Department Colloquia

Rose Marshall

Wallpaper Groups: The Mathematical Principles behind M.C. Escher’s Most Famous Works

While the fields of Mathematics and Art are often thought of as mutually exclusive, the intersection of these two disciplines is rich with an aesthetic beauty that is grounded in mathematical concepts. The Dutch graphic artist M.C. Escher is famous for exploring these concepts in his many artworks. In this talk, we will begin to explore the intersection of Art and Mathematics by delving into the mathematical world Escher created. Looking at Escher’s tessellation artworks, we will work towards a characterization of some of the seventeen distinct wallpaper groups.

• Done in partial fulfillment of the Mathematics major.

Presentation Details:

• May 26, 2023 at 4:00pm
• Room: SMC A-206
• Advisor: Andrew Leahy
  Please contact the advisor for more information about this presentation.

Aakriti Dahal

Forecasting Real Estate Trends in Cook County for Investment Decisions

In econometrics, much effort has been devoted to accurate forecasting of economic growth using time series forecasting tools. These time series models allow analysts to identify patterns and trends in data over time, and forecast future prices based on past performance. The realm of real estate valuation has notably reaped the benefits of time series analysis in predicting property values over time.
 This paper demonstrates a practical use case of the Auto-Regressive Integrated Moving Average (ARIMA) model to identify real estate pricing trends within Cook County, Illinois using the Zillow Home Value Index (ZHVI) dataset. The goal of this research is to identify the five best zip codes with a typical home value of $250K or under in Cook County with the highest return on investment over the next five years.

• Done in partial fulfillment of the Data Science major.

Presentation Details:

• May 25, 2023 at 4:00pm
• Room: SMC A-206
• Advisor: Ole J. Forsberg
  Please contact the advisor for more information about this presentation.
• Please download the flyer for more information.

Susheel Ravi

Abel's Theorem on the Lemniscate: Dividing it with Galois Theory

In this talk we will discuss Abel's Theorem on the lemniscate (the infinity symbol) given by the equation (x^2 + y^2)^2 = x^2 - y^2. The theorem states that you can divide the lemniscate into n equal parts using ruler and compass alone if and only if n is the product of a power of 2 and distinct Fermat primes. To prove this, we study a function that plays a role analogous to the sine function for circles. We extend this function to the complex plane through some nice applications of complex analysis, yielding interesting results about the function and polynomials that can result from multiplication by the Gaussian integers. With these polynomials, through an application of Galois Theory and Sylow's theorems, we can prove Abel's stunning result.

• Done in partial fulfillment of the Mathematics major.

Presentation Details:

• May 24, 2023 at 4:00pm
• Room: SMC A-203
• Advisor: Pedro Teixeira
  Please contact the advisor for more information about this presentation.

Richard Beck

Pell's Equation and Continued Fractions

This talk will go over a brief history and introduction to Pell's Equation, and some properties of continued fractions. Following that, connections between the two are discussed, and the talk concludes with how to solve Pell's Equation with continued fractions.

• Done in partial fulfillment of the Mathematics major.

Presentation Details:

• May 23, 2023 at 4:00pm
• This will be held online using Zoom.
• Advisor: Mary V. Armon
  Please contact the advisor for more information about this presentation.

Dustin Cates

Digital Signal Processing

Digital signal processing has been around since the beginning of the digital era of technology. Since it was first conceived, DSP has progressed through leaps and bounds and has worked its way into the heart of today’s technology-run world. In this talk, we explore the mathematical background of DSP, looking in depth at the discretization of audio signals as well as the connection with Fourier analysis. Combining these ideas, we construct the Discrete Fourier Transform and explore different applications of DSP, such as filtering and windowing.

• Done in partial fulfillment of the Mathematics major.

Presentation Details:

• May 22, 2023 at 4:00pm
• Room: SMC A-206
• Advisor: Andrew Leahy
  Please contact the advisor for more information about this presentation.

Kit Piepkorn

Predicting Through the Lens: A Look at Recommendation Systems

Streaming services are constantly looking for ways to increase their viewer interaction with their system. One of the primary ways that these companies (e.g. Netflix, Hulu etc.) accomplish this, is through the use of recommendation systems. These systems take existing user data, and through the use of machine learning algorithms, determine a user’s preferences. This paper will examine applications of Content-Based and Collaborative filtering systems, primarily through the use of similarity matrices and matrix factorization. These systems will be trained and tested on the MovieLens dataset.
 The goal of this research is to test several models in order to achieve the best level of accuracy and prediction when estimating a user's preferences and future viewing needs. Finally, I will discuss the results to show the effectiveness of fitting and training a model with Content-Based and Collaborative Filtering algorithms in order to increase user interaction within a streaming service.

