Browse real student projects, abstracts, and awards.
ISEF · 2021
Mathematics
The goal of my project is to evaluate multiple college football playoff formats involving different numbers of teams using the Monte Carlo simulation method. The computer simulation generate…
ISEF · 2021
Mathematics
This work is devoted to finding an element in a free group’s commutator subgroup such that the commutator length of the square is less than the commutator length. The results obtained allow…
ISEF · 2021
Mathematics
The Kimberling shuffle is an integer sequence generated by the shuffling and expulsion of numbers. From the sequence of natural numbers, 1 is expelled and the first integer in front (2) is p…
ISEF · 2021
Mathematics
This research approached the optimization of train curves in a mathematical way by using differential geometry and the calculus of variations. Our objective was to find the travel time-minim…
ISEF · 2021
Mathematics Third Award
In Alzer, Horst and Luca’s paper it is shown that the Diophantine equation (k!)^n+k^n= (n!)^k+n^k only has the trivial solution n=k, and (k!)^n- k^n= (n!)^k- n^k only has the solutions n=k,…
ISEF · 2021
Mathematics
Domain Specific Languages (DSL) give the user a rigorous environment for solving problems in a specific domain, in this case differential equations. Scott-Strachey semantics (also known as d…
ISEF · 2021
Mathematics
The performance of a modified Elo update rule was tested against the original Elo update rule. The Elo update rule can be interpreted as an application of gradient descent using a certain lo…
ISEF · 2021
Mathematics Second Award
The purpose of this research is to enumerate the number of ways of dissecting a convex polygon with arbitrary prescribed conditions on the allowable polygon pieces. It is well known that the…
ISEF · 2021
Mathematics
The work is devoted to the search and the expansion of knowledge about the complete solution of the historical problem called the "Fibonacci's Problem" (the XIIIth century), which was solved…
ISEF · 2021
Mathematics
Signed graphs are commonly used in social networks to model relationships, and Kirchhoff-type conservation laws can be applied to signed networks to simulate the diffusion of information or…
ISEF · 2021
Mathematics Third Award
Topdrops, a mapping of permutations first introduced by John Horton Conway, is examined. Topdrops has so far been under-researched compared to the similar topswops variant. A proof that the…
ISEF · 2021
Mathematics Third Award
Real world mathematical models are often built to incorporate dynamical features like Lebesgue measure preservation, but the algebraic, group theoretical properties of dynamical systems have…
ISEF · 2021
Mathematics Second Award
The analysis of human coronaviruses and the confirmed cases of COVID-19 reinfection are indicative of waning immunity present to some degree in patients recovering from COVID-19. Therefore,…
ISEF · 2021
Mathematics
Dengue fever is a widespread mosquito-borne disease, prevalent in the Americas, Africa, and Asia, that affects approximately 400 million people each year. The prevention of dengue fever is t…
ISEF · 2021
Mathematics
My research aims to study the finite separability of finitely generated commutative rings. It is of interest because of its connection with the so-called algorithmic problem of entering a su…
ISEF · 2021
Mathematics Third Award
Image and shape classification have been studied extensively with the growing popularity of convolutional neural networks (CNNs). However, CNNs operate on rasterized images rather than geome…
ISEF · 2021
Mathematics Fourth Award
In this work I give a complete description of the language of geodesic words for the central extension of the Klein Bottle group with respect to the standard two-element generating set. I cr…
ISEF · 2021
Mathematics
Both knot theory and origami have many relations to mathematics and the overall broader scientific world. The main problem in mathematical knot theory is identifying knot equivalence. In thi…
ISEF · 2021
Mathematics
The contents of the partial fractions contained in high school textbooks are presented in the form of formulas, and there is no explanation of the meaning. When we learn mathematics, formula…
ISEF · 2021
Mathematics
Li-Yorke theorem shows for a continuous self-mapping in interval, if it has a period-3 point, it will have period-n point with any positive integer n. Therefore, period-3 point is worth expl…
ISEF · 2021
Mathematics
The crossing number cr(G) of a graph G is the least number of edge crossings of a plane drawing of G. Determining the exact crossing number of a graph is NP-Complete. In this project, we pre…
ISEF · 2021
Mathematics
Quadratization is a transform of a system of ODEs with polynomial right-hand side into a system of ODEs with at most quadratic right-hand side via the introduction of new variables. It has b…
ISEF · 2021
Mathematics
Euler numbers E_n appear in many places of classic analysis, combinatorics, and topology. They can be defined as Taylor coefficients of the function tanh x + sech x or (in the terminology of…
ISEF · 2021
Mathematics
A graph represents a group of objects (network) and the relations between them. This research introduces ranking of vertices – a mathematical concept, applied to various areas (Google search…
ISEF · 2021
Mathematics
The purpose of this paper is to express Robinson-Schensted correspondence in two different ways, Schensted’s algorithm and a geometric interpretation by Viennot, and compare and prove differ…
ISEF · 2021
Mathematics
Closed geodesic lines on polyhedra are defined as locally shortest polylines not passing through vertices. In 2002 it was proven that the majority of convex polyhedra are free of simple (non…
ISEF · 2021
Mathematics
It is known that attempts to solve some equations and systems of equations by standard methods often cause great difficulties. However, it is more convenient to solve these equations and sys…
ISEF · 2021
Mathematics
Okamoto-Uchiyama encryption scheme is one of the Paillier cryptosystem’s foundations. Unfortunately, its “twin” signature scheme, properties and specialized kinds of digital signatures are n…
ISEF · 2021
Mathematics
After doing a survey about Math learning of grade 8 and 9 students at our school, we found that the level simulating the interest of students in Math and the ability to solve real-life probl…
ISEF · 2021
Mathematics
Arbelos is a plane region bounded by three semicircles with three apexes such that each corner of each semicircle is shared with one of the others, all on the same side of a straight line th…