Physical Sciences and Mathematics Commons^™

A Fractal Geometry For Hydrodynamics, Jonah Mears

Honors Theses

Experiments have shown that objects with uneven surfaces, such as golf balls, can have less drag than those with smooth surfaces. Since fractal surfaces appear naturally in other areas, it must be asked if they can produce less drag than a traditional surface and save energy. Little or no research has been conducted so far on this question. The purpose of this project is to see if fractal geometry can improve boat hull design by producing a hull with low friction.

Elliptic Curve Cryptography And Quantum Computing, Emily Alderson

Honors Theses

In the year 2007, a slightly nerdy girl fell in love with all things math. Even though she only was exposed to a small part of the immense field of mathematics, she knew that math would always have a place in her heart. Ten years later, that passion for math is still burning inside. She never thought she would be interested in anything other than strictly mathematics. However, she discovered a love for computer science her sophomore year of college. Now, she is graduating college with a double major in both mathematics and computer science.

This nerdy girl is me. …

Two Views Of The Projective Plane, Rebecca J. Thomas

Honors Theses

The projective plane is a mathematical object which can be defined in two ways. In the following paper, I will explain the two definitions and show how they are equivalent by establishing a homeomorphism between the two objects.

Intuitive Concepts In Elementary Topology, Gary Rothwell

Honors Theses

My hour special study in intuitive topology originated in a curiosity of what exactly topology was and how it might be related to physics, my field of interest. The book I used was, Intuitive Concepts in Elementary Topology, by B.H. Arnold. This book is designed as a sophomore-junior level three hour course. Needless to say, I didn't quite cover the whole book in an hour a week. I mainly stuck to the intuitive concepts. Intuitive topology is dealing with more physical objects where the point set topology involves set theory; their unions, intersections and subsets.

Radiation Problem, Gerald L. Fuller

Honors Theses

A sphere of radius 'a' which is radioactive and which has an average range 'b' in the sphere. What fraction of total radiation will escape the sphere?

Modern Art Through Geometric Eyes, Janice M. West

Honors Theses

When tourists--even homefolks--go through a modern art museum, many opinions are accumulated. Some people may have chills when they see a certain painting, while others get a sick feeling of dizziness when they see the same one. In fact, if there were an opinion box at the exit of an art show, I imagine you could almost accurately count the different opinions by counting the total number of people who viewed the show. Yet, there is one opinion that most 'ole foggies' (and I use the term loosely) would agree upon, and that is this: "Why that's nothing but a …

The Major Contribution Of Leibniz To Infinitesimal Calculus, Carolyn Rhodes

Honors Theses

A study of the work of Leibniz is of importance for at least two reasons. In the first place, Leibniz was not alone among great men in presenting in his early works almost all the important mathematical ideas contained in his mature work, In the second place, the main ideas of his philosophy are to be attributed to his mathematical work, not vice versa. He was perhaps, the earliest to realize fully and correctly the important influence of a calculus on discovery. The almost mechanical operations which one goes through when one is using a calculus enables one to discover …

The Regular Polyhedra: A Study In Visual Aids For Teaching Geometry, Sammye Halbert

Honors Theses

Traditionally, mathematics, past simple addition, subtraction, multiplication, and division, has been taught of as being so boring, irrelevant, and in short, one of the unavoidable evils of school. An advertisement in The Mathematics Teacher expressed the general attitude of many students when it said, "mathematics was invented by an old magician in the desert who, with the help of his talking monkey, bakes equations and cupcakes in the hot sun." It seems that many students think mathematics is just one problem after another that has some mystical answer floating around in the air somewhere. The object is to get that …

Comparison Of Three Schools Of Thought In The Foundations Of Mathematics, Carolyn Rhodes

Honors Theses

Some of the most memorable events of the twentieth century took place as a result of conflict. Out of the numerous conflicts staged during this period, only one was resolved not on a common everyday piece of writing paper. The proponents of the conflict--E. V. Huntington, Oswald Veblen, Bertrand Russell, A. N. Whitehead, and David Hilbert--did not use weapons, but they used basic mathematical structure to wage the most extensive and critical investigation into the foundations of mathematics. As a result three schools of thought which are of special prominence and interest were brought to light. These are the postulational …

Bayesian Statistics: The Fundamental Theorem, Carolyn Rhodes

Honors Theses

The problem of the foundation of statistics is to state a set of principles which entail the validity of all correct statistical inference, and which do not imply that any fallacious inferences is valid. This sentence describes the purpose of much writing on statistical inferences, in general, and Bayesian statistics, in particular. Bayesian statistics was first introduced in a publication by Thomas Bayes in The London Philosophical Transactions, volumes 53 and 54 for the years 1763 and 1764, after Bayes' death in 1761. However, since the entire statistical research of Bayes' involves enormous study, this paper will limit itself to …

The Evolution And Application Of Pi, Carolyn Rhodes

Honors Theses

There is no part of the arithmetic that deals with approximations that is more interesting than that which seeks to find the ratio of the circumference of a circle to its diameter. This ratio has been studied from both a practical and a theoretical standpoint. Under the name "quadrature of the circle" it occupied mathematicians for many thousands of years, beginning with the Bible and extending to the twentieth century.

Federal Careers And Opportunities For Mathematicians, Gail Ray

Honors Theses

The purpose of this paper is to research the opportunities for a math major in the Federal Civil Service, and the requirements for positions. Those occupations which require courses only in math are few. However, there are several more which requires a combination of math with some other subject matter.

Those positions requiring only math are: Agricultural marketing specialist, cartographer, equipment specialist, geodesist, and mathematician.

