Group: Joe Gibson Title: Z-Shutters Analysis Abstract: While appearing simple at a first glance, my project will center around the Mathematical relations regarding the dimensions of Z shutters. A few summers ago, I worked with a 3D modeling company that specialized in woodshop designs. Recently, my former boss discussed this possible problem for me to solve. My project will use linear algebra to examine every measurement of Z-shutters if given the height, width, and width of the z-board cutting across the panel. Group: Sergio Castanon-Diaz and Ryan Furukawa Title: Exploring Fractals Abstract: Fractals are shapes that are recursively constructed and my project will look into some of the different ways to create fractals. This will include explaining the process to generate the fractals and also showing images as a visual guide since the images are usually fairly interesting. The two categories of fractals that will be focused on are iterated function system fractals and escape-time fractals. Group: Charlotte Riley-Vonwagoner Title: Image compression Abstract: None supplied Group: Adam Davies Title: Assessing Document Similarity via Word Frequency Analysis Abstract: I propose to design and implement an automated word-frequency analyzer, which will utilize large text corpora to classify the similarity of input text documents. This will be achieved by constructing frequency matrices (with documents represented as rows, and the number of occurrences of particular words as columns), and using the tools of linear algebra to manipulate these matrices to assess their similarity to each other. My project may also include tools to assess how closely a particular document matches the frequency distribution of particular domains of discourse, or to assess individual words' similarities. Group: Johnny Zhang Title: Game Theory and linear Algebra Abstract: Two person zero-sum game, using linear algebra to represent the game model and analyze the payoff of the game. Group: Andrew Fraser Title: Testing the Use of Linear Algebra in Graphics Systems Abstract: I plan to research and test the uses of linear algebra in graphics systems. Many graphics systems rely on linear algebra to determine vector positions and project graphics to the screen. This is because in reality, graphics are simply a massive amount of vectors in 3D space. I plan to research the different ways that linear algebra is applied in graphics systems, and test out what makes each more useful or less useful in different applications (basic graphics, websites, 3D modeling, video games, etc) Group: Feng Zhu Title: Economics Abstract: Use the 2008 Summary. Use Annual I-O Table found at http://www.bea.gov/to construct a consumption matrix as in Section 2.6. Was this economy productive? Group: Joshua Jonas Title: Interesting Fractals Designed in Maple Abstract: Fractals are useful in modeling structures in which similar patterns recur at progressively smaller scales. They can be used to compose incredibly beautiful images and, in fact, they can already be found in many naturally occurring items. In this project I will look into the linear algebra surrounding fractals and use the computer program Maple to compose some of my own. Group: Ryan Pearson Title: Image compression by SVD and DCT encoding Abstract: Images take up a lot of memory and being able to make an image take up less space in memory while still maintaining the quality of the image is a balancing act. My project will explore how images are compressed via two different methods by compressing images using methods of linear algebra. It will also show at what point images start to lose quality through both methods. Group: Lindsay Finlayson; Noah Jackson; Garrett Bullough; Bryan Clark Title: Fractals Abstract: Fractals are a curve or geometric figure, each part of which has the same statistical character as the whole. Fractals are useful in modeling structures (such as eroded coastlines or snowflakes) in which similar patterns recur at progressively smaller scales, and in describing partly random or chaotic phenomena such as crystal growth, fluid turbulence, and galaxy formation. Our project will explore the modelling of fractals and simulate their structure and presence in nature and technology. Group: Jared Harmer and Bryce Fairbanks Title: Pockets of Crime in SLC Abstract: Use crime rate data from SLC area from the past several years to determine areas of high crime rate/type of crime rate, and determine the association between different factors also released in public data. Group: Katie Izatt, John Peterson, Carson Ivory Title: Automatic Balancing of Redox Reactions. Abstract: Redox reactions are chemical reactions involving reduction (RED) and oxidation (OX). In other words, it is a transfer of electrons between atoms. Balancing these reactions can be highly difficult, but can be accomplished using linear algebra. Our objective is to create software capable of automatically and (hopefully) quickly balancing redox reactions. We will discuss possible algorithms capable of accomplishing this purpose, and the effectiveness of these varying tactics. We will also present examples of the software’s functionality. Group: Sean Hurst Title: Game Theory Using Matrices Abstract: Game theory deals with the choices that players make in games. Psychologists call it the theory of social interaction because it attempts to take into account the choices that one player can make against another. Although game theory is focused around board games, cards, and other competitive games, it can also be applied to military strategy in war. My project will primarily focus on determining how a player's chances can improve by making certain choices, or by minimizing the amount of negative choices a player can make. By taking these into account, it may be possible to create a zero-sum game, or a game in which the losses equals the gains. Group: Kristen Stewart Title: Determining Temperature Distribution of Heated Plate Abstract: Heat transfer is a critical field in mechanical engineering, especially determining how temperature varies throughout different materials. Using linear algebra, the temperature distribution through a heated plate can be determined by knowing the boundary conditions. My project will explore how temperature distributions vary depending on different boundary conditions, and it will run simulations for different scenarios. Group: Cameron Yeomans, Emily Burke, Hunter Moffat, and Spencer Cameron Title: Calculating rhythmic pattern outcomes through matrix manipulation Abstract: Musical rhythms can be represented in the form of fractions of a beat. As a result they can be measured mathematically. In a piece of music with four beats per measure, a quarter note can be represented as 1, a half note as 2 and a whole note as 4, and so on. Each possible note can be represented as a variable in an augmented matrix. Because we know that each bar ends with 4 beats we can solve for the possible combinations of rhythms. Our project will be to solve for each possible rhythmic combination in x number of bars. We will display matrices using Maple, and create a rhythm building algorithm accordingly. Group: Gates Campbell, James Webb, Jesse Toftum Title: Optimal Meeting Location Triangulation Abstract: Based on the locations of our separate residences, we will determine the optimal meeting spot that best equalizes travel time between us. The information for these calculations will be collected from traffic analytics and route distances for varying times of the day, and will also consider from online listings the nearest venue to the determined location that can actually host a meeting. If possible, the procedure used to generate the meeting spot will be generalized to accommodate locations in any zone with the necessary data available. Group: Kelton White Title: Machine Learning, Support Vector Machines. Abstract: Support Vector Machines are an important tool in the toolbox that machine learning programmers have access to. The general goal is classifying or categorizing new data into distinct categories. In world of mathematics what they aim to do is make linear separating hyperplanes in high multi dimensional space to separate the data. It is my intention to talk about support vector machines and to construct an illustration.