Physical Sciences and Mathematics Commons^™

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 …

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.

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 …

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.

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 …

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 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

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No abstract provided.

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

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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.

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

All Works by Eneström Number

No abstract provided.

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.

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

All Works by Eneström Number

No abstract provided.

The Voice Of The Phi Sigma -- 1881 -- Volume 03, No. 15, Phi Sigma

The Voice of the Phi Sigma

This item is part of the Phi Sigma collection at the College Archives & Special Collections department of Columbia College Chicago. Contact archives@colum.edu for more information and to view the collection.

Auszüge Aus Briefen Von L. Euler An Johann I. Bernoulli 1729-1737, Leonhard Euler

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No abstract provided.

Series Maxime Idoneae Pro Circuli Quadratura Proxime Invenienda, Leonhard Euler

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No abstract provided.

De Emendatione Tabularum Lunarium Per Observationes Eclipsium Lunae, Leonhard Euler

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No abstract provided.

Astronomia Mechanica, Leonhard Euler

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No abstract provided.

Fragmentum Ex Adversariis Mathematicis Depromtum, Leonhard Euler

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No abstract provided.

De Motu Corporum In Tubis Circa Punctum Fixum Mobilibus, Leonhard Euler

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No abstract provided.

Théorie Générale De La Dioptrique, Leonhard Euler

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No abstract provided.

Vera Aestimatio Sortis In Ludis, Leonhard Euler

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No abstract provided.

Enodatio Insignis Cuiusdam Paradoxi Circa Multiplicationem Angulorum Observati, Leonhard Euler

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No abstract provided.

Sex Litterae Ad Nicolaum Bernoullium Ii, Basileensem J. U. D. Datae 1742 Ad 1745, Leonhard Euler

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No abstract provided.