Analysis Commons^™

Defining Characteristics That Lead To Cost-Efficient Veteran Nba Free Agent Signings, David Mccain

Honors Projects in Mathematics

Throughout the history of the NBA, decisions regarding the signing of free agents have been riddled with complexity. Franchises are tasked with finding out what players will serve as optimal free agent signings prior to seeing them perform within the framework of their team. This study hypothesizes that the adequacy of an NBA free agent signing can be modeled and predicted through the implementation of a machine learning model. The model will learn the necessary information using training and testing data sets that include various player biometrics, game statistics, and financial information. The application of this machine learning model will …

Using A Distributive Approach To Model Insurance Loss, Kayla Kippes

Student Research Submissions

Insurance loss is an unpredicted event that stands at the forefront of the insurance industry. Loss in insurance represents the costs or expenses incurred due to a claim. An insurance claim is a request for the insurance company to pay for damage caused to an individual’s property. Loss can be measured by how much money (the dollar amount) has been paid out by the insurance company to repair the damage or it can be measured by the number of claims (claim count) made to the insurance company. Insured events include property damage due to fire, theft, flood, a car accident, …

Changing Nfl Playoff Overtime Rules To Create Equal Opportunities To Win A Game, Matthew Silvia

Honors Projects in Mathematics

The NFL has attempted to create fair overtime rules over the course of the past decade; however, this study is interested in determining what playoff overtime rule (or rules) could the NFL implement to result in outcomes where both teams have a relatively equal chance of winning a game. This study aims to find which overtime rules work best at minimizing the differences between teams who possess the ball first versus teams that kick the ball off to start an overtime period. By collecting various NFL statistics from ESPN.com and FantasyOutsiders.com, this study hopes to run multiple simulations of different …

Elliptic Functions And Iterative Algorithms For Π, Eduardo Jose Evans

UNF Graduate Theses and Dissertations

Preliminary identities in the theory of basic hypergeometric series, or `q-series', are proven. These include q-analogues of the exponential function, which lead to a fairly simple proof of Jacobi's celebrated triple product identity due to Andrews. The Dedekind eta function is introduced and a few identities of it derived. Euler's pentagonal number theorem is shown as a special case of Ramanujan's theta function and Watson's quintuple product identity is proved in a manner given by Carlitz and Subbarao. The Jacobian theta functions are introduced as special kinds of basic hypergeometric series and various relations between them derived using the triple …

Introduction To Mathematical Analysis I - 3rd Edition, Beatriz Lafferriere, Gerardo Lafferriere, Mau Nam Nguyen

PDXOpen: Open Educational Resources

Video lectures explaining problem solving strategies are available

Our goal in this set of lecture notes is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs.

The lecture notes contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. In addition, the notes include many carefully selected exercises of various levels …

Topological Data Analysis And Ant Interaction Networks, Adam Banatwala, Esther Rønn

Mathematics & Computer Science Student Scholarship

Adam Banatwala ’22, Majors: Mathematics and Finance
Esther Rønn ’23, Majors: Physics and Mathematics
Faculty Mentor: Dr. Laura Murray, Mathematics and Computer Science

Our research group used topological data analysis (TDA) to quantify the movement and behavior of ants in a colony.

We extracted higher dimensional networks from point cloud data collected from Dr. James Waters’ lab. Varying the proximity parameter in this construction gives a sequence of networks. We analyzed the enduring topological features of these networks, and how these features evolve over time as the ants move in the colony. Both the experimental and null model simulation data …

Banach Spaces On Topological Ramsey Structures, Cheng-Chih Ko

Electronic Theses and Dissertations

A Banach space T₁(d, θ) with a Tsirelson-type norm is constructed on the top of the topological Ramsey space T₁ defined by Dobrinen and Todorcevic [6]. Finite approximations of the isomorphic subtrees are utilised in constructing the norm. The subspace on each “branch” of the tree is shown to resemble the structure of an ℓ_∞ⁿ⁺¹ -space where the dimension corresponds to the number of terminal nodes on that branch. The Banach space T₁(d, θ) is isomorphic to (∑_n∊ℕ⊕ℓ_∞ⁿ⁺¹)_p , where d ∈ ℕ with d ≥ 2, …

