Mathematics Commons^™

Math 215: Introduction To Statistics, Cuny School Of Professional Studies

Open Educational Resources

Introduces the basic principles of statistics and probability, with an emphasis on understanding the underlying concepts, real-world applications, and the underlying story that the numbers tell. Uses Microsoft Excel’s statistical functions to analyze data. Provides an introduction to probability, descriptive statistics, hypothesis testing, and inferential statistics.

Math 120 Precalculus Review, York College Math 120 Students, Virginia L. Thompson

Open Educational Resources

No abstract provided.

The Fundamental Limit Theorem Of Countable Markov Chains, Nathanael Gentry

Senior Honors Theses

In 1906, the Russian probabilist A.A. Markov proved that the independence of a sequence of random variables is not a necessary condition for a law of large numbers to exist on that sequence. Markov's sequences -- today known as Markov chains -- touch several deep results in dynamical systems theory and have found wide application in bibliometrics, linguistics, artificial intelligence, and statistical mechanics. After developing the appropriate background, we prove a modern formulation of the law of large numbers (fundamental theorem) for simple countable Markov chains and develop an elementary notion of ergodicity. Then, we apply these chain convergence results …

The Effectiveness Of Professional Punters, Arthur N. Tanyel

Senior Honors Theses

Sports analytics have become a major part of how many sports fans enjoy the games they love. The trend has touched sports from football to cricket. One aspect of football that has been less discussed is punting. The current standard metrics, gross yardage and net yardage, give an idea of how a punter performed in a given season, but they also may be skewed by a number of factors, such as the skill of the offense or the punt coverage team. In this paper, we will look at some previous attempts to measure punting prowess, and then further develop a …

A Numerical Investigation Of Fractional Models For Viscoelastic Materials With Applications On Concrete Subjected To Extreme Temperatures, Murray Macnamara

Theses and Dissertations

Materials exhibiting both elastic and viscous properties have been termed the name viscoelastic materials and have been modeled using a combination of integer order derivatives affixed in varying ways called viscoelastic models. This results in highly complicated numerical procedures necessitating highly expensive computational time which we will show. To that end the use of fractional derivatives were researched and determined to be the ideal solution for modeling these materials, of which this paper is focused on exploring. Such research began as a theoretical study, however over time the applied benefits were discovered and utilized and have since been expanded on, …

Mathematical Modeling In Finance, Owen Sweeney

Honors Projects

Financial tools play an integral role in the day-to-day lives of individuals and businesses. Many of these tools use predefined formulas to calculate items such as loan payments, interest and capital structure components. These tools do not usually provide the flexibility needed when new parameters are introduced. By utilizing mathematical modeling, these standard formulas can be derived and even improved to provide the needed flexibility.

Game Chromatic Number On Segmented Caterpillars, Paige Beidelman

Departmental Honors & Graduate Capstone Projects

Graph theory is the study of sets vertices connected by known as edges, which are depicted as lines. The graph coloring game is a game played on a graph with two players, Alice and Bob, such that they alternate to properly color a graph, meaning no adjacent vertices are the same color. Alice wins if every vertex is properly colored with n colors, otherwise Bob wins when a vertex cannot be colored using n colors. While strategies for winning this game may seem helpful, more interesting is the least number of colors needed for Alice to have a winning strategy, …

Free Semigroupoid Algebras From Categories Of Paths, Juliana Bukoski

Department of Mathematics: Dissertations, Theses, and Student Research

Given a directed graph G, we can define a Hilbert space H_G with basis indexed by the path space of the graph, then represent the vertices of the graph as projections on H_G and the edges of the graph as partial isometries on H_G. The weak operator topology closed algebra generated by these projections and partial isometries is called the free semigroupoid algebra for G. Kribs and Power showed that these algebras are reflexive, and that they are semisimple if and only if each path in the graph lies on a cycle. We extend …

Talking The Talk:” Mathematical Language, Linguistic Bias, And The Delusion Of Meritocracy In The Study And Practice Of Mathematics, Gene T. Witkowski , '21

Senior Theses, Projects, and Awards

Challenging the dominant narrative of meritocracy, objectivity and moral/ideological neutrality embraced by many mathematicians, this thesis critically interrogates the form and function of mathematical language within academic and professional mathematical spaces. Grounded in my own experience as a s tudent within the discipline and the frameworks of various scholars within the subdiscipline of literacy education, I offer an understanding of the language of these spaces as a veritable form of literacy implicated in a flexible sociocultural context and dependent on one’s access to forms of capital. I submit that this language serves various functions including, but not limited to: the …

A University Forest Fire: Examining The Spread Of The Coronavirus Through College Social Networks Using A Modified Forest Fire Probabilistic Model, Raechel Griffin

Senior Honors Projects

No abstract provided.

Spanning Trees Of Complete Graphs And Cycles, Minjin Enkhjargal

University Honors Theses

Spanning trees are typically used to solve least path problems for finding the minimal spanning tree of a graph. Given a number t ≥ 3 what is the least number n = α(t) such that there exists a graph on n vertices having precisely t spanning trees? Specifically, how will the factoring of t with the use of cycles connected by one vertex affect α(t)? Lower and upper bounds of α(t) are graphed by using properties of cycles and complete graphs. The upper bound of α(t) is then improved by constructing a graph of connected cycles {C_p1, C­ …

Gauge-Invariant Uniqueness And Reductions Of Ordered Groups, Robert Huben

Department of Mathematics: Dissertations, Theses, and Student Research

A reduction φ of an ordered group (G,P) to another ordered group is an order homomorphism which maps each interval [1, p] bijectively onto [1, φ(p)]. We show that if (G,P) is weakly quasi-lattice ordered and reduces to an amenable ordered group, then there is a gauge-invariant uniqueness theorem for P -graph algebras. We also consider the class of ordered groups which reduce to an amenable ordered group, and show this class contains all amenable ordered groups and is closed under direct products, free products, and hereditary subgroups.

