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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.

#### 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 ...

#### On some classes of non-analytic functions of a complex variable

(University of Missouri, 1909)

The fact, namely, that the analytic functions are a very limited and special class, with the additional fact that there seems to be no reason a priori why many of the theorems concerning analytic functions cannot be extended ...