Fall 2020 Graduate Student Master Thesis Defense

Grobner Bases and Systems of Polynomial Equations

Monday, November 23 4:00-5:00 PM

Speaker: Ms. Rachel Holmes

Abstract: The goal of this paper is to explore the use and construction of Grobner bases through Buchberger’s algorithm. Specifically, applications of such bases for solving systems of polynomial equations will be discussed. Furthermore, we relate many concepts in commutative algebra to ideas in computational algebraic geometry.

Thesis Advisor: Dr. Wook Kim

Fall 2020 Graduate Student Master Thesis Defense

Improvement in Regression Analysis through Optimal Clustering Algorithms with Machine Learning

Wednesday, November 18, 3:00-4:00 PM

Speaker: Mr. Taeyoung Choi

Abstract: The primary purpose of the project is to enhance the quality of data analysis by adapting various clustering systems with machine learning and apply the advanced clustering techniques to regression model in order to improve the efficiency of the analysis. First and foremost, this research aims to expand the knowledge of data analysis through diverse clustering algorithms, including Hierarchical, K-Means, Partition Around Medoid (PAM), Clustering Large Applications (CLARA), and Clustering Large Applications based upon Randomized Search (CLARANS). The clustering algorithms assist in high-quality data analysis by constructing particular groups within the given data. The clustering techniques could be easily applicable to multiple fields, including clinical, manufacturing, or business sectors. For example, large type II diabetes patient information data sets with numerous variables could be classified with relevant personal medical histories, physical activity level, response to a certain treatment, or diet habits through the appropriate cluster analysis.

Thesis Advisor: Dr. Mezbahur Rahman

Nomination for Membership

The following students are nominated by faculty of Department of Mathematics and Statistics for membership of American Mathematical Society for 2020-2021:
Moussa Abdoulaye Aboubacar, Eric Adu, Afrah Alhammad, Manori Ampe Mohottige Dona, Kayode Ayorinde, Aroni Basak, Shangyi Bi, Huyen Cao, Taeyoung Choi, Zhenhan Fang, Rachel Holmes, Masudul Hoque, Hans Kapend, Sujin Kim, Brianna Klapoetke, Abimbola Kolebaje, Katelyn LaPorte, Changhong Li, Bishal Maharjan, Charlie Moe, Tracy Morrison, Jasson Motzko, Ammishaddai Ogyiri, Franck Arnaud Olilo, Dong Young Park, Deanna Pautzke, Aninda Roy, Michael Schaefer, Nicholas Wagner, Erin Watt, Austin Whitcombm.


Nomination for Membership

The following student is nominated by faculty of Department of Mathematics and Statistics for membership of American Statistical Assosciation for 2020-2021:
Zhenhan Fang


Nomination for Membership

The following students are nominated by faculty of Department of Mathematics and Statistics for membership of Association for Women in Mathematics for 2020-2021:
Alison Millerbernd, Fatuma Abdulkadir, Serida Zosse, Morgan Olson, Sonja Kohout, Samantha Banwell, Erica Johnson, Joan Fuhrman, Samantha Doom, and Taylor Burke


Summer 2020 Graduate Student Master Thesis Defense

Multiple Regression Analysis with Continuous and Binary Response Variable

Friday, August 14 11:00-12:00 AM

Speaker: Ms. Eunhye Lee

Abstract: This alternate plan paper aimed to analyze student data in different Regression models to fit the best model and find the best model out of different types of regression models. The inferential statistics could provide more information beyond the descriptive statistics by answering questions in terms of data, testing hypotheses, and fitting into a proper model not only to describe the relationship in data set but also to predict a target. A statistical method, regression can be utilized in numerous fields in order to reveal the relationship between variables including finance, marketing, biology, investment, health, even psychology, etc. The main question in this paper is what variables are affecting to the final grade the most. The goal is to fit a multiple linear regression model and multiple logistic regression model properly, to detect the most relevant and effective variables in the fitted model to help understanding in respect to final mathematics grade. I will cover the linear regression model, one of the basic types of regression to describe the simultaneous associations of observed variables with a continuous dependent variable. To get the valid linear regression model, the assumptions of residual normality, linearity, independence of residual terms, zero mean of residual and homogeneity of residual variance checked to satisfy. Secondly, the logistic regression is to study the effect of binary outcomes regardless of the other regressor measurement. Logistic model is based on the logit function with the interpretation of probability than a value. The assumption for logistic regression comes with the response variable to be ordinal, the error terms to be independent, absence of multicollinearity, and linearity of independent variables and log odds with large sample size.

