Mathematics Commons^™

Getting Over It, Thomas Kade, Kevorc Ibrahimian, Max Simpson

Arts & Sciences Student Symposium

The research extended a 2D motion planning system to three dimensional environments. The updated system is now able to plan the motion for robots over 3D terrains modeled by polyhedrons.

The School Mathematics Study Group: Lessons In Mathematics Education, Madeline Polhill

Arts & Sciences Student Symposium

This work argues that the "new math" project called the School Mathematics Study Group offers a valuable case study for mathematics educators seeking to venture into the future better informed about both the successes and failures of previous projects. Understanding this project requires recognizing that the School Mathematics Study Group was wholly a product of the forces—personal, educational, mathematical, and political—that shaped it. Admittedly, some of the SMSG's shortcomings resulted from its members' lack of understanding of the changes needed in mathematics education. Still, the majority of the SMSG's public vilification resulted through no fault of its own, but rather …

Curve Reconstruction From The Apparent Contour Graph, Nkosi Alexander-Williams

Showcase of Osprey Advancements in Research and Scholarship (SOARS)

Project of Merit Winner

This project concerns the two-dimensional Scenery Reconstruction Problem (2D-AC), a simplified version of the Scenery Reconstruction Problem (3D-AC) studied by Bellettini, Beorchia, Paolini, and Pasquarelli. In our research, we take a picture of a 2D object, take information from the picture, specifically the edges of the object as seen in the picture, and from this information, we determine if we can reconstruct the original 2D object. Utilizing knowledge of the concepts regarding contour generators and apparent contours, we determine the labelings for these points and call the labelings the Apparent Contour Graph. This project answers the …

Opioid Epidemic On The First Coast​, Jeremiah Baclig, Noah Dedeo, Rukhaiya Husain, Iliya Kulbaka, Michelle Dedeo

Showcase of Osprey Advancements in Research and Scholarship (SOARS)

Project of Merit Winner

The nation has been focusing on the opioid epidemic for many years. Aggregate quarterly data on opioid distribution at a general level has been available through the Drug Enforcement Administration (DEA) but cannot be used to do analyses on the effects of opioids in local areas. Quantifying impacts of the opioid epidemic at the local level has never been easy: what little data was provided by the DEA was not user-friendly, overly broad and did not follow the desired timeline of data collection. This project focuses on database exploration and uses statistical methods and Decision Tree …

Determination Of The Traits In Leguminous Crops Under Saline Condition, Tojiddin Kuliev, Karomat Ismailova

Karakalpak Scientific Journal

In this study, the variability and determination of genetic traits for winter legume crop varieties the Vostok-55 (Pisum arvense L) and Mirzachul-1 (Vicia villoza Roth L) were investigated under moderate saline soil condition. Results show that the weight of the bean was marked as variable and highly deterministic, and the height of the plants was the most stable. The selection of plants based on these traits is the most effective way of salinity. Both variety the forage pea Vostok-55 and vetch Mirzachul-1 is highly recommended as a sideration and forage crop in saline lands.

The Agnostic Structure Of Data Science Methods, Domenico Napoletani, Marco Panza, Daniele Struppa

MPP Published Research

In this paper we argue that data science is a coherent and novel approach to empirical problems that, in its most general form, does not build understanding about phenomena. Within the new type of mathematization at work in data science, mathematical methods are not selected because of any relevance for a problem at hand; mathematical methods are applied to a specific problem only by `forcing’, i.e. on the basis of their ability to reorganize the data for further analysis and the intrinsic richness of their mathematical structure. In particular, we argue that deep learning neural networks are best understood within …

Lecture 10: Preconditioned Iterative Methods For Linear Systems, Edmond Chow

Mathematical Sciences Spring Lecture Series

Iterative methods for the solution of linear systems of equations – such as stationary, semi-iterative, and Krylov subspace methods – are classical methods taught in numerical analysis courses, but adapting these methods to run efficiently at large-scale on high-performance computers is challenging and a constantly evolving topic. Preconditioners – necessary to aid the convergence of iterative methods – come in many forms, from algebraic to physics-based, are regularly being developed for linear systems from different classes of problems, and similarly are evolving with high-performance computers. This lecture will cover the background and some recent developments on iterative methods and preconditioning …

Lecture 00: Opening Remarks: 46th Spring Lecture Series, Tulin Kaman

Mathematical Sciences Spring Lecture Series

Opening remarks for the 46th Annual Mathematical Sciences Spring Lecture Series at the University of Arkansas, Fayetteville.

