Browse real student projects, abstracts, and awards.
ISEF · 2018
Mathematics
Let G=(Z_2)^k. That is, the set of k-dimensional vectors with binary components. We say that a subset of G (call this A) is a 'Sidon Set' if all pairwise sums, a_i+a_j (i<j) in A, are distin…
ISEF · 2018
Mathematics Fourth Award
Learning from classified and unclassified data is generally categorized as semi-supervised learning (SSL). Traditional, graph-based SSL (GBSSL) algorithms operate by designing a relatively s…
ISEF · 2018
Mathematics
The purpose of this project is to develop a cipher (encryption algorithm) and cryptosystem that is both practical and provably secure. First, I investigate the relationship between continued…
ISEF · 2018
Mathematics
The Diophantine equation Ax^2+By^2+Cz^2=0 is named for Adrien-Marie Legendre, who found in 1785 a necessary and sufficient condition for the existence of non-trivial integer solutions to thi…
ISEF · 2018
Mathematics
In the completion of a big festival that involves many people, the number of participants will be announced. There could be up to 5 times differences in estimation, Therefore in this study,…
ISEF · 2018
Mathematics Fourth Award
In this project, we aim to prove certain properties about a particular function c(n) = b_nr(n). This is where b_n is a Boolean function with b_n being 1 if n = x^2 + y^2 for some integers x…
ISEF · 2018
Mathematics Second Award
The mathematical field of algebraic topology studies the association of algebraic data to topological spaces, which are generalizations of geometric shapes. Since its creation in the early 2…
ISEF · 2018
Mathematics Third Award
My work is devoted to studying the combinatorics of 216 maximal C3 circular codes - a special sets of words. Circularity means, that every new word, formed from the elements of this set and…
ISEF · 2018
Mathematics
Graph connectivity is a critical concept for a variety of applications in both pure and applied math. Identifying the connectivity of the graphs underlying neural networks, for example, woul…
ISEF · 2018
Mathematics
This project demonstrated the problem of deconstructing graphical models is polynomial time solvable, with an O(mn^r+3 + nr) algorithm. The execution was split into two parts: one involving…
ISEF · 2018
Mathematics
Riemann sums are a way of understanding integrals. Riemann sums have practical applications as they can be used to measure areas such as a lake easier than other methods. However, Riemann su…
ISEF · 2018
Mathematics Fourth Award
A random matrix is a matrix whose entries are given by random variables. The spectral statistics of high dimensional random matrices have shown deep connections with physics over the past ce…
ISEF · 2018
Mathematics
Our project is motivated by the following property: “For four focal radii originating equiangularly from a focus of an ellipse, the sum of their squared reciprocals is a constant.” We genera…
ISEF · 2018
Mathematics
We successfully extended Soddy’s theorem for the original Soddy’s hexlet to derive the number of spheres of what we refer to as the n-th generation hexlet: 6^n. The number of spheres composi…
ISEF · 2018
Mathematics
The present work is used to set a mathematical problem to discover absolute barycentric coordinates of locus $P^n_{min}$ in the triangle plane, featured with the $n^{\text{th}}$ powers of di…
ISEF · 2018
Mathematics
\textit{Draw of choice} (Finnish: "hutunkeitto") in Finnish baseball can be seen as a finite two-player game with winning and losing positions. By inspecting winning and losing positions one…
ISEF · 2018
Mathematics
Considering all of the different areas of math, including advanced geometry, one of the least heard of is fractals, geometric figures in which each part has the same statistical characterist…
ISEF · 2018
Mathematics Fourth Award
I study Lucas Sequences, recursive sequences that generalize the Fibonacci Sequence, and Lucas Groups, solutions of a variant of Pell’s Equation mod p. Lucas Sequences have a broad backgroun…
ISEF · 2018
Mathematics
In this investigation, an active investment strategy based on the principles of game theory was tested against the passive strategy of buy-and-hold to determine which was more effective. Inv…
ISEF · 2018
Mathematics Third Award
The fundamental paradigm of persistent homology is to vary an unknown parameter while computing algebraic invariants. The stability of the invariants is then analyzed to determine significan…
ISEF · 2018
Mathematics Third Award
The concept of a free object is one that relates to all kinds of algebraic structures, i.e. free groups, free algebras. In this project we investigate one of the most fundamental free object…
ISEF · 2018
Mathematics
Hilbert's space is a complete unitary space that allows you to operate with complex n-tics (vectors), complex sequences and complex functions in exactly the same way. The basic element of th…
ISEF · 2018
Mathematics
The dynamics of polynomials in the space of 2X2 real matrices of the form Q(Z) = Z^2+C with a Constant C consisting of complex eigenvalues, identical eigenvalues, and distinct real eigenvalu…
ISEF · 2018
Mathematics Second Award
A finite dynamical system (FDS) is a function f: F_m^n?F_m^n, where F_m^n is a set of m^n elements. Due to its applications to gene regulatory networks, it is desirable to develop mathematic…
ISEF · 2018
Mathematics
The most important geometric invariant of a degree-n complex rational function f(X) is its monodromy group, which is a set of permutations of n objects. This monodromy group determines sever…
ISEF · 2018
Mathematics
Voice leading in music is a key element of the Western tradition. It is closely associated with homotopy, the exploration of chordal paths in higher dimensional configuration spaces. Musicia…
ISEF · 2018
Mathematics
The N-Queens Problem is the problem of placing N chess queens on a NxN chessboard so that no two queens attack each other. Calculation of the number of different solutions is related to the…
ISEF · 2018
Mathematics Fourth Award
In this project, it is investigated a problem of exploring of the rule of number patterns. In fact, the problem is to find general term of the number sequences, if we have some consecutive t…
ISEF · 2018
Mathematics
In this project we study the energy functional on the set of Lagrangian tori in CP^2. The energy conjecture asserting that the value of energy functional for any Lagrangian torus in CP^2 is…
ISEF · 2018
Mathematics
Although the infinite sum of the reciprocals of Mersenne primes has already been approximated to 0.51645417894, that result has not been compared with (a) the infinite sum of the reciprocals…