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#### Definition of improper groups by means of axioms : a dissertation

(University of Missouri, 1906)

Essentially, a group is an associative field, in which the inverse combinations are uniquely possible. This is a concise statement of the classical definition of a group. The conditions which it connotes will be used here ...

#### Convergence of an infinite series

(University of Missouri, 1902)

This thesis gives some of the more important tests for the convergence of an infinite series; also the conditions that must be fulfilled in order that certain operations and transformations may be applied to an infinite series.

#### On the motion of a sphere on a rough horizontal plane

(University of Missouri, 1902)

The problem discussed in these pages is that of the motion of a billiard ball when struck by a horizontal cue. This is a special case of the motion of a sphere on a rough horizontal plane.

#### On integrals over sets of points

(University of Missouri, 1910)

The developments of the last twenty years in the theory of sets of points and in the applications of this theory to the theory of functions of real variables, besides leading to a tremendous extension of the ordinary theory ...

#### Pointwise discontinuous functions

(University of Missouri, 1912)

The concept of pointwise discontinuity is a fairly recent one in mathematics. Originally introduced as a convenient term in the study of integration, it has quite outgrown its former sphere of usefulness and has had an ...

#### Convergence of infinite series

(University of Missouri, 1900)

We shall define an infinite series as a succession of series formed after sum definite law. Most generally the series are actual numbers or are at least regarded as constraints, and we are concerned with their sum. There ...

#### The treatment of irrational numbers in the secondary schools

(University of Missouri, 1908)

The subject matter of this paper was suggested by the belief that a treatment of irrational numbers, from the stand point of the "cut" number, has certain points of superiority over the common treatment from the standpoint ...

#### Vectors in four dimensions

(University of Missouri, 1909)

The interest attaching to n-dimensional geometry comes chiefly from two sources, first the light thrown upon analysis by a geometric interpretation of its results when more than three variables are involved, and second, ...

#### On finite groups with special reference to Klein's Ikosaeder

(University of Missouri, 1904)

In speaking of the icosahedron and other regular solids in the following work we shall include not only the space construction but also the sphere surface upon which the corners, edges and faces of the solids may be ...

#### Minimum surfaces

(University of Missouri, 1904)

In this dissertation I propose to give some of the theory and develop some of the important formulas upon which Minimum Surfaces are based. In order to proceed with the development of Minimum Surfaces, it will be necessary ...

#### On surfaces of constant negative curvature and their deformation

(University of Missouri, 1904)

We have shown that the pseudosphere is applicable to itself in an infinity of ways. Therefore these surfaces that are applicable to it can, after they are folded on the pseudosphere, be made to pass through the same ...

#### Solutions of differential equations not obtained by giving particular values to the constant of integration in the general solution

(University of Missouri, 1903)

In considering the solution of Differential Equations, let the equation be taken in the form f(x,y,p)=c, in which p denotes dy/dx, and f is a rational, integral, and algebraic function of x, y, and p of degree n in p. It ...

#### Geometry of four dimensions

(University of Missouri, 1902)

In this thesis a brief outline of Four Dimensional Geometry, as far as the classification of quadrics, is attempted.

#### Foundations of geometry

(University of Missouri, 1901)

Geometry has been called the science of in-direct measurement, and as such is founded on certain definitions, postulates, and some assumptions or axioms which are said to be self-evident. It is a physical science idealized. ...

#### Singular solutions of differential equations of the first order

(University of Missouri, 1900)

A differential equation may be formed from all algebraic equations by the elimination of the arbitrary constants between the latter and its derivatives. The number of derivations being equal to the number of arbitrary ...

#### Conditionally convergent vector series

(University of Missouri, 1914)

In this paper we propose to study the behavior of series of complex numbers, or of vectors in two dimensions; and to generalize this study to the case of vectors in n dimensions. The particular properties to be studied are ...

#### Lorentzian warped products and static space-times

(University of Missouri--Columbia, 1985)

Let (M, g) be a Lorentzian manifold, (H, h) a Reimannian manifold, and let f: H [right arrow] (0, [infinity symbol] be an arbitarary smooth function. Then the product manifold M x H with Lorentzian metric g = (f[suprscript ...

#### A vector treatment of the projective properties of plane curves

(University of Missouri, 1916)

1. Notations. Suppose that we have given a plan curve C, and a point O, not lying in the plane of the curve. If we draw vectors from point O, one to every point of the given curve, we produce a conical surface, the elements ...

#### Errors in graphical methods

(University of Missouri, 1914)

The author suggests methods for determining errors in graphical computations and discusses errors in the graphical methods in the infinitesimal calculus.

#### Some new aspects of the Galois theory

(University of Missouri, 1913)

Realizing that the Galois theory of algebraic equations as commonly presented seems artificial, abstract, and intricate, we have been led in the following paper to attempt to present in a clear, tangible fashion the general, ...