• Done in partial fulfillment of the Data Science major.

Presentation Details:

• May 19, 2023 at 4:00pm
• Room: SMC A-206
• Advisor: Ritwik Bose
  Please contact the advisor for more information about this presentation.
• Please download the flyer for more information.

Samantha M. Lorenz

A Study of Generalized and Vector Generalized Linear Models

In many real-life applications, modeling using the classical linear modeling paradigm (CLM) will not suffice due to violations of its requirements, namely that the response variable has a conditionally Normal distribution. When this requirement is not met, one usually opts for using a generalized linear model (GLM). GLMs require that the response variable has a conditional distribution in the exponential family of distributions. Should this requirement also be violated, we can perform an extension of the GLM— a vector generalized linear model (VGLM).
 In this paper, we will discuss some of the key similarities and differences between these modeling paradigms by comparing the models in R with a data set and studying the mathematical foundation of CLM,GLM, and VGLM.

• Done in partial fulfillment of an Honors Project in Data Science.

Presentation Details:

• May 15, 2023 at 4:00pm
• Room: SMC A-206
• Advisor: Ole J. Forsberg
  Please contact the advisor for more information about this presentation.
• Please download the flyer for more information.

Josie Spence

Supreme Court First Amendment Trends Over Time

This research examines a subset of all SCOTUS cases that concerned significant questions about the First Amendment. It then tracks the support for the First Amendment through time in terms of the entire Supreme Court and in terms of the individual Justices.

• Done in partial fulfillment of the Statistics minor.

Presentation Details:

• May 11, 2023 at 4:00pm
• Room: SMC A-206
• Advisor: Ole J. Forsberg
  Please contact the advisor for more information about this presentation.

Annie Phung

A Random? Walk Down Wall Street, Part I

Time series analysis plays a unique role in the field of Data Science. In the financial industry, it has become a powerful tool for predicting future stock price movements. We explore how investors can take advantage of the lack of independence in the rate of return process over time and examine the application of different time series models.

• Done in partial fulfillment of the Financial Mathematics major.

Presentation Details:

• November 15, 2022 at 4:00pm
• This will be held online using Zoom.
• Advisor: Kevin Hastings
  Please contact the advisor for more information about this presentation.

Ashus Owaisi

A Random? Walk Down Wall Street, Part II

In this study we use AR, MA, ARMA and ARIMA models to look at a random sample of companies from the Fortune 500 list for 2022. Using the aforementioned models and techniques such as the autocorrelation, partial and extended autocorrelation, decomposition, forecasting and residual analysis, we will uncover the truth about their rates of return. These rates may be a lot more predictable than we previously thought.

• Done in partial fulfillment of the Financial Mathematics major.

Presentation Details:

• November 15, 2022 at 4:00pm
• This will be held online using Zoom.
• Advisor: Kevin Hastings
  Please contact the advisor for more information about this presentation.

Anastasiia Ganshina

Grading individuals based on American Political Landscape: A Wikipedia exercise

It is well known that there are two main opposing parties in the United States of America today: Republicans and Democrats. Both parties have their solutions to major topics in all sectors of life of Americans and the world, and, in many cases, those opinions are contradictory. Most people in those parties, however, do not always fully agree with their party rules and opinions. For example, they might have most of their opinions aligned with republicans, but still have some ideas that are democrat leaning. For instance, they may be pro-choice and pro-gun but believe in universal healthcare. In this study, our main goal was to create a system that would grade politicians based on their political opinions on a scale from 0 to 10. We studied a few different topics, such as abortion, guns, healthcare, etc. to find out what the democrats and republicans think about them and grade a politician based on opinions. For our grading system, we developed over 50 machine-learning language-based models that can determine the sentiment based on a portion of the Wikipedia article on a specific topic.

• Special presentation for the Statistics Program

Presentation Details:

• November 10, 2022 at 4:00pm
• Room: SMC A-203
• Advisor: Ole J. Forsberg
  Please contact the advisor for more information about this presentation.
• Please download the flyer for more information.

Ashus Owaisi

The Japanese Warring States: A Statistical Study

The Warring States period, also known as “Sengoku Jidai” is the period known within the archipelago between 1467-1615. An era known for its brutality and heroic displays thanks to constant social upheaval, civil wars, and power struggles. This study attempts to show a historical analysis of all the major events that transpired during this period. The nation was unified three separate times, under three vastly different ruling entities. During which a multitude of clans took part in shaping the history of the modern nation, as we know it today.
 Battles, Army Counts, Battle Locations, Sieges, Naval Tactics, Battle Instigations, Forced Defenses, Japanese Prefectures/Regions, and Political Conspiracies are all taken into account in this study. Using regression and prediction analysis techniques, we produce this statistical and historical recap and take a look back at one of the most infamous periods in time.

