Browse real student projects, abstracts, and awards.
ISEF · 2019
Mathematics
Attention deficit is always a confusing disease: the exact causes of this disorder is still unclear. However, the prevalent idea is that genetics is a major factor of ADHD. Based on that ide…
ISEF · 2019
Mathematics
The purpose of this investigation is to identify patterns, if any exist, among primitive Pythagorean triples so that a triple, given an initial value, can be found. Specifically, the researc…
ISEF · 2019
Mathematics
Many functions do not have elementary antiderivatives and different analytical methods to evaluate the definite integral fail. These functions appear in fields such as biology, physics and e…
ISEF · 2019
Mathematics
One-dimensional cellular automata have been studied by looking at morphisms and properties of growth; however, no proof or demonstration has been made to explain these conjectured patterns a…
ISEF · 2019
Mathematics
Divisibility rules which are used to detect divisibility of numbers are memorable and practical rules and methods which are different for each number. A new study has been conducted to impro…
ISEF · 2019
Mathematics
How is it possible to calculate the direction of the reflection of an arbitrary ray of light off of a surface existing in any number of dimensions without the use of trigonometry? This proje…
ISEF · 2019
Mathematics
The purpose of my research and project is to create a dynamical comprehensive mathematical model that represents the flow of non-Newtonian polymeric fluids through a pipe. For industries fro…
ISEF · 2019
Mathematics
A stock option is a contract that grants the right to buy or sell an underlying stock at a predetermined price. In the United States, almost 20 million stock options are sold every trading d…
ISEF · 2019
Mathematics
The purpose of the experiment entitled “Are MVPs Really the Most Valuable Players?” was to test the accuracy of the sabermetric statistic known as wins above replacement (WAR). To test its a…
ISEF · 2019
Mathematics
Bootstrap percolation, which originated from the field of statistical mechanics, is a class of monotone cellular automata describing an activation process which follows certain activation ru…
ISEF · 2019
Mathematics
Magic squares are defined as matrices whose rows, columns, and main diagonals all add to the same number. They have existed and have been a topic of great interest since as early as 190 BCE,…
ISEF · 2019
Mathematics
This number theory project investigates identities found by multiplying together quaternions in L[x,y,z,w], the Lipschitz quaternions L adjoined with the indeterminates x, y, z, w. Recall th…
ISEF · 2019
Mathematics
Small pieces of plastic from 0.05 mm to 0.5 mm, called microplastics, pollute the ocean by congregating and moving through oceanic currents. Initial regions were defined along coasts to repr…
ISEF · 2019
Mathematics
This project focuses on a contradictory case within the Banach-Tarski paradox. The paradox outlines how any three-dimensional figure can be transformed into any other figure while only using…
ISEF · 2019
Mathematics
Naturally, silkworms construct ellipsoidal cocoons by spinning silk fibers around themselves. When we consider a cocoon in two dimensions, a cocoon has an elliptical shape which is one of th…
ISEF · 2019
Mathematics Fourth Award
I developed a new method to analyze expanding maps with indifferent fixed points. I applied this method to specifically analyze the iterations of the tangent map, proving both measure-theore…
ISEF · 2019
Mathematics
This paper shows a thorough examination of fully homomorphic encryption schemes and their performance in programs. We do an analysis of one specific, widely-used scheme – the Gentry-Sahai-Wa…
ISEF · 2019
Mathematics Third Award
This project is motivated by studying Chebyshev polynomials such as cos?(mx) is a polynomial of cos?(x). It is interesting to know if there are other non-constant continuous functions f havi…
ISEF · 2019
Mathematics
Traditionally introduced in terms of advanced topological constructions, many link invariants may also be defined in much simpler terms given their values on a few initial links and a recurs…
ISEF · 2019
Mathematics
Purpose: The problem of finding the shortest path between the two given points is a classical problem in geometry. These paths are called geodesic lines. The existence of non-self-intersecti…
ISEF · 2019
Mathematics
A wonderful fact called Thurston's geometrization conjecture states that there are essentially only eight three-dimensional geometries. One of them is Nil geometry, which is a Lie group call…
ISEF · 2019
Mathematics
There is the theory of doodles and twins in combinatorial topology, which is similar to link and braid theory. A doodle on a surface is a union of several closed curves that are intersecting…
ISEF · 2019
Mathematics
Traditional economic theory relies on assumptions of homogeneous agents reaching equilibrium under ideal conditions; there has been a push away from classical economics toward more real worl…
ISEF · 2019
Mathematics
In this study, we consider a discrete dynamic system starting with n arbitrary points on a circle. In one transition, each point moves simultaneously from its current state counterclockwise…
ISEF · 2019
Mathematics Fourth Award
Given a Vector Bundle (Coherent Sheaf) with Integrable Connection on a variety in positive characteristic, its p-curvature measures the amount of horizontal sections of the bundle and its va…
ISEF · 2019
Mathematics
*Introduction Mersenne Primes:- A number of the form 2^n – 1 where n is a natural number is a Mersenne number. If its value is prime then it is known as a Mersenne Prime. Mersenne primes are…
ISEF · 2019
Mathematics
Cooperative games are systems in which entities, players, can join to form subsets, known as coalitions. While players contribute varying amounts, known as marginal impacts, to different coa…
ISEF · 2019
Mathematics
There’s no doubt that in recent years the connection between different subjects is really cruical. For this exact reason I intend to proof mathematical theories with the help of syllogisms.…
ISEF · 2019
Mathematics
In low-dimensional topology, one of the most beautiful and complex topics is braid theory. There are deep connections between braids, knots, mappings on surfaces, and even algebraic geometry…
ISEF · 2019
Mathematics Third Award
Dimensionality reduction techniques are becoming widely used in academia, business, and machine learning to reduce the time required to process a higher dimensional dataset. In this context,…