A Brief Study Of Topology, Mary Beth Mangrum

Honors Theses

Topology is the study of topological properties of figures -- those properties which do not change under "elastic" motion. It is generally divided into two branches: set topology and algebraic topology. Set topology discusses the nature of a topological space, the properties of sets of points, the definitions of limits and continuity, the special properties of metric spaces, and questions concerning separation and connectedness. Algebraic topology deals with groups which are defined on a space, their structure and invariants.

Mathematics On An International Basis, Sandra Lee Sawyer

Honors Theses

Is the math of the United States inferior? In 1967 there was an international study of mathematics comparing twelve different countries: United States, Japan, Australia, Belgium, England, Finland, France, Germany, Israel, The Netherlands, Scotland, and Sweden. Funded in part by the United States Office of Education and five years in the making, the report was based on a test given to 133,000 students in different countries at the age of thirteen and at the end of high school.

The Beginnings Of Mathematics, Gail Ray

Honors Theses

Our first conceptions of number and form date back to times as far removed as the Old Stone Age. Little progress was made in understanding numerical values and space relations until the transition occurred from the mere gathering of food to its actual production, from hunting and fishing to agriculture. With this fundamental change, a revolution in which the passive attitude of man toward nature turned into an active one, we enter the New Stone Age. The tempo of technical improvement was enormously accelerated.

A History Of Mathematics Through The Time Of Greek Geometry, Janet Moffett

Honors Theses

The concept of numbers and the process of counting developed long before the time of recorded history. The manner of its development is not known for certain but is largely conjectural. It is presumed that man, even in most primitive times, had some number sense, at least to the extent of recognizing "more" or "less" when objects were added or taken away from a small group. As civilization progressed it became necessary for man to count. He needed to know the number of sheep he owned, the number of people in his tribe, etc. The most logical method was to …

Selections From "Mathematics: Our Great Heritage" Edited By William L. Schaaf, Mary Beth Mcgee

Honors Theses

This paper reviews and summarizes several essays within the text, Mathematics: Our Great Heritage edited by William L. Schaaf.

Mathematical Philosophy, Janie Ferguson

Honors Theses

The purpose of Mathematical Philosophy by Cassius J. Keyser is to delve into some of the more essential and significant relations between mathematics and philosophy. To see this relation, one must gain insight into the nature of mathematics as a distinctive type of thought. The standard of excellence in the quality of thinking to which mathematicians are accustomed is called "logical rigor;" clarity and precision are essentials. The demands of logic, however, cannot be fully satisfied even in mathematics, but it meets the requirements much more nearly than any other discipline. Thus, the amount of mathematical training essential to education …

The Development Of The Calculus, Janie Ferguson

Honors Theses

The Greeks made the first step in the inquiry of the infinitely small quantities by an attempt to determine the area of curves. The method of exhaustions they used for this purpose consisted of making the curve a limiting area, to which the circumscribed and inscribed polygons continually approached by increasing the number of their sides. The area obtained was considered to be the area of the curve. The method of integration is somewhat similar, to the extent that it involves finding the limits of sums. Zeno of Elea (c. 450 B.C.) was one of the first to work with …

Plane Protective Geometry, Lana Sue Legrand

Honors Theses

The following study was based on the text A Modern Introduction to Geometries by Annita Tuller, Associate Professor of Mathematics at Hunter College. The study consisted of problem solving at the end of each topic studied. Therefore, this paper contains a brief summary of the topics covered followed by the problems solved with theta respective drawings. No attempted is made to include all of the theorems, axioms, or definitions necessary to solve the problems but page references are given to refer to the text.

Nomography, Scotty Andrews

Honors Theses

No abstract provided.

Industrial Mathematicians, Mary Beth Mcgee

Honors Theses

What is an industrial, or professional, mathematician? What does he do? Generally, there are two kinds: workers in pure mathematics and workers in applied math.

The pure mathematician likes to play with mathematical laws and principles just to see what will happen. They have mathematical curiosity; they are not especially interested in whether anyone ever finds any use for the result or not. They have the fun of working their problems, and that is the only reward they ask. There is a large group of men and women getting paid good salaries for having such fun; they are the pure …

Groups, Janie Ferguson

Honors Theses

This paper explores abstract algebra groups.

Mathematics And Logic, Janet Moffett

Honors Theses

Mathematics is interested in the methods by which concepts are defined in terms of others and statements are inferred from others. It therefore uses a primarily deductive form of reasoning. It is almost impossible to distinguish where logic leaves off and mathematics begins. "... logic is the youth of mathematics and mathematics is the manhood of logic." Mathematics starts from certain premises and, by a strict process of deduction, arrives at the various theorems which constitute it.

In order to understand the congruence of mathematics and deductive logic, one must understand the principles of each and the relation between them. …

An Introduction To Linear Programming, Lana Sue Legrand

Honors Theses

This paper represents a study of the text An Introduction to Matrices, Vectors, and Linear Programming. It is composed chapter by chapter taking the more important statements, definitions, and theorems from each and working out exercises to illustrate their meaning. Other exercises were worked in the course of the study than are included in this paper but these were selected as brief illustrations of the type of problems that were worked.

Vectors: A Study Of Vector Analysis By H. B. Phillips, Robert Bray

Honors Theses

This paper solves several mathematics problems listed in Vector Analysis by H. B. Phillips.

The Development Of The Slide Rule, Robert Bray

Honors Theses

Although the slide rule has been used extensively in business, industry, and science only in recent years, it is not a modern invention. Since the slide rule is a mechanical device whereby the logarithms of numbers may be manipulated, the slide rule of today was made possible over three and one-half centuries ago by John Napier, Baron of Merchiston in Scotland. In 1594, Napier privately communicated his results to Tycho Brake, a Danish astronomer, but did not publicly announce his system of logarithms until 1614. Napier set forth his purpose.