Mathematics, Engineering and Computer Science
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A Mathematical Analysis of Scheduling for AWARE
(2020)AWARE is a nonpro t organization that provides care and services for people with challenging mental health, emotional, and in some instances, physical disabilities [1]. Many of the clients in AWARE residential programs ... 
The Effect of Programming on Students' Understanding of Mathematics
(2020)Many schools are aware that technology and coding needs to be implemented more within their curriculum in order to have students become more literate in the heavily technology oriented society. Previously, researchers have ... 
A Prime Look into the Field of Cryptography
(2020)Data encryption is vital in protecting the information that we send over the internet on a daily basis. This paper will explore two of the most commonly used public key encryption algorithms today: RSA and elliptic curve. ... 
Leaking Underground Storage Tank Impact Model
(20190401)Leaking underground storage tanks (UST) pose a threat to the surrounding environment and population. The Montana Department of Environmental Quality (MT DEQ) has completed two phases of a risk analysis with the purpose of ... 
Predicting Chaotic Behavior in Electrical Circuits
(20190401)Chaotic behavior is a natural phenomenon that can be found all around us in our daily lives. This project is focused on analyzing the behavior in forced RLDiode (resistor, inductor, and diode) electrical circuits. We ... 
A Numerical Model of the Subaerial Landslide Generated Waves of the Berkeley Pit
(20190401)Southwestern Montana has a very rich history because of its mining activities. Butte, home to the richest hill on earth, is no exception. Underground operations resulted in 10,000 miles of horizontal underground workings ... 
Utilizing Role Based Modeling Language to Determine a System’s Safety From an Advanced Persistent Threat
(20190401)With Advanced Persistent Threats (APTs) becoming a larger threat among the cyber world, it is important that software is designed with security in mind. In order to aide this process, software developers can use security ... 
DataDriven Discovery of Ordinary Differential Equations
(20190401)We suggest that using datadriven methods on collected sensor data, we can recreate the ordinary differential equation. In this case we are applying data to find the ODE as opposed to deriving an ODE from basic principles. ... 
The Development And Application Of Decision Theory Analysis
(19710401)Nearly everything a person does, every action taken, is the result of making a decision. With the exception of a few physiological actions, such as breathing, every action involves a decision, even though some are very ... 
Solution Of Parabolic Partial Differential Equations By Finite Difference Methods
(19730401)This paper is concerned with finding the solutions to a particular type of partial differential equations. It will be left up to the engineers and physicists to derive the actual equations which describe a physical situation. ... 
Optimizing Investment Portfolio Allocation
(20190401)This analysis presents a model that could be used to inform a portfolio manager in which sectors of the stock market to invest in for the equity portion of an investment portfolio. The model incorporates a linear program ... 
The Relations Between Mathematics and Philosophy
(19340401)"The history of mathematics is one of the large windows through which the philosophic eye looks into past ages and traces the line of intellectual development." Thus does a prominent mathematician characterize the general ... 
An Introduction to Complex Analysis
(19730401)The purpose of this paper is to present an introductory survey of the basic ideas and concepts which form a foundation for the analytic study of the singlevalued functions of a complex variable. In no way does it purport ... 
The Singular Solution Of Differential Equations
(19320401)In the latter half of the seventeenth century Sir Isaac Newton, eminent mathematician and physicist, developed his theory of Fluxions, treating with the subject by which he is probably best known. The Calculus, as the ... 
Topological Spaces and Jordan's Theorem
(19640401)What is topology? What is it based upon and what can I relate it to that I already know? These and many other questions were asked by those who attended the lecture given by J. Eldon Whitesitt, a guest lecturer from Montana ... 
The Teaching Of Trigonometry In The Secondary School
(19570401)It is my purpose in the writing of this thesis to give reasons for the teaching of trigonometry in the high school; give a short history of trigonometry and show the importance that trigonometry has played in the world; ... 
The Linear Fractional Transformation Of A Complex Variable: w=(az/b)/(cs/d)
(19640401)A complex number is represented in rectangular coordinates as x/iy, where x and y are real. It is also represented as r(cos e/i sin e) in polar coordinates, where r and e are real. r is called the absolute value, or modulus ... 
Riemannian Geometry
(19650401)Mathematics enjoys special esteem above all the other sciences for several reasons. Its laws are absolutely certain and indisputable. This priority would not be momentous if the laws of mathematics referred only to objects ... 
Trigonometric Fourier Series
(19650401)A function f(x) is called periodic if there exists a constant T > o for which f(x+T)=f(x) for any x. The constant T is called the period of the function f(x). The most familiar periodic functions are sin x, cos x, tan x, ... 
Analog Computers
(19650401)This thesis has been written with the intention that it will aid those students interest in the operation of the Heathkit Educational Electronic Analog Computer acquired by Carroll College in this year 1965 and which will ...