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Physical Sciences and Mathematics Commons

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Articles 1 - 12 of 12

Full-Text Articles in Physical Sciences and Mathematics

Approximation By The K^Lambda Means Of Fourier Series And Conjugate Series Of Functions In H_{Alpha,P}, Ben Landon, Holly Carley, R. N. Mohapatra Dec 2020

Approximation By The K^Lambda Means Of Fourier Series And Conjugate Series Of Functions In H_{Alpha,P}, Ben Landon, Holly Carley, R. N. Mohapatra

Publications and Research

No abstract provided.


An Enticing Study Of Prime Numbers Of The Shape �� = ��^2 + ��^2, Xiaona Zhou Dec 2020

An Enticing Study Of Prime Numbers Of The Shape �� = ��^2 + ��^2, Xiaona Zhou

Publications and Research

We will study and prove important results on primes of the shape ��2 + ��2 using number theoretic techniques. Our analysis involves maps, actions over sets, fixed points and involutions. This presentation is readily accessible to an advanced undergraduate student and lay the groundwork for future studies.


Math 310: Applied Regression Analysis, Yu Wang Oct 2020

Math 310: Applied Regression Analysis, Yu Wang

Open Educational Resources

Introduce the different linear statistical models and develop critical thinking for statistical modeling in scientific and policy contexts; Apply statistical computer software tools to develop useful data analysis skills based on the use of linear regression models. Topics to be covered: simple linear regression, multiple regression, nonlinear regression and logistic regression models; Random and mixed effects models; The application of statistical software tools.


A Differential-Algebraic Criterion For Obtaining A Small Maximal Cohen-Macaulay Module, Hans Schoutens Jun 2020

A Differential-Algebraic Criterion For Obtaining A Small Maximal Cohen-Macaulay Module, Hans Schoutens

Publications and Research

We show how for a three-dimensional complete local ring in positive characteristic, the existence of an F-invariant, differentiable derivation implies Hochster’s small MCM conjecture. As an application we show that any three-dimensional pseudo-graded ring in positive characteristic satisfies Hochster’s small MCM conjecture.


An In-Depth Look At P-Adic Numbers, Xiaona Zhou May 2020

An In-Depth Look At P-Adic Numbers, Xiaona Zhou

Publications and Research

In this study, we consider $p$-adic numbers. We will also study the $p$-adic norm representation of real number, which is defined as $\mathbb{Q}_p = \{\sum_{j=m}^{\infty }a_j p^j: a_j \in \mathbb{D}_p, m\in\mathbb{Z}, a_m\neq 0\} \cup \{0\}$, where $p$ is a prime number. We explore properties of the $p$-adics by using examples. In particular, we will show that $\sqrt{6},i \in \mathbb{Q}_5$ and $\sqrt{2} \in \mathbb{Q}_7 $. $p$-adic numbers have a wide range of applicationsnin fields such as string theory, quantum mechanics, and transportation in porous disordered media in geology.


Winding Numbers And Full Extendability In Holomorphic Motions, Yunping Jiang May 2020

Winding Numbers And Full Extendability In Holomorphic Motions, Yunping Jiang

Publications and Research

We construct an example of a holomorphic motion of a five-point subset of the Riemann sphere over an annulus such that it satisfies the zero winding number condition but is not fully extendable.


Estimating Population Immunity Without Serological Testing, Andrew Lesniewski Apr 2020

Estimating Population Immunity Without Serological Testing, Andrew Lesniewski

Publications and Research

We propose an approximate methodology for estimating the overall level of immunity against COVID-19 in a population that has been affected by the recent epidemic. The methodology relies on the currently available mortality data and utilizes the properties of the SIR model. We illustrate the application of the method by estimating the recent levels of immunity in 10 US states with highest case numbers of COVID-19.


Math 120bc – Precalculus, Virginia Thompson Apr 2020

Math 120bc – Precalculus, Virginia Thompson

Open Educational Resources

Students will explore advanced topics in algebra, functions and graphs, inverse functions, composite functions, polynomial and rational functions, trigonometry, exponential and logarithmic functions.


Math 220p Foundations Of Mathematics, Nicholas Vlamis Jan 2020

Math 220p Foundations Of Mathematics, Nicholas Vlamis

Open Educational Resources

No abstract provided.


An Invitation To Linear Algebra (2nd Edition), David N. Pham, Jonathon Funk, Wenjian Liu Jan 2020

An Invitation To Linear Algebra (2nd Edition), David N. Pham, Jonathon Funk, Wenjian Liu

Open Educational Resources

This is an OER textbook on linear algebra.


Trigonometry: A Brief Conversation, Carolyn D. King Phd, Tam Evelyn, Fei Ye Phd, Beata Ewa Carvajal Jan 2020

Trigonometry: A Brief Conversation, Carolyn D. King Phd, Tam Evelyn, Fei Ye Phd, Beata Ewa Carvajal

Open Educational Resources

These five units are specifically tailored to foster the mastery of a few selected trigonometry topics that comprise the one credit MA-121 Elementary Trigonometry course. Each unit introduces the topic, provides space for practice, but more importantly, provides opportunities for students to reflect on the work in order to deepen their conceptual understanding.

These units have also been assigned to students of other courses such as pre-calculus and calculus as a review of trigonometric basics essential to those courses. This is the second edition of the materials. Units 4 and 5 have been edited to reflect suggestions from instructors who …


The Tsukano Conjectures On Exponential Sums, Brad Isaacson Jan 2020

The Tsukano Conjectures On Exponential Sums, Brad Isaacson

Publications and Research

We prove three conjectures of Tsukano about exponential sums stated in his Master’s thesis written at Osaka University. These conjectures are variations of earlier conjectures made by Lee and Weintraub which were first proved by Ibukiyama and Saito.