• Done in partial fulfillment of the Statistics minor.

Presentation Details:

• May 26, 2022 at 4:00pm
• Room: SMC A-203
• Advisor: Ole J. Forsberg
  Please contact the advisor for more information about this presentation.

Ole J. Forsberg

Beyond Frequentist Statistics: A brief introduction to Bayesian statistics

The vast majority of undergraduate statistics follow the frequentist framework as conceived by Ronald Fisher (18-19) and others. This framework leads to mental gymnastics when handling such foundational concepts as confidence intervals and p-values. This talk briefly introduces Bayesian statistics and how it allows for a much cleaner interpretation of the data.

• Special presentation for the Statistics Program

Presentation Details:

• May 24, 2022 at 4:00pm
• Room: SMC A-203

Beck Baird

What Is "Not Statistically Significant:" Bayesian Insight on Data Analysis

Data was collected longitudinally through surveys completed daily for two weeks by participants in an experimental or a control group. The aim was to find a significant correlation between experimental condition, self-determination, and self-concept clarity. Frequentist analysis suggested that manipulation was not statistically significant, but further Bayesian analysis gives a stronger insight into the meaning of our findings.

• Special presentation for the Statistics Program

Presentation Details:

• May 24, 2022 at 4:15pm
• Room: SMC A-203
• Advisor: Ole J. Forsberg
  Please contact the advisor for more information about this presentation.

Samantha Lorenz

Testing Differential Invalidation with Frequentist and Bayesian Analysis

Democratic backsliding has recently become a trend. In Hungary's case, one party seems to have triggered this event: the Fidesz party. In this study, I examine the changed electoral system and study the effects of differential invalidation for the Fidesz party in order to make a conclusion on whether or not there is evidence of differential invalidation in the case of Democratic Backsliding. I have taken an initial project a step further and evaluated the data both with Frequentist and with Bayesian methods. My goal is to go over the differences between the two types of analysis, and which one is better.

• Special presentation for the Statistics Program

Presentation Details:

• May 24, 2022 at 4:30pm
• Room: SMC A-203
• Advisor: Ole J. Forsberg
  Please contact the advisor for more information about this presentation.

Anastasiia Ganshina

Surgical Mask Detection

In 2020, the world was shaken by COVID-19, the pandemic that continues to affect our lives. Due to mutations and constant challenges humanity is facing, this illness will stay in our day-to-day lives for some time. In order to limit the spread of the disease and keep each other safe, CDC primary recommendation is to wear masks in public places or when closely interacting with others. However, there is no good way to monitor whether these rules are followed and people are protected. Thus, the creation of the system of autonomous mask detection might be helpful to make sure people are keeping each other safe and healthy.
 The autonomous system described above can be simply implemented by using Machine Learning and, more specifically, the Computer Vision component of the field. Computer Vision is a part of the Machine Learning field that deals with images and videos, and bases the predictions from feature extraction of patterns detected in images or frames. Thus, to build the mask detection model, the images of peoples' faces with and without masks are needed.
 This research project creates such a system using freely available materials, including Python and Keras. The accuracy of this model is explored and explained.

• Done in partial fulfillment of the Data Science major.

Presentation Details:

• March 1, 2022 at 4:00pm
• Room: SMC A-203
• Advisor: Ole J. Forsberg
  Please contact the advisor for more information about this presentation.
• Please download the flyer for more information.

Dieu Kim (Zoey) Nguyen

Analyzing the Olympic Record

The modern Olympic Games have been held, with three exceptions, every four years since 1896. Much has changed from Coubertin's inaugural 1896 Olympics in Athens, which had just 241 athletes competing in 43 events. The 2020 Tokyo Olympics had 11,656 athletes competing in 339 events. Each event offered a gold, silver, and bronze medal.
 This research uses several data science techniques to determine the effects of height, weight, and age on the likelihood of an athlete medaling in an event. Several events, from both Summer and Winter Games, are examined. Results are explored using data visualization.

• Done in partial fulfillment of the Data Science major.

Presentation Details:

• March 3, 2022 at 4:00pm
• Room: SMC A-203
• Advisor: Ole J. Forsberg
  Please contact the advisor for more information about this presentation.
• Please download the flyer for more information.