SENIOR COMPS PRESENTATIONS
in Mathematics
Data
Compression:
An Introduction to Lossy and Lossless
Image Compression Techniques
Michael
Cheung
Data compression is a process where files are reduced in size to save memory or decrease transmission time. Algorithms of this type are categorized as lossy or lossless. Lossy algorithms accept the loss of data deemed insignificant in the context of the file type. Lossless algorithms keep all original data such that a file before compression is identical to the same file after decompression. During this presentation, I will prove theorems about encoding schemes and discuss the mathematical processes behind lossy JPEG and lossless GIF image compression. I will also compress and decompress images using JPEG compression and provide an analysis of my findings.
The n-Queens Problem
Saleem
Karamali
The n-queens problem is an optimization problem which is a generalization of the better-known 8-queens problem. The goal is to place n queens on an n x n chessboard such that no queen attacks any other queen. We briefly present the history of the problem, and then discuss what is known of the behavior of Q(n), the number of solutions for a given n. Finally, we present and demonstrate some of the known methods for solving the problem, and analyze the complexity of these methods.
Methods
of Monte Carlo Integration
Sarah
Klenha
Monte Carlo simulation is used to numerically evaluate stochastic models by evaluating the model with a sequence of random numbers. Although Monte Carlo Simulation has many uses, one important application is as a method of numerical integration. This presentation will discuss two of the methods of integration, the Hit-or-Miss method and the Sample Mean method and compare the two algorithms' efficiencies in terms of time complexity and accuracy. While the two algorithms take approximately the same amount of time to run, the Sample Mean method offers a higher degree of accuracy in estimation and is therefore more efficient.
Tuesday
March 22nd, 2016
4:30-6:30pm
Fowler 302
**Refreshments Will Be Served**
Everyone is invited!