Mathematical Sciences
Second Award
Modern computer chess programs capable of easily beating any human player are causing a crisis in the world of competitive chess. These programs are simple to use and can be run on personal…
Mathematics
My research looks at a self-similar triangular fractal known as the Sierpinski Gasket through the perspective of graph theory, by replacing intersections of line segments in the fractal with…
Mathematics
Fourth Award
We investigate a special variant of chip-firing, in which we consider an infinite set of rooms on a number line, some of which are occupied by violinists. In a move, we take two violinists i…
Mathematics
The project differs not only from the scientific side, but also from the social broadcasting point of view. The number e is widely used in mathematics. I have researched all possible context…
Mathematics
Collatz Conjecture was created in the 1930s by Lothar Collatz and has perplexed mathematicians for almost a century. The Collatz problem is an iteration of n/2, when n is even, and 3x+1, whe…
Mathematics
Systems of polynomial equations are of fundamental importance to mathematics, and have been applied to numerous areas, including physical problems, chemical reactions, robotics, communicatio…
Mathematics
Distance-based indices on graphs are of interest to chemical graph theorists for their connections to the chemical properties of molecules. In this paper, I study several extremal properties…
Mathematics
Second Award
Environmental damage is an ever-present issue for our generation, especially in the supply chain, which has suffered heavily since the beginning of 2020. Large amounts of packaging materials…
Mathematics
This research proposes to approach forecasting using classes defined by a fractal scheme. In time series analysis, forecasting is understood as generating a prediction based on known previou…
Mathematical Sciences
Honorable_mention Award
Introduction: Every year, immense amounts of food is wasted. ~6 million tons of perfectly good food is thrown out in California yearly. Engineering Goal: Using Python, BeautifulSoup, Request…
Mathematics
The relationship between atomicity and ACCP, two properties measuring the way elements factor in integral domains, is central to abstract factorization theory. It is known that all integral…
Mathematics
Third Award
Quantum computing is revolutionizing cryptography, as it will render the classical digital signature schemes such as Bitcoin's ECDSA (Elliptic Curve Digital Signature Algorithm) insecure. Th…
Mathematics
Pancreatic metastatic cancer prompts the aggressive emergence of a subsect of cancer cells known as Poly-aneuploid Cancer Cells (PACCs) which sustain a state of dormancy called quiescence wh…
Mathematics
Benford’s Law is a mathematical law that dictates the percentages of the appearances of initial digits 1-9 in a naturally occurring data set with no limits. This experiment tested to see if…
Mathematics
Domino tiling problem for (m, n)-grid was solved by Kasteleyn, Temperley and Fisher in 1961. L-tromino is a 2x2 rectangle without one cell. We consider the L-tromino tilings problem for (m,n…
Mathematical Sciences
Third Award
Robotic control is often divided into four categories: mapping, localization, path planning, and control. Recent innovations related to path planning often center around search-based plannin…
Mathematics
Various investigations propose a misconception of algebra, leading students to resolve problems in a deficient and careless way. Algebraic exercises constitute the basis for problem solving,…
Mathematics
For centuries, prime factorization has been a fundamental theoretical problem in the mathematical world. Conventionally, the algorithms for prime number factorization demand a computational…
Mathematics
Computing the Frobenius number for numerical semigroups with more than three generators is a famous unsolved problem in number theory and computational complexity. Given a numerical semigrou…
Mathematics
Fractals and knots are intriguing mathematical objects with similar applications and visual appeal, yet there have been very few reports on combining the two. In this project, an algorithmic…
Mathematics
Third Award
This study was motivated by a trance in my bathroom, looking at puddles on the ground, and imagining a curved mirror in mid-air. Then, emit a light beam to the curved mirror, in what circums…
Mathematics
It is known that there are countably many non-integers a > 1 which possess the property that ?a^n? is not a prime for all integers n = 1. There are however very few known explicit examples o…
Mathematics
This project explores the application of complex analysis techniques for solving combinatorial problems, particularly in the context of an enumeration problem in the theory of regular langua…
Mathematics
Third Award
Quantum computing is a rapidly growing field that applies quantum mechanics to computer science and its algorithms, and it has many applications, including optimization problems, where the g…
Mathematics
Fourth Award
Linear Delta robots (LDRs) are a relatively new subset of parallel robots, used in some 3D printing and manufacturing applications due to their rigidity and speed. However, there are just tw…
Mathematical Sciences
Honorable_mention Award
Linear Delta robots (LDRs) are a relatively new subset of parallel robots, used in some 3D printing and manufacturing applications due to their rigidity and speed. However, there are just tw…
Mathematics
A fundamental study in the field of quantum algebra is the study of fusion categories, which generalize finite groups and their representation categories. They also yield the structures of t…
Mathematics
A zigzag chord is a broken line with vertices on the circle and connecting in a zigzag way, and any two adjacent segments form a fixed certain angle. The initial observation of this project…
Mathematics
Third Award
Ever since the deferred acceptance algorithm was first proposed by Gale and Shapley (1962), there has been much research about mechanisms that optimally match high school seniors to colleges…
Mathematics
Dummit, Granville and Kisilevsky have recently shown that the proportion of semiprimes (products of two primes) not exceeding a given x, whose factors are congruent to 3 modulo 4, is more th…