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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.

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.

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.

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.

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 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 …

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 …

Mathematical Short Cuts And Checks, Leon Schram

Bachelors’ Theses

A computer naturally should be the master of short cuts and methods for checking his work. The latter is perhaps of more importance than the former because one must be able to show his employer that he knows that his work is correct.

Methods Of Obtaining Asymptotes, Paul Sweetland

Master's Theses or Doctor of Nursing Practice

The purpose of this thesis is to present in logical order the more important methods of obtaining asymptotes. In several cases where two or more different methods for obtaining the same type of asymptotes were found the simpler method is given first and then the more difficult method. Most of the simpler methods are based on Analytic Geometry, while the more difficult are based on the Calculus.

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 …