Digital Commons Network^™

Quadratic Equations, Floyd George Hydar

Bachelors’ Theses

In algebra, an equality which exists only for particular values of certain letters representing the unknown quantities is called an equation. These particular values are called the roots of the equation, and the determination of these roots is known as the solution of the equation.

Modern Geometry Of The Triangle, Irene Nolan

Bachelors’ Theses

It has been the object of t he writer to present in this thesis theorems and proofs of modern geometry which seemed most useful and most interesting to her. Concepts of modern geometry have been presented and developed with reference to the triangle.

Periodic Functions, W. Kenneth Koehler

Bachelors’ Theses

The first known publications on the periodic functions were those of Fantet de Lagnv, a French mathematician born at Lyons in the year 1660. Although previous to this, mathematicians, notably Galilio in his analysis of the cycloid, had studied functions and curves whose properties necessarily involved periodic functions, no specific mention of this property was made.

Mathematical Induction, Lucille A. Mccann

Bachelors’ Theses

No abstract provided.

Symmetric Functions Of N-Ic Residues (Mod P), T. A. Pierce

Department of Mathematics: Faculty Publications

If p be an odd prime, q is said to be an n- ic residue of p if the congruence xⁿ = q (mod p) has solutions; otherwise q is an n-ic non-residue of p. A necessary and sufficient condition that q be an n-ic residue of p is that
(1) q ^{(p- 1)/δ} ≡ 1, (mod p),
where δ = g.c.d. (p - 1, n). The numberf of n-ic residues of a given prime p is (p-1)/δ.
It is with the symmetric functions of these …

Graphical Calculation And Computation, Alice Hudson Vallier

Bachelors’ Theses

The word ’’graph” has lately become a part of the active vocabulary of the ordinarily educated person of today. We may say lately because even fifty years ago the use of the graph to represent data was limited to the knowledge of a few theorizing mathematicians and the miscellaneous disorganized usage of some practical mechanics, engineers, business men and statisticians. The situation is not that fifty years ago the rudiments of graphing were not identical with the bases of graphing data today, at least by such simple methods as are commonly employed in periodicals and newspapers for the enlightenment of …

The Theory Of Limits, Molly E. Davis

Bachelors’ Theses

The theory of limits is among the most important theories in mathematics as mensuration of curves, and surfaces, the treatment of series and the foundation of calculus rest upon this theory.

The Study Of The Curves Of Equations Having The Type Form Of Y=XN, Frank Kohn

Bachelors’ Theses

The purpose of this thesis is to investigate those properties of curves having the general type form of y = xⁿ that will enable us to determine the graph of a particular curve of this type. The investigations will not only determine the graph as it appears in the finite region of the curve but its appearance in infinite regions as well.

Applications Of Infinite Products, Lillian Schnell

Bachelors’ Theses

Jacob Nicolaus Bernoulli (1654-1705) wrote a work on "Ars Conjectandi." It was published eight years after his death. The work consists of four parts. The second part is on permutations and combinations, which Bernoulli used in a proof of the binomial theorem for the case of positive integral exponents. The book contains a formula for the sum of the rth powers of the first n integers. This involves the famous Bernouillian numbers. Bernouilli boasted that by means of his formula he could calculate "Intra semi-quadrantem Horae" the sum of the 10th power: the first thousand integers.

Experimental And Observational Geometry, Albert D. Field

University of the Pacific Theses and Dissertations

Geometry has the distinction of being one of the oldest subjects given in the high-school.

Its subject-matter was formulated and organized by the Greeks into a fine system of thought before the time of Christ. Since leaving the hands of the Greeks, geometry has received only a few minor changes, and these largely in recent years.

Heretofore, the study of geometry has been made almost entirely dependent upon memory and reasoning. Geometricians have been slow in adopting the laboratory and observational methods.

This thesis has been written to encourage the student in his work of observing geometrical forms, and in …

Irrational Numbers, Paul O. Smith

Bachelors’ Theses

By an irrational number is meant a number which cannot be expressed by an Integer or by a fraction. The definition in itself is rather vague and to many would not mean very much but by a definite geometric example the idea of just what an irrational number is can be much more clearly shown. Suppose we are given a line of a definite length of two inches. It can easily be seen how this line can be divided into a great number of smaller parts which can be expressed by integers and fractions.

History And Proof Of The Binomial Theorem, Ethel B. Ray

Bachelors’ Theses

Everyone realizes what a wonderful place the world really is. Yet, we of this day little think of the many generations that have gone to make our universe as it is. We think we have done wonders. We pride ourselves on our modern way. There is a tendency in man to "pat himself on the back" and boast of how well he has done. Little do we realize that millions and millions of people have given their whole lives so that we might be as we are. Of course the soldier gives his life for his country; but what of …

Methods Of Tracing Curves, Stephen Lewandowski

Bachelors’ Theses

There are two kinds of equations, algebraic equations and transcendental equations. An algebraic equation is one that involves a finite number of ordinary operations of algebra i.e. addition, multiplication, subtraction, division, extraction of roots, and raising to powers denoted by constant exponents.

