Physical Sciences and Mathematics Commons^™

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

Orthogonal Polynomials With Orthogonal Derivatives, M. S. Webster

Department of Mathematics: Faculty Publications

We are concerned with the following assertion:
THEOREM. If {φ_n(x)} and { φ_n’(x)} are orthogonal systems of polynomials, then {φ_n(x)} may be reduced to the classical polynomials of Jacobi, Laguerre, or Hermite by means of a linear transformation on x.

A Brief Consideration Of The Different Methods Of Integration, Donald Golden

Master's Theses

Any student of mathematics is familiar with the importance of the process of integration. Integration is as fundamental to analysis as the basic principles of the number theory are to arithmetical calculation. Some of the common applications of integration are, finding the distance a falling body has travelled during a particular interval of time; to determine the equation of a curve, given different conditions (such as slope of the curve equal numerically to one-half the abscissa, or some similar problem); motion of a projectile; motion in a resisting medium; finding areas and volumes of revolution; length of a curve; areas …

The Asymptotic Development Of A Special Type Of Power Series, David A. Lawson

Mathematics & Statistics ETDs

It is the purpose of this study to consider certain aspects of the theorem due to Walter B. Ford, may be considered as a function g(w) of the complex variable w=x+iy and as such satisfies two conditions chosen by the author.

The Theory Of Determinants: Some Special Forms And Applications, William Ralph Eikelberger

Master's Theses

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, …

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.

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.

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 …

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[( …

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 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.

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

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 …

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.

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 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.

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.

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

Master's Theses

No abstract provided.

Methods Of Obtaining Asymptotes, Paul Sweetland

Master's Theses

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.

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 …

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 .

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 …

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. …