Under Pressure: A Case Study Of The Effects Of External Pressure On Mlb Players Using Twitter Sentiment Analysis, Jonathan Huntley

Honors Projects in Mathematics

Performance under pressure and psychological momentum are well-documented topics in sports psychology, but most research focuses on “in-game” pressure. This study views pressure more broadly to examine how the external pressure of fans, quantified using the sentiment of tweets mentioning the players, can affect how MLB players perform. Although external pressure is intangible, it can impact a player’s psyche and performance. This investigation focuses on players Chris Sale and David Price. A new process was developed leveraging the Vader package in Python that can generate tweet sentiment to compare to several performance metrics from Baseball Reference. Results proved to be …

An Exploratory Analysis Of The Bgsu Learning Commons Student Usage Data, Emily Eskuri

Honors Projects

The purpose of this study was to explore past student usage data in individualized tutoring sessions from the Learning Commons from two academic years. The Bowling Green State University (BGSU) Learning Commons is a learning assistance center that offers various services, such as individualized tutoring, math assistance, writing assistance, study hours, and academic coaching. There have been limited research studies into how big data and analytics can have an impact in higher education, especially research utilizing predictive analytics.

This project applied analytics to individualized tutoring data in the Learning Commons to create a better understanding of why those trends happen …

Multivariate Distributions Of Correlated Binary Variables Generated By Pair-Copulas, Huihui Lin, N. Rao Chaganty

Mathematics & Statistics Faculty Publications

Correlated binary data are prevalent in a wide range of scientific disciplines, including healthcare and medicine. The generalized estimating equations (GEEs) and the multivariate probit (MP) model are two of the popular methods for analyzing such data. However, both methods have some significant drawbacks. The GEEs may not have an underlying likelihood and the MP model may fail to generate a multivariate binary distribution with specified marginals and bivariate correlations. In this paper, we study multivariate binary distributions that are based on D-vine pair-copula models as a superior alternative to these methods. We elucidate the construction of these binary distributions …

Cross-Model Parameter Estimation In Epidemiology, Julia R. Fitzgibbons

Honors Theses and Capstones

No abstract provided.

Sum Of Cubes Of The First N Integers, Obiamaka L. Agu

Electronic Theses, Projects, and Dissertations

In Calculus we learned that 􏰅Sum^{n}_{k=1} k = [n(n+1)]/2 , that Sum^{􏰅n}_{k=1} k^2 = [n(n+1)(2n+1)]/6 , and that Sum^{n}_{k=1} k^{3} = (n(n+1)/2)^{2}. These formulas are useful when solving for the area below quadratic or cubic function over an interval [a, b]. This tedious process, solving for areas under a quadratic or a cubic, served as motivation for the introduction of Riemman integrals. For the overzealous math student, these steps were replaced by a simpler method of evaluating antiderivatives at the endpoints a and b. From my recollection, a former instructor informed us to do the value of memorizing these formulas. …

The Decline Of The Mid-Range Jump Shot In Basketball: A Study Of The Impact Of Data Analytics On Shooting Habits In The Nba, Shawn Kilcoyne

Honors Projects in Mathematics

The purpose of this thesis paper is to investigate the strategic shift away from the mid-range jump shot in basketball over the past decade. This paper will cover the rationale for the decline of the mid-range, as well as the general impact of data analytics on the way the game of basketball is played at the professional level. Following a review of the existing literature relating to the use of analytics in the NBA, this paper will analyze the differences in shooting habits between two seven-season periods. Data visualization tools, including boxplots, statistical trends, and distribution plots, will be used …

