Physical Sciences and Mathematics Commons^™

Primality Proving Based On Eisenstein Integers, Miaoqing Jia

Honors Theses

According to the Berrizbeitia theorem, a highly efficient method for certifying the primality of an integer N ≡ 1 (mod 3) can be created based on pseudocubes in the ordinary integers Z. In 2010, Williams and Wooding moved this method into the Eisenstein integers Z[ω] and defined a new term, Eisenstein pseudocubes. By using a precomputed table of Eisenstein pseudocubes, they created a new algorithm in this context to prove primality of integers N ≡ 1 (mod 3) in a shorter period of time. We will look at the Eisenstein pseudocubes and analyze how this new algorithm works with the …

Computing The (Un)Computable: A Computationally-Augmented Perspective On The Yasukuni Shrine Controversy, Ryan Muther

Honors Theses

Computational methods have been used with increasing frequency in the social sciences and humanities, due to the availability of digital sources and computing power to study everything from changes in the meanings of words in Latin texts to how knowledge was categorized in eighteen century encyclopedias. Recent trends in the fields of digital humanities and computational social science include statistical methods like machine learning, requiring large pre-tagged and annotated sets of documents which in turn necessitates a great deal of prior work to create data to use with such methods. This reliance on large corpora of annotated data limits the …

Blending Two Automatic Playlist Generation Algorithms, James Curbow

Honors Theses

We blend two existing automatic playlist generation algorithms. One algorithm is built to smoothly transition between a start song and an end song (Start-End). The other infers song similarity based on adjacent occurrences in expertly authored streams (EAS). First, we seek to establish the effectiveness of the Start-End algorithm using the EAS algorithm to determine song similarity, then we propose two playlist generation algorithms of our own: the Unbiased Random Walk (URW) and the Biased Random Walk (BRW). Like the Start-End algorithm, both the URW algorithm and BRW algorithm transition between a start song and an end song; however, issues …

Reading Between The Lines: Verifying Mathematical Language, Tristan Johnson

Honors Theses

A great deal of work has been done on automatically generating automated proofs of formal statements. However, these systems tend to focus on logic-oriented statements and tactics as well as generating proofs in formal language. This project examines proofs written in natural language under a more general scope of mathematics. Furthermore, rather than attempting to generate natural language proofs for the purpose of solving problems, we automatically verify human-written proofs in natural language. To accomplish this, elements of discourse parsing, semantic interpretation, and application of an automated theorem prover are implemented.

Applications Of The Sierpiński Triangle To Musical Composition, Samuel C. Dent

Honors Theses

The present paper builds on the idea of composing music via fractals, specifically the Sierpiński Triangle and the Sierpiński Pedal Triangle. The resulting methods are intended to produce not just a series of random notes, but a series that we think pleases the ear. One method utilizes the iterative process of generating the Sierpiński Triangle and Sierpiński Pedal Triangle via matrix operations by applying this process to a geometric configuration of note names. This technique designs the largest components of the musical work first, then creates subsequent layers where each layer adds more detail.

Audio Software (Vst Plugin) Development With Practical Application, Zachary Hummel

Honors Theses

Audio engineers around the world routinely utilize small pieces of software, known as “plugins,” to help shape the sound of the media they are working with. These plugins are inserted into a digital audio workstation (DAW) and contain digital signal processing (DSP) algorithms that can affect audio in a number of ways limited only by the creativity of the software developer. Common implementations of plugins include equalizers, compressors and limiters, gain, phase rotation or polarity inversion algorithms, reverb and delay, and emulation of the non-linearities of analog audio equipment. The intent of this thesis project is to design and produce …

Making Meyers Clear: An Exploration Of The Chemistry And Art Of Ceramic Glazes, Sara Catherine Williams

Honors Theses

For both seasoned potters and students, looking at a line of unglazed bisque-ware can be a terrifying moment. Terrifying because you know that if you choose the wrong glazes, all of your hard work up until now could be wasted. The form of any clay creation, be it functional or artistic, is equal in importance with the glaze. Bad forms cannot be covered with good glazes, but good forms may be ruined with them. It is through the pairing of the two that a truly beautiful piece is made.

During my undergraduate years and much of my life I have …

Creating Color: Unearthing The Chemistry Of Ceramic Glazes, Jessica Mariah Hargis

Honors Theses

There is something magical about taking lumps of cold clay and turning them into a functional form. The transofrmation process is what first peaked my interest in ceramics. I turned this visual art form my junior year of college after being completely overwhelmed by my chemistry major. Not only did Ceramics 1 teach me basic hand building and surface design techniques, but it allowed me to literally pound out my stress. I've gained a strong adoration for ceramics because it relieves my stress and gives me the opportunity to express myself.

After taking Ceramics 1, enrolling in Ceramics 2 was …