Long-Time Asymptotics For Mkdv Type Reduced Equations Of The Akns Hierarchy In Weighted L2 Sobolev Spaces, Fudong Wang

USF Tampa Graduate Theses and Dissertations

The long-time asymptotics of nonlinear integrable partial differential equations is one of the important research areas in the field of integrable systems. The main tool to analyze the long-time behaviors is the so-called nonlinear steepest descent method, or Deift-Zhou's method, which was born in 1993. To apply Deift-Zhou's method, one first uses the inverse scattering transform to formulate the nonlinear PDEs in terms of an oscillatory 2 by 2 matrix Riemann-Hilbert problem (RHP). After about 15 years of development, a generalized version of Deift-Zhou's method, the ∂—steepest method, came out. The ∂—steepest descent method is a useful method for analyzing …

Computational Difficulty And Invariants Of The Snake Cube Puzzle, Adrian Negrea

Honors Theses

The snake cube is a popular puzzle that has been analyzed for its computational difficulty and shown to be NP-complete. Conceiving of the puzzle as a Hamiltonian path in an n x n x n graph, we offer a novel mathematical analysis by considering invariants of the puzzle. This allows us to determine necessary conditions for a particular snake cube to be solvable and eliminate a large class of possible puzzles as unsolvable. In particular, we establish upper and lower bounds on the possible number of straight components in solvable snake cube puzzles.

Examining Middle School Students' Methods Of Justification, Leslie Reyes- Hernandez

Mathematics

Researching students’ thinking is imperative to improving the education system throughout the world. From extensive research, it is noted that students are unaccustomed and struggle with providing valid mathematical justifications (e.g. Inglis & Alcock 2012). The National Council of Teachers of Mathematics (NCTM, 2000) and Common Core State Standards of Mathematics (CCSSM, 2010) suggest that students should have several opportunities to construct mathematical arguments across all grade levels. To take a closer look at this educational phenomenon, we prompt fifth to eighth-grade students with nine mathematical tasks. Within our research, we focus on tasks based on number properties, algebraic thinking, …

A Direct Method For Modeling And Simulations Of Elliptic And Parabolic Interface Problems, Kumudu Gamage, Yan Peng

College of Sciences Posters

Interface problems have many applications in fluid dynamics, molecular biology, electromagnetism, material science, heat distribution in engines, and hyperthermia treatment of cancer. Mathematically, interface problems commonly lead to partial differential equations (PDE) whose in- put data are discontinuous or singular across the interfaces in the solution domain. Many standard numerical methods designed for smooth solutions poorly work for interface problems as solutions of the interface problems are mostly non-smoothness or discontinuous. Moving interface problems depends on the accuracy of the gradient of the solution at the interface. Therefore, it became essential to derive a method for interface problems that gives …

Quantifying Eco-Friendliness Of Plastic, Paper, And Reusable Bags, Leah Ryan

Honors Projects in Science and Technology

The plight of the consumer in regards to making eco-conscious decisions is growing as concerns regarding the environment increase. This study was conducted in an effort to give consumers a tool to combat some of this issue and compare the types of shopping bags they use in terms of eco-friendliness. Research conducted in this avenue thus far contains convoluted conclusions, all made with consideration of some variables, but not all. This purpose of this study therefore lay in trying to give consumers a standardized tool to compare bag types that considered variables across all stages of a bags’ life (pre-use, …

Why Decimal System? Why Communities With More Than 150 Folks Tend To Split? New Consequences Of The Seven Plus Minus Two Law, Leobardo Orea Amador, Vladik Kreinovich

Departmental Technical Reports (CS)

Why are we using the decimal system to describe numbers? Why all over the world, communities with more than 150 folks tend to split? In this paper, we show that both phenomena -- as well as some other phenomena -- can be explained if we take into account the seven plus minus two law, according to which a person can keep in immediate memory from 5 to 9 items.

Stitching Dedekind Cuts To Construct The Real Numbers, Michael P. Saclolo

Analysis

No abstract provided.

Why, In Deep Learning, Non-Smooth Activation Function Works Better Than Smooth Ones, Daniel Cruz, Richard Godoy, Vladik Kreinovich

Departmental Technical Reports (CS)

Since in the physical world, most dependencies are smooth (differentiable), traditionally, smooth functions were used to approximate these dependencies. In particular, neural networks used smooth activation functions such as the sigmoid function. However, the successes of deep learning showed that in many cases, non-smooth activation functions like max(0,z) work much better. In this paper, we explain why in many cases, non-smooth approximating functions often work better -- even when the approximated dependence is smooth.

