Berchmans Gentinetta

Bachelors’ Theses

No abstract provided.

On The Summability Of A Certain Class Of Series Of Jacobi Polynomials, A. P. Cowgill

Department of Mathematics: Faculty Publications

The result obtained in this paper is as follows:
The series Σnⁱ[((p + 1)(p +3)…(p +2n -1)) ÷(2ⁿn!) X^((p-1)/2)_n (x), where X_n^(p-1)/2(x) (hereafter indicated simply by X_n) is a symmetric Jacobi polynomial p >-1, and i a positive integer, is summable (C, k),k>i—1/2, for the range -1 <x<1.

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 …

A Comparison Of I.Q. And Achievement In Plane Geometry Among Students In The Senior High School At Joplin, Missouri, Vivian L. Hummer

Electronic Theses & Dissertations

No Abstract

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.

Certain Transformations Of The Apollonion Circles On The Triangle 1,W, And W2, Marion J. Kaminski

Master's Theses

No abstract provided.

A Generalized Kronecker Symbol And Cubic Determinants, Lota Lucile Campbell

Electronic Theses & Dissertations

The object of this thesis is to present a further generealization of Kronecker's symbol and apply it to cubic determinants.

Part I contains preliminary work on the Kronecker smbol as generliazed by Murnaghan, and applied to the plane determianntns. It includes only material that is necessary in the explanation of part II.

In part II we make a further generalization by defining a symbol composed of three rows of indices. The elementary properties of this symbol are given, the cubic determinant is define by means of the generalized symbol, and certain theorems on cubic determinants are demonstrated.

These theorems were …