Adviser: Mark Brittenham and David Pitts

Functional Singular Spectrum Analysis: Nonparametric Decomposition And Forecasting Approaches For Functional Time Series, Jordan Christopher Trinka

Dissertations (1934 -)

In this dissertation, we develop nonparametric decomposition methods and the subsequent forecasting techniques for functional, time-dependent data known as functional time series (FTS). We use ideas from functional data analysis (FDA) and singular spectrum analysis (SSA) to introduce the nonparametric decomposition method known as functional SSA (FSSA) and its associated forecasting techniques. We also extend these developed methodologies into multivariate FSSA (MFSSA) over different dimensional domains and its subsequent forecasting routines so that we may perform nonparametric decomposition and prediction of multivariate FTS (MFTS). The FSSA algorithm may be viewed as a signal extraction technique and we find that the …

On Problems With Weighted Elliptic Operator And General Growth Nonlinearities, John Villavert

School of Mathematical & Statistical Sciences Faculty Publications

This article establishes existence, non-existence and Liouville-type theorems for nonlinear equations of the form −div(|x| aDu) = f(x, u), u > 0, in Ω, where N ≥ 3, Ω is an open domain in R N containing the origin, N−2+a > 0 and f satisfies structural conditions, including certain growth properties. The first main result is a non-existence theorem for boundary-value problems in bounded domains star-shaped with respect to the origin, provided f exhibits supercritical growth. A consequence of this is the existence of positive entire solutions to the equation for f exhibiting the same growth. A Liouville-type theorem is then established, …

Place Value In Primary Sources Oer Activity, Cynthia Huffman Ph.D.

Open Educational Resources - Math

An activity for student to examine the use of place-value in the Hindu-Arabic numeration system from a historical viewpoint by looking at primary sources. Includes the key.

(Revised May 2021)

Detecting Sars-Cov-2 3clpro Expression And Activity Using A Polyclonal Antiserum And A Luciferase-Based Biosensor, Amornrat O’Brien, Da-Yuan Chen, Matthew Hackbart, Brianna J. Close, Timothy O'Brien, Mohsan Saeed, Susan C. Baker

Mathematics and Statistics: Faculty Publications and Other Works

The need to stem the current outbreak of SARS-CoV-2 responsible for COVID-19 is driving the search for inhibitors that will block coronavirus replication and pathogenesis. The coronavirus 3C-like protease (3CLpro) encoded in the replicase polyprotein is an attractive target for antiviral drug development because protease activity is required for generating a functional replication complex. Reagents that can be used to screen for protease inhibitors and for identifying the replicase products of SARS-CoV-2 are urgently needed. Here we describe a luminescence-based biosensor assay for evaluating small molecule inhibitors of SARS-CoV-2 3CLpro/main protease. We also document that a polyclonal rabbit antiserum developed …

Dna Curve Classification With Unsupervised Learning, Ben Thomas

Honors Capstones

No abstract provided.

On The Burr Xii-Power Cauchy Distribution: Properties And Applications, Fiaz Ahmad Bhatti, Gholamhossein Hamedani, Mashail M. Al Sobhi, Mustafa Ç. Korkmaz

Mathematical and Statistical Science Faculty Research and Publications

We propose a new four-parameter lifetime model with flexible hazard rate called the Burr XII Power Cauchy (BXII-PC) distribution. We derive the BXII-PC distribution via (i) the T-X family technique and (ii) nexus between the exponential and gamma variables. The new proposed distribution is flexible as it has famous sub-models such as Burr XII-half Cauchy, Lomax-power Cauchy, Lomax-half Cauchy, Log-logistic-power Cauchy, log-logistic-half Cauchy. The failure rate function for the BXII-PC distribution is flexible as it can accommodate various shapes such as the modified bathtub, inverted bathtub, increasing, decreasing; increasing-decreasing and decreasing-increasing-decreasing. Its density function can take shapes such as exponential, …

Squigonometry, Andrew Hatfield, Riley Klette, Christopher Moore, Beth Warden

Mathematics

Trigonometry is the study of circular functions - functions defined on the unit circle where distances are measured with respect to the Euclidean norm. In our research, we develop a parallel theory of trigonometric and inverse trigonometric functions for the p-norm. This is called squigonometry because the resulting functions are defined on a squircle. This approach leads to new transcendental periods, formulas, and identities. It also extends to exponential, hyperbolic, and logarithmic functions in the p-norm.

Controllability And Observability Of Blood Glucose Levels And The Impact Of Covid-19 On Diabetic Patients, Mahra Salem Nasser Abdulla Alblooshi

Theses

Diabetes is a metabolic disorder that is characterized by high blood glucose concentrations resulting from insulin deficiency in case of type 1 or insulin inefficiency in case of type 2. While no cure for diabetes exists, the artificial pancreas is a possible way to manage diabetes, especially for type 1 diabetics. Where an artificial pancreas is a closed-loop control system with an integrated mathematical model. This control system imitates the function of a healthy pancreas. The first part of this thesis is concerned with the control system of an artificial pancreas that is based on Bergman’s minimal model of glucose-insulin …