Mathematics
A stock option is a contract that grants the right to buy or sell an underlying stock at a predetermined price. In the United States, almost 20 million stock options are sold every trading d…
Mathematics
The purpose of the experiment entitled “Are MVPs Really the Most Valuable Players?” was to test the accuracy of the sabermetric statistic known as wins above replacement (WAR). To test its a…
Mathematics
Bootstrap percolation, which originated from the field of statistical mechanics, is a class of monotone cellular automata describing an activation process which follows certain activation ru…
Mathematical Sciences
Honorable_mention Award
Objectives The two main goals of my project were to reliably detect invasive insects and design a platform to alert the presence of invasive bugs to farmers and to state and local agricultur…
Mathematics
Magic squares are defined as matrices whose rows, columns, and main diagonals all add to the same number. They have existed and have been a topic of great interest since as early as 190 BCE,…
Mathematics
This number theory project investigates identities found by multiplying together quaternions in L[x,y,z,w], the Lipschitz quaternions L adjoined with the indeterminates x, y, z, w. Recall th…
Mathematics
Small pieces of plastic from 0.05 mm to 0.5 mm, called microplastics, pollute the ocean by congregating and moving through oceanic currents. Initial regions were defined along coasts to repr…
Mathematics
This project focuses on a contradictory case within the Banach-Tarski paradox. The paradox outlines how any three-dimensional figure can be transformed into any other figure while only using…
Mathematics
Naturally, silkworms construct ellipsoidal cocoons by spinning silk fibers around themselves. When we consider a cocoon in two dimensions, a cocoon has an elliptical shape which is one of th…
Mathematical Sciences
Honorable_mention Award
Objectives My project explores a genetic algorithm as a method for producing a resultant digital neural network competent at a strategy game, namely Connect Four. I quantify competency as a…
Mathematical Sciences
Objectives The main objective of this project was to create an algorithm that could take the image of a drawn curve and find a function to model it. This objective can be broken down into th…
Mathematical Sciences
Objectives The objective is to determine which anomaly detection method is the most accurate at classifying lightcurves of stars, and which is the most suitable for use by astrophysicists. M…
Mathematical Sciences
First Award
Objectives The objective of this project was to develop an efficient algorithm to detect pneumonia looking at a Chest Radiograph X-ray image with an emphasis on minimizing False Negatives. W…
Mathematical Sciences
Fourth Award
Objectives In his monograph "Solutio facilis problematum quorumdam geometricorum difficillimorum," the Swiss mathematician Leonhard Euler first publicized the concept of the Euler Line, whic…
Mathematical Sciences
Third Award
Objectives DBSCAN is an unsupervised learning algorithm that connects locally dense regions of data to form data clusters. This algorithm is frequently used for medical, engineering, and fin…
Mathematics
Fourth Award
I developed a new method to analyze expanding maps with indifferent fixed points. I applied this method to specifically analyze the iterations of the tangent map, proving both measure-theore…
Mathematical Sciences
First Award
Objectives Analyze the distribution of the iterations of the tangent map for most starting values, both measure- theoretically and topologically. Characterize sets of starting values whose t…
Mathematical Sciences
Honorable_mention Award
Objectives Identifying high-centrality nodes in large networks can be computationally inefficient, given that the most efficient exact algorithm runs in O(MN) time. A number of randomized ap…
Mathematics
This paper shows a thorough examination of fully homomorphic encryption schemes and their performance in programs. We do an analysis of one specific, widely-used scheme – the Gentry-Sahai-Wa…
Mathematical Sciences
Objectives Testing 3D point cloud neural networks to see if they are susceptible to adversarial attacks like previous results on 2D images, proposing new algorithms for both attacking and de…
Mathematics
Third Award
This project is motivated by studying Chebyshev polynomials such as cos?(mx) is a polynomial of cos?(x). It is interesting to know if there are other non-constant continuous functions f havi…
Mathematical Sciences
Objectives The objective of this study is to determine the gin rummy playing strategy with the highest likelihood of winning. Methods Computer, Python coding language. Coded a 2-player gin r…
Mathematical Sciences
Objectives The Tower of Hanoi is a problem where in a system of m pegs, n rings are on the first peg, arranged from smallest on the top to largest on the bottom. One ring can be moved at a t…
Mathematics
Traditionally introduced in terms of advanced topological constructions, many link invariants may also be defined in much simpler terms given their values on a few initial links and a recurs…
Mathematics
Purpose: The problem of finding the shortest path between the two given points is a classical problem in geometry. These paths are called geodesic lines. The existence of non-self-intersecti…
Mathematics
A wonderful fact called Thurston's geometrization conjecture states that there are essentially only eight three-dimensional geometries. One of them is Nil geometry, which is a Lie group call…
Mathematics
There is the theory of doodles and twins in combinatorial topology, which is similar to link and braid theory. A doodle on a surface is a union of several closed curves that are intersecting…
Mathematical Sciences
Objectives The objective of this project is to design, implement, test, and analyze simple algorithms to find the one that can achieve the highest tiles in the Google Chrome Extension of the…
Mathematics
Traditional economic theory relies on assumptions of homogeneous agents reaching equilibrium under ideal conditions; there has been a push away from classical economics toward more real worl…
Mathematical Sciences
Objectives The objective of my project is to compare several different strategies used in the game Iterated Prisoner s Dilemma. I investigate how each strategy performs against all other ava…