Hyperbolic Functions, Margaret S. Johnston

Bachelors’ Theses

A Study of hyperbolic functions is both interesting and fruitful because of their important and historical relation to the more elementary branches of Mathematics: Trigonometry, Analytical Geometry and Differential and Integral Calculus. Historically the development of hyperbolic functions has been closely associated with the development of the properties of the circle, ellipse, and hyperbola; the earliest knowledge of the functions rising out of a comparative study of these curves, and resting on more analogy rather than clear definition and proof.

Indeterminate Coefficients, Armond William Bear

Bachelors’ Theses

No abstract provided.

Summable Types Of Series, Dorothea Maria Baumann

Bachelors’ Theses

By an infinite series we mean a polynomial, or a sequence of terms, each of which derives from its predecessor according to a fixed formula or process; there is a one to one correspondence, consequently between the terms of the series and the set of positive integers 1,2,----,n,----. Summation means the finding of a finite expression equivalent numerically to the given series; known functions only may occur, connected by a fixed number of steps; such a closed expression is called the "sum" of the series.

An Approximation To The Least Root Of A Cubic Equation With Application To The Determination Of Units In Pure Cubic Fields, T. A. Pierce

Department of Mathematics: Faculty Publications

Approximation to the Least Root of a Cubic Bernoulli's method of approximating the largest root of an equation
(1) x³ = ax² + bx + c,
with real coefficients, is to use (1) as a scale of relation for the recursion formula A_n = aA_n-1 + bA_n-2 + cA_n-3. Successive A’s are calculated starting from any initial values. Then A_n+i/A_n for increasing values of n approximates that root of (1) which has the greatest absolute value if that root is real. The method here given for …

Graphic Methods For Solving Algebraic Equations, L. Tremaine Dunlap

Bachelors’ Theses

No abstract provided.

Ua94/6/1 English & Grammar Notebook, Ruth Whitlow

Student Organizations

Grammar and English notebook used by Ruth Whitlow, includes diagrammed sentences and some math problems on the back page.

Ua94/6/1 English & Grammar Notebook, Ruth Whitlow

Student/Alumni Personal Papers

Grammar and English notebook used by Ruth Whitlow, includes diagrammed sentences and some math problems on the back page.

A Set Of Completely Independent Postulates For The Linear Order Η*, M. G. Gaba

Department of Mathematics: Faculty Publications

Professor E. V. Huntington has published three sets of completely independent postulates for serial order. His set A involves four postulates, which is as high a number of postulates as had been proved completely independent. In the present paper are given seven postulates which form a categorical and completely independent set for the linear order.
Our basis is a class of elements [p] and an undefined dyadic relation (called 'less than') among the elements. If we are given two elements p₁p₂ and if the relation p₁ less than p₂ holds, we will symbolize …

A Theorem On Semi-Continuous Functions, Henry Blumberg

Department of Mathematics: Faculty Publications

Recently G. C. Young and A. Denjoy have communicated theorems—those in Denjoy's memoir are of an especially comprehensive character—dealing, in particular, with point sets where the four derivatives of a given continuous function are identical. It is the purpose of this note to treat an analogous problem that arises when "derivative" is replaced by "saltus." However, instead of confining ourselves to "saltus," we prove a more general theorem that applies essentially to all semi-continuous functions. We preface the proof of this theorem with the following

Ein Brief Eulers An D'Alembert, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Several Lines Of A Letter From Euler To The Royal Society Dated 21 October/1 November 1768, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Three Letters From Euler To Daniel Bernoulli, 1734-1740, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Extracts Of Letters From Euler To Johann I Bernoulli, 1728-1729, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Inversion Applied To The Common Equations Of The Conic Sections, Edna Maria Cargill

Student and Lippitt Prize Essays

A solution of applying inversion to the mathematic equation of conic sections, beginning with a definition of inversion and statement of the problem.

Some Contributions Of Pure Math To Science, Herbert B.E. Case

Student and Lippitt Prize Essays

An examination of the connection between math and science through discoveries in the subjects of astronomy, mechanics, physics and chemistry.

Extracts Of Letters From Euler To Johann I Bernoulli, 1739-1740, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Fourteen Letters From Euler To P. L. M. De Maupertuis, 1752-1759, Leonhard Euler

All Works by Eneström Number

No abstract provided.