Thesis Advisor: Dr. Metzbahur Rahman

Summer 2020 Graduate Student Master Thesis Defense

Soybean Price Prediction Using Time Series Foresting with Google Trend

Friday, August 7 10:00-11:00 AM

Speaker: Mr. Zhuoning Li

Abstract: We use the time series methods to analyze the trend, predict price in U.S. soybean commodity market, and find the impact on the soybean price by the "trade war" between China and the U.S.. We use autoregressive integrated moving average and autoregressive conditional heteroskedasticity models to predict soybean price by using the U.S soybean daily price data, and we also use vector autoregression(VAR) and long short time memory models to predict soybean price by using the previous data and google trend data. By comparing these methods, we get the best prediction from VAR model.

Thesis Advisor: Dr. Deepak Sanjel

Summer 2020 Graduate Student Master Thesis Defense

An Application for Bank Loan Default Prediction Analysis using Logistic Regression and Support Vector Machine

Friday July 31, 2020 10:00-11:00am

Speaker: Ms. Shuk Ping Wong

Abstract: Risk Management is one of the most crucial areas for banks. Banks are constantly working on effective models to estimate the likelihood of whether a customer could default to maintain a sustainable and profitable business. Although credit scoring is a common indicator for bankers, some financial datasets simply do not come with this variable. This study built a logistic regression model and a support vector machine (SVM) model to predict whether the loan borrower will default based on different categorical variables. The performance of the models is compared based on accuracy and efficiency. We found that a logistic regression model generally provides more depth in analysis of the variables and is better in terms of interpretability. Although SVM has a higher accuracy rate, the method took too much time for the computer to run and it suffers from a lack of interpretability. Logistic regression model has a better performance in general.

Thesis Advisor: Dr. Metzbahur Rahman

Summer 2020 Graduate Student Master Thesis Defense

Number Construction

Monday, July 20, 2020, 11:00-12:00pm

Speaker: Mr. Brian Bertness

Abstract: This paper describes how numbers are constructed via sets and equivalence relations. The necessary Zermelo-Franko set theory axioms are used to define basic sets, relations, and functions. Employing the Axiom of Infinity, the natural numbers are then constructed in terms of sets with an ordering that also conforms to the Peano axioms. Using the set of natural numbers and an equivalence relation the set of integers with an ordering are created followed, in turn, by the set of rational numbers. Lastly, Cauchy sequences are introduced and, using an equivalence relation, these are turned into the set of real numbers which are shown to have an ordering and the completeness property.

Thesis Advisor: Dr. Wook Kim

Spring 2020 Graduate Student Master Thesis Defense

The Roots of Root Finding

Wednesday, May 6, 2020, 2:00-3:00pm

Speaker: Mr. Kurt Grunzke

Abstract: One of the biggest challenges facing teachers is convincing students that their intuition about a concept is incorrect. In particular, our current social climate fuels an intuition that mathematicians are “nerds,” “geeks,” or other terms that generally refer to a boring person who lacks social skills. The goal of this paper is to demolish that stereotype by demonstrating that mathematicians are independent, argumentative, and vibrant individuals, whose energy is fueled by the social climate of their time. In order to demonstrate these characteristics, we will consider the question of solving polynomial equations, and not just one of them, but all of them. The answer to our question will span thousands of years, cross through multiple civilizations and continents, and introduce us to some lively mathematicians. Furthermore, this investigation will provide an approachable access point to concepts in higher mathematics.

Thesis Advisor: Dr. Namyong Lee

Spring 2020 Graduate Student Master Thesis Defense

Discrete Morse Theory by Vector Fields: A Survey and New Directions

Tuesday, May 5, 2020, 4:00-5:00pm

Speaker: Mr. Matthew Nemitz

Abstract: We synthesize some of the main tools in discrete Morse theory from various sources. We do this in regards to abstract simplicial complexes with an emphasis on vector fields and use this as a building block to achieve our main result which is to investigate the relationship between simplicial maps and homotopy. We use the discrete vector field as a catalyst to build a chain homotopy between chain maps induced by simplicial maps.

