Browse real student projects, abstracts, and awards.
ISEF · 2025
Mathematics
For the last 20 years, many researchers have explored divisibility properties of integer sequences arising from combinatorial structures. In particular, binomial coefficients have been the s…
ISEF · 2025
Mathematics
Financial models for stock prices play a crucial role in maintaining economic stability by enabling risk assessment, informed investing, and regulatory oversight. However, many conventional…
ISEF · 2025
Mathematics
To improve artificial vision systems, human vision should be better understood. Many aspects of human vision are tuned to the characteristics of its natural inputs. These characteristics inc…
ISEF · 2025
Mathematics
Purpose In this study, Rowlands' sequence, a recursive sequence discovered in 2003, was studied. The aim was to develop a conditional proof of: Conjecture 1: The first difference of Rowlands…
ISEF · 2025
Mathematics
This research looks to define a basis and the behavior of the Tau-divisor topology. This can be viewed as a permutation of the usual divisor topology by implementing the Tau-factorization th…
ISEF · 2025
Mathematics
Pólya's Enumeration Theorem utilizes group theory in order to count the number of distinct arrangements of a substituted three-dimensional system based on the fixed points on a shape and its…
ISEF · 2025
Mathematics
There are many unsolved diophantine equations involving factorials in the field of number theory, such as Brocard's Problem. This research enhances the understandings of factorials with nove…
ISEF · 2025
Mathematics
The representation of prime numbers as quadratic forms is one of the central topics of number theory, dating back to Fermat and Euler. This study investigates prime numbers expressed as x^2+…
ISEF · 2025
Mathematics
The difficulty of prime factorization is essential to keeping our world secure. However, the rise of quantum computing poses a major threat to this security, and thus, it is imperative to di…
ISEF · 2025
Mathematics
This project investigates the representation of polygons through the roots of unity. Since the points in the complex graph of power functions lead to equidistant solutions, they can then be…
ISEF · 2025
Mathematics
Lothar Collatz defined a function on natural numbers: divide x by 2 when it is even, multiply by three and add one otherwise. He conjectured that repeated application of this function to any…
ISEF · 2025
Mathematics
The smooth sliceness of a knot is an important property with connections to longstanding problems in topology such as the smooth four-dimensional Poincare Conjecture (4SPC) and the Slice-Rib…
ISEF · 2025
Mathematics
We propose a gated neural framework for solving partial differential equations (PDEs) of the form L(u(x)) = f(x), where x ? O ? Rn and u : O ? R. The solution u(x) is expressed as a residual…
ISEF · 2025
Mathematics
This study aimed to develop a theorem that algebraically calculates the maximum number of spheres inscribed within a ring torus and its resulting total volume. A ring torus is a circle with…
ISEF · 2025
Mathematics
For a polynomial P(x) with integer coefficients and a maximum positive integer root m, we consider the product of its values from x=m+1 to n and denote it as Fp(n). Building up on previous w…
ISEF · 2025
Mathematics
We explore the Euler-Lagrange equations in which tangent spaces have non-coordinate bases. This generalized form is the Boltzmann-Hamel (BH) equation, which contain a term dependent on a coe…
ISEF · 2025
Mathematics
This research aimed to explore the behavior of particles in high-energy proton collisions through a Markovian model to identify cohesive patterns and predict particle behavior. One fundament…
ISEF · 2025
Mathematics
Understanding whether selfish or altruistic behavior benefits an individual more remains challenging using traditional approaches like studying human samples. The prisoner's dilemma, a game…
ISEF · 2025
Mathematics
Polygons, a fundamental concept within the sub-learning area of geometry, have a versatile structure that makes them highly suitable for generalization. With applications extending across ma…
ISEF · 2025
Mathematics
There are over 400,000 cases of Sudden Cardiac Arrest (SCA) recorded annually, with over 90% of these events being fatal. The current detection system used to detect cardiac arrest in hospit…
ISEF · 2024
Mathematics
Inspired by the famous function of the D.Kaprekar K(n)=n+S(n), I invented and investigated various properties of a new function A(n)=(n-S(n))/9 where S(n) is the sum of digits of the natural…
ISEF · 2024
Mathematics Second Award
The rise of modern cryptosystems introduced the problem of modular exponentiation. Modular exponentiation is the problem of computing a perfect power a^n modulo some modulus, say m. This pro…
ISEF · 2024
Mathematics
This study explored various general properties related to the theta curve’s arc index. The arc index not only serves to classify spatial graphs but also plays a crucial role in computing a s…
ISEF · 2024
Mathematics Second Award
Classification tasks in machine learning, essential for applications ranging from fraud detection to medical diagnoses, frequently encounter the challenge of imbalanced datasets. These imbal…
ISEF · 2024
Mathematics
Students across the United States live with the fear of school violence. Schools combat this through rehearsal lockdowns, dress codes, metal detectors, and professional development for polic…
ISEF · 2024
Mathematics
Typical Ramsey theory refers to that, if all edges of a complete graph with n vertices are colored in red or blue, each edge in either color of the two, when n becomes large enough, we can c…
ISEF · 2024
Mathematics
For a fixed positive integer b?N, let the b-sight lines be defined by f(x)=ax^b, for a?Q, with the origin O as the observing point (the position of the eyes). A point in the square lattice V…
ISEF · 2024
Mathematics
Over the course of history, different ways of hiding messages have been created, and this investigation was done to achieve that using RSA and dates. The way that this encryption system work…
ISEF · 2024
Mathematics
Studying population dynamics is key to protecting vital aquatic ecosystems and the economic activities they support, such as those of the Chesapeake Bay. Mathematics is a powerful tool that…
ISEF · 2024
Mathematics
Spacetime is a mathematical model of our universe based on the general relativity theory. Our observable world in this spacetime is represented by causally related points, defined as points…