Discrepancy Inequalities In Graphs And Their Applications, Adam Purcilly

Electronic Theses and Dissertations

Spectral graph theory, which is the use of eigenvalues of matrices associated with graphs, is a modern technique that has expanded our understanding of graphs and their structure. A particularly useful tool in spectral graph theory is the Expander Mixing Lemma, also known as the discrepancy inequality, which bounds the edge distribution between two sets based on the spectral gap. More specifically, it states that a small spectral gap of a graph implies that the edge distribution is close to random. This dissertation uses this tool to study two problems in extremal graph theory, then produces similar discrepancy inequalities based …

New Challenges In Neutrosophic Theory And Applications, Florentin Smarandache, Stefan Vladutescu, Miihaela Colhon, Wadei Al-Omeri, Saeid Jafari, Muhammad Zahir Khan, Muhammad Farid Khan, Muhammad Aslam, Abdur Razzaque Mughal

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic theory has representatives on all continents and, therefore, it can be said to be a universal theory. On the other hand, according to the three volumes of “The Encyclopedia of Neutrosophic Researchers” (2016, 2018, 2019), plus numerous others not yet included in Encyclopedia book series, about 1200 researchers from 73 countries have applied both the neutrosophic theory and method. Neutrosophic theory was founded by Professor Florentin Smarandache in 1998; it constitutes further generalization of fuzzy and intuitionistic fuzzy theories. The key distinction between the neutrosophic set/logic and other types of sets/logics lies in the introduction of the degree of …

Math 456 Student Project Reports For Valleybike Operations Optimization, Ezra Small

Student Showcase

In the fall semester of 2019 UMass Amherst students in Professor Annie Raymond's MATH 456 course used ValleyBike share route data and applied mathematic algorithms to develop recommendations to the system operators and participating communities on how to optimize bike balancing operations, maintenance, station dock allocation, station locations, incentive programs, etc.

The Encyclopedia Of Neutrosophic Researchers - Vol. 3, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This is the third volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: …

Neutrosophic Triplet Structures - Vol. 1, Florentin Smarandache, Memet Sahin

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory was firstly proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs, the properties of neutrosophic sets …

Under The Influence, Leonardo Cavicchio

Honors Projects in Mathematics

The purpose of this Honors Capstone entitled Under the Influence is to assess the validity of claims concerning the possible influence of roommates on one another, concerning alcohol on college campuses. This will be done by examining data collected in a prior study conducted over a two-year period. This analysis will focus on how alcohol consumption changes in correlation with the personality factors of roommates over an extended period of time. This secondary analysis of de-identified data will focus on primary and secondary subquestions. The primary question that will be addressed with the data set collected from the University of …

Introduction To Mathematical Analysis I - 2nd Edition, Beatriz Lafferriere, Gerardo Lafferriere, Mau Nam Nguyen

PDXOpen: Open Educational Resources

Video lectures explaining problem solving strategies are available

Our goal in this set of lecture notes is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs.

The lecture notes contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. The lecture notes also contain many well-selected exercises of various levels. Although …

The Development Of Notation In Mathematical Analysis, Alyssa Venezia

Honors Thesis

The field of analysis is a newer subject in mathematics, as it only came into existence in the last 400 years. With a new field comes new notation, and in the era of universalism, analysis becomes key to understanding how centuries of mathematics were unified into a finite set of symbols, precise definitions, and rigorous proofs that would allow for the rapid development of modern mathematics. This paper traces the introduction of subjects and the development of new notations in mathematics from the seventeenth to the nineteenth century that allowed analysis to flourish. In following the development of analysis, we …

What Is The True Cost To Stay In The Hospital?, Samantha Alicandro

Honors Projects in Mathematics

Currently, the unfortunate reality that receiving diverse health procedures can be extremely expensive is widely acknowledged and woefully accepted. However, have you inquired or been curious about the specific factors that influence the cost per day expensed by a hospital? Through examination, investigation, and evaluation operating SAS Enterprise Guide, SAS Enterprise Miner and Tableau I have attempted to arrive at a conclusion for this very question. Utilizing a 1.5 million row data set provided by Rhode Island, for the years 2003-2013, I analyzed the assorted elements conceivably bearing impact on the cost per day at a hospital. Regressions, decision trees, …

