Browse 62 real Mathematics projects entered in 2021, with abstracts, awards and links to the original entries.
ISEF · 2021
Mathematics
The COVID-19 outbreak has caused a huge demand of masks which can effectively protect people from the virus. However, the raw materials of masks are limited in such a short time. Thus, it be…
ISEF · 2021
Mathematics
The SIR model is one of the simplest examples of a class of mathematical models, called 'compartmental models', that are used to predict the spread of an epidemic. A number of efficient nume…
ISEF · 2021
Mathematics
The Collatz Conjecture and another of similar structure revolving around congruence modulus 3, can be represented as fractals when they are written as holomorphic functions. However, the met…
ISEF · 2021
Mathematics
Covid-19 reports have a substantial impact on the decisions that are made in making sure people are able to continue living their lives. Yet there have been multiple controversies on the acc…
ISEF · 2021
Mathematics
I started since I was intrigued by the by the beautiful derivation of "Buffon's needle" by integrating, and thought that it would be possible to calculate the probability of plane figures su…
ISEF · 2021
Mathematics
The goal of this project is to do fundamental research on Gray codes and develop a new algorithm to determine a Gray code given its corresponding decimal number. A Gray code sequence is a se…
ISEF · 2021
Mathematics First Award
Motivation: Many applications in the medical and engineering fields benefit from identifying topological features in a three-dimensional geometric model. Problem statement: When an object’s…
ISEF · 2021
Mathematics
The asteroid population is incomprehensibly large. Understanding, discovering and tracking asteroids are important to avoid catastrophic events to human civilization. Around one million aste…
ISEF · 2021
Mathematics
Research question: How the quadratic congruence could be solved using methods of modular arithmetic and group theory? Procedures used: An algebraic method for confirming the existence of any…
ISEF · 2021
Mathematics Fourth Award
It is known that each periodic orbit can be assigned to a spatial braid. The goal of the project is to check the hypothesis on the possibility of applying the braid theory to the classificat…
ISEF · 2021
Mathematics Fourth Award
Dacey established a class of simple, finite graphs, called Dacey graphs, which maps bijectively to the set of finite orthomodular posets, posets where the join of orthogonal elements always…
ISEF · 2021
Mathematics Second Award
It is a basic question in contact geometry to classify all non-isotopic tight contact structures on a given 3-manifold. If the manifold has a boundary, this classification is based on the di…
CSEF · 2021
Mathematical Sciences First Award
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…