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Articles 1 - 8 of 8
Full-Text Articles in Physical Sciences and Mathematics
Proving Dirichlet's Theorem On Arithmetic Progressions, Owen T. Abma
Proving Dirichlet's Theorem On Arithmetic Progressions, Owen T. Abma
Undergraduate Student Research Internships Conference
First proved by German mathematician Dirichlet in 1837, this important theorem states that for coprime integers a, m, there are an infinite number of primes p such that p = a (mod m). This is one of many extensions of Euclid’s theorem that there are infinitely many prime numbers. In this paper, we will formulate a rather elegant proof of Dirichlet’s theorem using ideas from complex analysis and group theory.
Solving Partial Differential Equations Using The Finite Difference Method And The Fourier Spectral Method, Jenna Siobhan Parkinson
Solving Partial Differential Equations Using The Finite Difference Method And The Fourier Spectral Method, Jenna Siobhan Parkinson
Undergraduate Student Research Internships Conference
This paper discusses the finite difference method and the Fourier spectral method for solving partial differential equations.
Some Progress On Random Matrix Theory (Rmt), Feiying Yang
Some Progress On Random Matrix Theory (Rmt), Feiying Yang
Undergraduate Student Research Internships Conference
This is a research report about Random Matrix Theory (RMT), which studies Gaussian Orthogonal Ensemble (GOE), Gaussian Unitary Ensemble (GUE) and Gaussian Symplectic Ensemble (GSE), the purpose is to prove Wigner’s semicircle law.
Searching For New Relations Among The Eilenberg-Zilber Maps, Owen T. Abma
Searching For New Relations Among The Eilenberg-Zilber Maps, Owen T. Abma
Undergraduate Student Research Internships Conference
The goal of this project was to write a computer program that would aid in the search for relations among the Eilenberg-Zilber maps, which relate to simplicial objects in algebraic topology. This presentation outlines the process of writing this program, the challenges faced along the way, and the final results of the project.
Contemporary Mathematical Approaches To Computability Theory, Luis Guilherme Mazzali De Almeida
Contemporary Mathematical Approaches To Computability Theory, Luis Guilherme Mazzali De Almeida
Undergraduate Student Research Internships Conference
In this paper, I present an introduction to computability theory and adopt contemporary mathematical definitions of computable numbers and computable functions to prove important theorems in computability theory. I start by exploring the history of computability theory, as well as Turing Machines, undecidability, partial recursive functions, computable numbers, and computable real functions. I then prove important theorems in computability theory, such that the computable numbers form a field and that the computable real functions are continuous.
Categorical Aspects Of Graphs, Jacob D. Ender
Categorical Aspects Of Graphs, Jacob D. Ender
Undergraduate Student Research Internships Conference
In this article, we introduce a categorical characterization of directed and undirected graphs, and explore subcategories of reflexive and simple graphs. We show that there are a number of adjunctions between such subcategories, exploring varying combinations of graph types.
Spectral Graph Theory And Research, Nathan H. Kershaw, Lewis Glabush
Spectral Graph Theory And Research, Nathan H. Kershaw, Lewis Glabush
Undergraduate Student Research Internships Conference
Our topic of study was Spectral Graph Theory. We studied the algebraic methods used to study the properties of graphs (networks) and became familiar with the applications of network analysis. We spent a significant amount of time studying the way virus’s spread on networks, with particular applications to Covid-19. We also investigated the relationship between graph spectra and structural properties.
Studies Of Subvarieties Of Classical Complex Algebraic Geometry, Wenzhe Wang
Studies Of Subvarieties Of Classical Complex Algebraic Geometry, Wenzhe Wang
Undergraduate Student Research Internships Conference
My project in this USRI program is to study subvariety of classical complex algebraic geometry. I observed the orbit of elements in the unit sphere in space ℂ² ⊗ ℂ², the structure of unit sphere of ℂ² ⊗ ℂ². After this, I tried to generalize the result to ℂ^n ⊗ ℂ^n.