Does Academic Performance Predict Workplace Productivity?, Jodie-Gaye Hunter

Honors Projects in Economics

This research examines if college GPA affects productivity and compensation in the workplace. It uses data collected from a survey of approximately 23,000 Bryant University graduates in different stages of their career. About 10 percent of the alumni surveyed completed the survey. The econometric model used in this study allows estimating the effect of GPA on income after controlling for various demographic and socioeconomic variables, including education, major, occupation, gender, among others. The empirical work provides evidence that GPA has a positive and statistically significant impact on workplace productivity for females, but GPA seems to be a weaker predictor of …

The Effect Of Tommy John (Ucl) Reconstructive Surgery On A Pitcher’S Arm And Career Progression, Jack Grant

Honors Projects in Mathematics

Injuries have plagued professional athletes since their sports have been in existence. The examination of how teams can diminish the side effects of the injuries en route to a speedy recovery remains an evolving process and a topic of concern for all. Injury preventative tactics have been implemented by coaching staffs and various training personnel. Major League Baseball (MLB) pitchers are noticing an increase in the number of surgeries performed each year. The tearing of the ulnar collateral ligament (UCL) in the elbow has become a predominant injury among pitchers in the MLB. Reconstructive surgery, also known as Tommy John …

Predictions Of Success In The Actuarial Major, Jessica Soojian

Honors Projects in Mathematics

This study finds predictive factors that have a significant effect on the ending Mathematics/Actuarial GPA of Actuarial majors at Bryant University. This was done to add clarity to incoming students for what it takes to do well in the actuarial major. There were 266 subjects consisting of Bryant students that graduated between the years 2009 and 2015. The data was received in the form of final transcripts upon graduation for these students. Through manipulation of these transcripts, GPAs were calculated for Mathematics/Actuarial, English/Literary Cultural Studies, History/Politics, Economics, Science, Social Sciences, Computer Information Systems, Finance, Accounting, Management, and Marketing. These GPAs …

Mathematics. Possible Subjects For The High School Entrance Examination And The Capacity Examination In Romania, Florentin Smarandache, Constantin Coanda, Ionuț Ivanescu

Branch Mathematics and Statistics Faculty and Staff Publications

The present book tries to offer students and teachers knowledge evaluation tools for all the chapters from the current Romanian mathematics syllabus. In the evolution of teenagers, the phase of admission in high schools mobilizes particular efforts and emotions. The present workbook aims to be a permanent advisor in the agitated period starting with the capacity examination and leading to the admittance to high school. The tests included in this workbook have a complementary character as opposed to the many materials written with the purpose to support all those who prepare for such examinations and they refer to the entire …

Sisteme Vibrante Trilobice, Florentin Smarandache, Mircea Eugen Selariu

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Mathematics For Everything With Combinatorics On Nature – A Report On The Promoter Dr. Linfan Mao Of Mathematical Combinatorics, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The science’s function is realizing the natural world, developing our society in coordination with natural laws and the mathematics provides the quantitative tool and method for solving problems helping with that understanding. Generally, understanding a natural thing by mathematical ways or means to other sciences are respectively establishing mathematical model on typical characters of it with analysis first, and then forecasting its behaviors, and finally, directing human beings for hold on its essence by that model.

Mathematical Modeling Of Trending Topics On Twitter, Jonathan S. Skaza

Honors Projects in Mathematics

Created in 2006, Twitter is an online social networking service in which users share and read 140-character messages called Tweets. The site has approximately 288 million monthly active users who produce about 500 million Tweets per day. This study applies dynamical and statistical modeling strategies to quantify the spread of information on Twitter. Parameter estimates for the rates of infection and recovery are obtained using Bayesian Markov Chain Monte Carlo (MCMC) methods. The methodological strategy employed is an extension of techniques traditionally used in an epidemiological and biomedical context (particularly in the spread of infectious disease). This study, which addresses …

My Finite Field, Matthew Schroeder

Journal of Humanistic Mathematics

A love poem written in the language of mathematics.