Thesis Advisor: Dr. Brandon Rowekamp

Student News

Congratulations to MSU team on winning second place in advanced Data Derby 2020.

Team members:Tania Hasanpoor, Abdelrahman Elkenawy, Nishchint Upadhyaya, Arlton Cox, Shuk-ping Wong

Advisor: Dr. Cyrus Azarbod

Special congratulations to Shuk-ping Wong, Applied Statistics graduate student and Vice president of Stats Club.

Spring 2020 Graduate Student Master Thesis Defense

Heat Kernel Voting with Geometric Invariants

Friday, May 1, 2020, 4:00-5:00pm

Speaker: Mr. Alexander Harr

Abstract: Here we provide a method for comparing geometric objects. Two objects of interest are embedded an infinite dimensional Hilbert space using their Laplacian eigenvectors and eigenfunctions into an infinite dimensional space, truncated to a finite dimensional Euclidean space, where correspondences between the objects are found and voted on. To simplify correspondence finding, we propose using several geometric invariants to reduce the necessary computations. This method improves on voting methods by identifying isometric regions in shapes of dimension greater than 3, and genus greater than 0, as well as almost retaining isometry. The voting approach evaluates local correspondences while at the same time respecting the global structure.

Thesis Advisor: Dr. Ke Zhu

Spring 2020 Graduate Student Master Thesis Defense

A Mathematical Model for Malaria with Age-Heterogenous Biting Rate

Wednesday, April 22, 2020, 3:00-4:00pm

Speaker: Mr. Sho Kawakami

Abstract: We propose a mathematical model for malaria with age-heterogeneous biting rate. The existence of the model, the local behaviour of the disease free equillibrium are explored. Furthurmore the model is extended to an optimal control problem and the correspond- ing adjoint equations and optimality conditions are derived. Age dependent parameter values are estimated and numerical simulations are carried out for the model. The new model better accounts for difference in biting rates between different age groups, and improvements in stability to the explicit algorithm. The optimal control is also shown to depend on the age distribution of the biting rate.

Thesis Advisor: Dr. Ruijun Zhao

Spring 2020 Graduate Student Master Thesis Defense

Apply logistic regression procedures to datasets with a binary and a nominal response variable

Wednesday, April 15, 2020, 2:00-3:00pm

Speaker: Ms. Duaa Alsubhi

Abstract: A major emphasis of this paper is on applying a binomial and a multinomial regression. In binomial regression, we used a heart disease dataset to illustrate how to build a modeling strategy by using a purposeful selection variable to determine the model with the best fit. In multinomial regression, we used an Adolescent Placement Study dataset to compare the logistic regression model with and without insignificant independent variables. In addition, we are interested in the impact of the insignificant predictor variable, which is explained in terms of an odds ratio.

Thesis Advisor: Dr. Mezbahur Rahman

Spring 2020 Graduate Student Master Thesis Defense

Theory of Principal Components for Applications in Exploratory Crime Analysis and Clusting

Thursday, April 9, 2020, 3:00-4:00pm

Speaker: Mr. Daniel Silva

Abstract: The purpose of this paper is to develop the theory of principal components analysis succinctly from the fundamentals of matrix algebra and multivariate statistics. Principal components analysis is sometimes used as a descriptive technique to explain the variance-covariance or correlation structure of a dataset. However, most often, it is used as a dimensionality reduction technique to visualize a high dimensional dataset in a lower dimensional space. Principal components analysis accomplishes this by using the first few principal components, provided that they account for a substantial proportion of variation in the original dataset. In the same way, the first few principal components can be used as inputs into a cluster analysis in order to combat the curse of dimensionality and optimize the runtime for large datasets. The application portion of this paper will apply these methods to a US Crime 2018 dataset extracted from the Uniform Crime Reports on the FBI’s website.

Thesis Advisor: Dr. Iresha Premarathna

Student News

Congratulations to MSU team on winning second place in Data Visualization at 2020 MUDAC.

Team members:Taisuke Usumi, Nusrat Chaity, Lindsay Miller, Alison Millerbernd, Junsoo Seo

Advisor: Dr. Soumya Banerjee