Browse real student projects, abstracts, and awards.
ISEF · 2023
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…
ISEF · 2023
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…
ISEF · 2023
Mathematics Second Award
Knot theory is the mathematical study of tangled loops of string. Over the last 50 years, a number of applications have been found. For instance: molecules created with the same atoms, but s…
ISEF · 2023
Mathematics
For any given curve, integration is the customary method for determining the area under the curve. However, finding the actual length of the curve is a far more complex task and one rarely e…
ISEF · 2023
Mathematics First Award
The Two-Way Partitioning Problem is an NP-Complete problem that seeks to find a partition of a set of integers: given an input multiset S of n positive integers, separate the integers of S i…
ISEF · 2023
Mathematics
In this project we aim to study the structures of graph, generated by the transformations x? kx^n in Zp, with the goal to obtain results, in a sense equivalent to the result in Lee Deville's…
ISEF · 2023
Mathematics
A positive square matrix is an n × n array of positive real number entries. The Sinkhorn-Knopp alternate minimization algorithm transforms these matrices into their respective doubly stochas…
ISEF · 2023
Mathematics Fourth Award
Gerrymandering is one of the biggest problems in American democracy. Political parties have, in the past few decades, used redistricting as a method of maintaining political control. Often,…
ISEF · 2023
Mathematics
Two matrices, in which their numbers are separated by a number defined by “n” or “ni”, being ‘i’ the imaginary unit, will be similar. This research will work with various types of squared ma…
ISEF · 2022
Mathematics Fourth Award
In this study, we propose a general solution to the Broken Pick-up Sticks Problem which is a variation of the well-known Broken Sticks Problem. Since its solution is unknown to the mathemati…
ISEF · 2022
Mathematics Second Award
The Closest String problem (CSP) is an NP-Complete problem which seeks to find the geometrical center of a set of input strings: given k strings of length L and a non-negative integer d, con…
ISEF · 2022
Mathematics
Lego, like many other alternative investments, increases in value over time, with some sets increasing more than gold since 2000 (Wolff-Mann, 2015). However, what makes certain sets increase…
ISEF · 2022
Mathematics
Thue and Alon has laid the foundation of non-repetitive vertex colorings for certain graphs, discovering and proving many of its theorems. In this paper we explore the problem of how many co…
ISEF · 2022
Mathematics
Tetration is a fundamental mathematical operation that follows in the sequence of addition, multiplication, and exponentiation. x^^n is defined as x to the power of itself, n times. Naturall…
ISEF · 2022
Mathematics
If arm velocity, bat exit velocity, running speed, height, and weight of the high school baseball player is tested, the likelihood of success at different types of college baseball programs…
ISEF · 2022
Mathematics
The CNMI heavily relies on tourism. With the COVID-19 pandemic, this poses a concern for the tourism industry. In this project, the stats and data regarding the amount of worldwide COVID-19…
ISEF · 2022
Mathematics
Graph theory is the study of relationships between objects. Whether those objects are city blocks or web pages, graph theory can provide significant insight into optimization. A specific are…
ISEF · 2022
Mathematics
A mathematical model was created to explore the possibilities of balancing government financial debt caused by distributing stimulus checks (ERF) through the creation of the Emergency Saving…
ISEF · 2022
Mathematics
This study modified the Susceptible-Infected-Recovered (SIR) model, taking into account the population migration and vaccine to predict the dynamics of the third wave Covid-19 outbreak. The…
ISEF · 2022
Mathematics Fourth Award
The question of the existence and uniqueness of integers is one of the oldest and most fundamental questions in mathematics. Studied by mathematicians such as Euler, Fermat, and Dedekind sin…
ISEF · 2022
Mathematics
Farey sequence F_n of order n is the sequence of all irreducible fractions between 0 and 1 with denominators no greater than n arranged in increasing order. Farey sequence has a geometric in…
ISEF · 2022
Mathematics
Matrix multiplication is the fundamental building block of machine learning. All neural networks, when being trained, use matrix multiplication. However, multiplying a significantly large nu…
ISEF · 2022
Mathematics
Together, the Pascal triangle and the Newton binomial, can predict sequences of numbers. Procedures will be performed with binomial , were the value of one of the variables will remain const…
ISEF · 2022
Mathematics Second Award
The non-trivial zeros of L-functions encode important information about primes, which are essential to both number theory and modern cryptography. The zeros near the central point, s = 1/2,…
ISEF · 2022
Mathematics
Torus knots are knots that lie on the surface of a torus. Torus knots have a wide variety of applications in quantum mechanics, molecular chemistry, and topology. In this paper, a comprehens…
ISEF · 2022
Mathematics
Given a circle of radius r centered at the origin, the Gauss Circle Problem concerns counting the number of lattice points C(r) within this circle. It is known that as r grows large, the num…
ISEF · 2022
Mathematics
In this study, a linear recurrence relation, a(n)=a(n-1)+ (a(n-1) mod m) where m is any odd positive integer, is investigated for potential applications in cryptography. The periodic sequenc…
ISEF · 2022
Mathematics
My novel method of machine learning that I utilized with cluster analysis can be done on any computer and is fast and easy to learn. My novel method investigated a genome-wide association st…
ISEF · 2022
Mathematics
The max-cut problem as part of extremal combinatorics was formulated by Paul Erdos in the 1960s. Multiple papers have been written on the topic regarding its role in mathematics as an extrem…
ISEF · 2022
Mathematics First Award
The abc-conjecture (Masser and Oesterlé) is an active problem that has remained open for several decades. The conjecture would imply a direct proof of Fermat’s Last Theorem and also shine ne…