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Articles 1 - 12 of 12
Full-Text Articles in Other Mathematics
Logistics Planning: Putting Math To Work In A Business Setting, Michael C. Hannan
Logistics Planning: Putting Math To Work In A Business Setting, Michael C. Hannan
Senior Projects Spring 2023
The optimization of business procedures benefits all aspects of the product. Maximizing efficiency can lead to more profits for the business, cheaper products for the consumer, and less fuel consumption for the environment. Tracing the history of optimization, we can see that people have always strived for the most efficient way to allocate scarce resources. However, the field of optimization did not blossom until innovations in mathematics allowed us to solve a majority of real world problems. The discovery of linear and nonlinear programming in the 1940s allowed us to optimize problems that were unsolvable before. This paper introduces how …
Hidden Symmetries Of The Kepler Problem, Julia Kathryn Sheffler
Hidden Symmetries Of The Kepler Problem, Julia Kathryn Sheffler
Senior Projects Spring 2022
The orbits of planets can be described by solving Kepler’s problem which considers the motion due to by gravity (or any inverse square force law). The solutions to Kepler’s problem, for energies less then 0, are ellipses, with a few conserved quantities: energy, angular momentum and the Laplace-Runge-Lenz (LRL) vector. Each conserved quantity corresponds to symmetries of the system via N ̈other’s theorem. Energy conservation relates to time translations and angular momentum to three dimensional rotations. The symmetry related to the LRL vector is more difficult to visualize since it lives in phase space rather than configuration space. To understand …
Module Basis Of Mixed Splines Over R[X], Philip G. Barnet
Module Basis Of Mixed Splines Over R[X], Philip G. Barnet
Senior Projects Spring 2021
A mixed spline is a piecewise polynomial with varying degrees of smoothness. In this project, we characterize a basis for mixed splines over subdivisions of the reals based on a characterization for integer spline bases. We use our new characterization to find bases for modules of splines with boundary conditions with particular differentiability requirements on their boundaries and compare various aspects of the two.
An Exploration On Condorcet-Approval-Range Voting Function With Limits, Jiangli Liu
An Exploration On Condorcet-Approval-Range Voting Function With Limits, Jiangli Liu
Senior Projects Spring 2021
In contrast to most social choice methods, which use ranked ballots, range voting is a well-known social choice method that offers the voters more choices in the form of an allowed range of possible scores. In this project, by allowing voters to give positive and negative scores, we hope to find a way that can explicitly show how voters disapprove, feel neutral, or approve of the alternatives instead of just giving ranking orders. Also, by applying a function to constrain the scores given in range voting, each voter will have the same influence when they give scores. After combining these …
Dimentia: Footnotes Of Time, Zachary Hait
Dimentia: Footnotes Of Time, Zachary Hait
Senior Projects Spring 2021
Time from the physicist's perspective is not inclusive of our lived experience of time; time from the philosopher's perspective is not mathematically engaged, in fact Henri Bergson asserted explicitly that time could not be mathematically engaged whatsoever. What follows is a mathematical engagement of time that is inclusive of our lived experiences, requiring the tools of storytelling.
From Constant To Stochastic Volatility: Black-Scholes Versus Heston Option Pricing Models, Hsin-Fang Wu
From Constant To Stochastic Volatility: Black-Scholes Versus Heston Option Pricing Models, Hsin-Fang Wu
Senior Projects Spring 2019
The Nobel Prize-winning the Black-Scholes Model for stock option pricing has a simple formula to calculate the option price, but its simplicity comes with crude assumptions. The two major assumptions of the model are that the volatility is constant and that the stock return is normally distributed. Since 1973, and especially in the 1987 Financial Crisis, these assumptions have been proven to limit the accuracy and applicability of the model, although it is still widely used. This is because, in reality, observing a stock return distribution graph would show that there is an asymmetry or a leptokurtic shown in the …
Analysing Flow Free With One Pair Of Dots, Eliot Harris Roske
Analysing Flow Free With One Pair Of Dots, Eliot Harris Roske
Senior Projects Spring 2019
Flow Free is a smartphone puzzle game where the player is presented with an m by m grid containing multiple pairs of colored dots. In order to solve the puzzle, the player must draw a path connecting each pair of points so that the following conditions are met: each pair of dots is connected by a path, each square of the grid is crossed by a path, and no paths intersect. Based on these puzzles, this project looks at grids of size m by n with only one pair of dots to determine for which configurations of dots a solution …
A Strength Test For The Borda Count, Jade Monroe Waring
A Strength Test For The Borda Count, Jade Monroe Waring
Senior Projects Spring 2019
When running an election with more than two candidates, there are many ways to choose the winner. A famous theorem of Arrow states that the only mathematically fair way to choose is to do so at random. Because this is not a desirable way to choose a winner of an election, many mathematicians have devised alternate ways of aggregating ballots. In my project I consider one of these ways -- the Borda Count, considered to be one of the most desirable from both the point of view of mathematics and economics -- and came up with a method to test …
The Mathematics Of Cancer: Fitting The Gompertz Equation To Tumor Growth, Dyjuan Tatro
The Mathematics Of Cancer: Fitting The Gompertz Equation To Tumor Growth, Dyjuan Tatro
Senior Projects Spring 2018
Mathematical models are finding increased use in biology, and partuculary in the field of cancer research. In relation to cancer, systems of differential equations have been proven to model tumor growth for many types of cancer while taking into account one or many features of tumor growth. One feature of tumor growth that models must take into account is that tumors do not grow exponentially. One model that embodies this feature is the Gomperts Model of Cell Growth. By fitting this model to long-term breast cancer study data, this project ascertains gompertzian parameters that can be used to predicts tumor …
Winning Strategies In The Board Game Nowhere To Go, Najee Kahil Mcfarland-Drye
Winning Strategies In The Board Game Nowhere To Go, Najee Kahil Mcfarland-Drye
Senior Projects Spring 2016
Nowhere To Go is a two player board game played on a graph. The players take turns placing blockers on edges, and moving from vertex to vertex using unblocked edges and unoccupied vertices. A player wins by ensuring their opponent is on a vertex with all blocked edges. This project goes over winning strategies for Player 1 for Nowhere To Go on the standard board and other potential boards.
Envy-Free Fair Division With Two Players And Multiple Cakes, Justin J. Shin
Envy-Free Fair Division With Two Players And Multiple Cakes, Justin J. Shin
Senior Projects Fall 2016
When dividing a valuable resource amongst a group of players, it is desirable to have each player believe that their allocation is at least as valuable as everyone else's allocation. This condition, where nobody is envious of anybody else's share in a division, is called envy-freeness. Fair division problems over continuous pools of resources are affectionately known as cake-cutting problems, as they resemble attempts to slice and distribute cake amongst guests as fairly as possible. Previous work in multi-cake fair division problems have attempted to prove that certain conditions do not allow for guaranteed envy-free divisions. In this paper, we …
Exploring Tournament Graphs And Their Win Sequences, Sadiki O. Lewis
Exploring Tournament Graphs And Their Win Sequences, Sadiki O. Lewis
Senior Projects Fall 2016
In this project we will be looking at tournaments on graphs and their win sequences. The main purpose for a tournament is to determine a winner amongst a group of competitors. Usually tournaments are played in an elimination style where the winner of a game advances and the loser is knocked out the tournament. For the purpose of this project I will be focusing on Round Robin Tournaments where all competitors get the opportunity to play against each other once. This style of tournaments gives us a more real life perspective of a fair tournament. We will model these Round …