Why Semi-Supervised Learning Makes Sense: A Pedagogical Note, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

The main idea behind semi-supervised learning is that when we do not enough human-generated labels, we train a machine learning system based on what we have, and we add the resulting labels (called pseudo-labels) to the training sample. Interesting, this idea works well, but why is somewhat a mystery: we did not add any new information so why is this working? There exist explanations for this empirical phenomenon, but most these explanations are based on complicated math. In this paper, we provide a simple intuitive explanation.

Why ∞ Is A Reasonable Symbol For Infinity, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

The fact that ∞ is actively used as a symbol for infinity shows that this symbol is probably reasonable in this role, but why? In this paper, we provide a possible explanation for why this is indeed a reasonable symbol for infinity.

Prediction Of Individual Income: A Machine Learning Approach, Michael Matkowski

Honors Projects in Economics

The use of machine learning models to improve prediction problems and handle increasingly large datasets is a rising trend in economics. Prediction plays a particularly important role in applied economics because it provides critical insights to assess market outcomes. This study builds on previous literature to showcase the relative power of these modelling methodologies in economics through the prediction of income. This research utilizes data from the Current Population Survey from 2017 – 2020, containing 467,811 observations and 264 variables. 2017-2018 data served as training data for the models and 2019-2020 served as data for the two testing sets. The …

Lev Landau's Marital Advice Explained, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Nobelist physicist Lev Landau was known for applying mathematical and physical reasoning to human relations. His advices may have been somewhat controversial, but they were usually well motivated. However, there was one advice for which no explanation remains -- that a person should not marry his/her first and second true loves, and only start thinking about marriage starting with the third true love. In this paper, we provide a possible Landau-style motivation for this advice.

Millennials' Retirement Struggle: The Interaction Between Student Loans, Financial Decisions, And Financial Literacy., Rebecca Michaud

Honors Projects in Finance

As millennials grow older and begin their careers in the workforce, saving for retirement begins to become an important part of spending. This paper analyzes a variety of factors and challenges that impact an individual’s retirement savings. This thesis ultimately looks to determine whether the driving force for the general inadequacy of retirement savings is student loan debt, financial decision making, or both. Through both research and survey responses, this thesis will also look at whether a public policy that removes a certain percentage of student loan repayment obligations will have any impact on the amount that young workers are …

Limit Theorems As Blessing Of Dimensionality: Neural-Oriented Overview, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

As a system becomes more complex, at first, its description and analysis becomes more complicated. However, a further increase in the system's complexity often makes this analysis simpler. A classical example is Central Limit Theorem: when we have a few independent sources of uncertainty, the resulting uncertainty is very difficult to describe, but as the number of such sources increases, the resulting distribution get close to an easy-to-analyze normal one -- and indeed, normal distributions are ubiquitous. We show that such limit theorems often make analysis of complex systems easier -- i.e., lead to blessing of dimensionality phenomenon -- for …

What Is 1/0 From The Practical Viewpoint: A Pedagogical Note, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

What is 1/0? Students are first taught -- in elementary school -- that it is undefined, then -- in calculus -- then it is infinity. In both cases, the answer is usually provided based on abstract reasoning. But what about the practical meaning? In this paper, we show that, depending on the specific practical problem, we can have different answers to this question: in some practical problems, the correct answer is that 1/0 is undefined, in others, the correct answer is that 1/0 =0 -- and there are probably other practical problems where we can have different answers. Bottom line: …

Evaluation Of Broadcast Steam Application With Mustard Seed Meal In Fruiting Strawberry, Dong Sub Kim, Steven Kim, Steven A. Fennimore

Mathematics and Statistics Faculty Publications and Presentations

Soil disinfestation with steam has potential to partially replace fumigants such as methyl bromide, chloropicrin, and 1,3-dichloropropene because it is effective, safer to apply, and has less negative impact on the environment. Here, we compared the efficacy of steam and steam + mustard seed meal (MSM) to chloropicrin on soil disinfection, plant growth, and fruit yield in a strawberry (Fragaria ×ananassa) fruiting field. The MSM was applied at 3368 kg·ha−1 before the steam application. Steam was injected into a 3-m-wide reverse tiller that was set to till 30 to 40 cm deep. Soil temperatures at depths of …

Riemann Versus Lebesgue Integrals, Justin Moore

Spring Showcase for Research and Creative Inquiry

The purpose of this project is to examine how integrals work and compare Reimann integrals to Lebesgue integrals, determining their applications and distinctions.

Math 102: Mathematics In Contemporary Society, Cuny School Of Professional Studies

Open Educational Resources

Designed to provide students with an understanding of the mathematical ideas and methods found in the social sciences, the arts, and business, this course covers the fundamentals of statistics, scatter plots, graphics in the media, problem-solving strategies, dimensional analysis, and mathematical modeling. Students can expect to explore real world applications.

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 …