Physical Sciences and Mathematics Commons^™

The Mathematical And Historical Significance Of The Four Color Theorem, Brock Bivens

Honors Theses

Researching how the Four Color Theorem was proved, its implications on the mathematical community, and interviews with working mathematicians to develop my own personal opinions on the significance of the Four Color Theorem.

Parity Periodicity: An Eliminative Approach To The Collatz Conjecture, Austin J. Phillips

Honors Theses

The 3n + l Conjecture states that when the Collatz function is applied repeatedly to an initial value, the sequence of values generated always converges to 1, regardless of the starting value. This paper strengthens the claim that all such sequences are convergent by showing that certain types of nonconvergent sequences cannot exist. Specifically, no sequence with parity-periodic values can exist This eliminates all possible nontrivially periodic sequences and all divergent sequences with periodic parity. Therefore, if a counterexample to the conjecture exists, It must be a divergent sequence whose values display no parity periodicity.

Dynamic Phase Steepening In Alfven Waves, Stephen R. Granade

Honors Theses

Our solar system contains more activity and complexity than can be seen through a telescope. One such "invisible" phenomenon is the solar wind, created by a steady stream of particles blasted away from the sun in all directions. The sun's donut-shaped magnetic field lines channel this stream. Particles moving along the field lines perform an intricate helical dance, with ions winding one way and electrons the other.

The solar wind shapes and is shaped by the magnetic fields of the planets and the sun. If left undisturbed by outside influences, the earth's magnetic field, like the sun's, would resemble a …

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 …

Mathematics Of Investment, Claudia Morgan Griffin

Honors Theses

By using the text Mathematics of Investment by William L. Hart, Griffin examines the mathematics of investments.

A Special Studies Paper On The General Mathematics Requirements At Ouachita Baptist University, Linda Gamble

Honors Theses

The object of this paper has been to study the opinions of graduates and present students about the required math hours (presently three hours) at Ouachita Baptist University. It has formerly been my opinion that this may be insufficient math background for many of our students going out seeking jobs. Many times the student, while still in college does not realize he may need more math but it may show up on graduate tests, in his occupational work, or personal matters such as income tax calculations, bookkeeping, or budgeting.

To compile the opinions of students on this subject a form …

A Special Studies Paper On Mathematics In Computer Programing, Linda Gamble

Honors Theses

The profession of programing has existed for two decades or longer. Computer programing and the organization of computer analysis have gone beyond the reach of careful clerks with high school education. There is a growing demand for persons who are competent researchers, experienced in the use of multivariate methods, and skilled as computer users and programers. Mathematics and engineering predominate. The programer should have a knowledge of mathematics and a familiarity with computer hardware and must understand the content of the problem to be solved.