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Full-Text Articles in Mathematics

Proving Dirichlet's Theorem On Arithmetic Progressions, Owen T. Abma Aug 2022

Proving Dirichlet's Theorem On Arithmetic Progressions, Owen T. Abma

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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 Aug 2022

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.