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Articles 31 - 60 of 177
Full-Text Articles in Physical Sciences and Mathematics
Math 102: Mathematics In Contemporary Society, Cuny School Of Professional Studies
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.
Covid-19 And Knowledge Based Computation, Rohit J. Parikh
Covid-19 And Knowledge Based Computation, Rohit J. Parikh
Publications and Research
The problem of dealing with Covid-19, until a vaccine is universally administered, is to decrease the rate of transmission while getting some social and economic activity going.
Infection passes from one person A to another person B when A is infected and B is susceptible. That is to say that B is not infected and not yet immune.
Social activity also takes place when one person interacts with another. Perhaps A is a taxpayer and B is a tax consultant. Then filing the tax return may take the form of the two of them meeting. Much can be done electronically …
Math 111: Introduction To Statistics And Probability, Yu Wang
Math 111: Introduction To Statistics And Probability, 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.
Floor Plan Assignment In Elementary Mathematics Education, Tunde Jakab
Floor Plan Assignment In Elementary Mathematics Education, Tunde Jakab
Open Educational Resources
In this upper elementary mathematics education assignment, the prospective teachers gain hands-on experience in measuring distances in feet and inches, calculating areas, and converting distance and area measurements. Moreover, they solve a real-life situation by choosing the most economical tiles for their kitchen. This last part (3) of the assignment develops critical thinking and expressing one's thought processes. Part 3 can be used as an in-class discussion, which further promotes reasoning skills.
Elementary College Geometry (2021 Ed.), Henry Africk
Elementary College Geometry (2021 Ed.), Henry Africk
Open Educational Resources
This text is intended for a brief introductory course in plane geometry. It covers the topics from elementary geometry that are most likely to be required for more advanced mathematics courses. The only prerequisite is a semester of algebra. The emphasis is on applying basic geometric principles to the numerical solution of problems. For this purpose the number of theorems and definitions is kept small. Proofs are short and intuitive, mostly in the style of those found in a typical trigonometry or precalculus text. There is little attempt to teach theorem proving or formal methods of reasoning. However the topics …
Dynamics Of The Meromorphic Families $F_\Lambda=\Lambda \Tan^Pz^Q$, Tao Chen, Linda Keen
Dynamics Of The Meromorphic Families $F_\Lambda=\Lambda \Tan^Pz^Q$, Tao Chen, Linda Keen
Publications and Research
This paper continues our investigation of the dynamics of families of transcendental meromorphic functions with finitely many singular values all of which are finite. Here we look at a generalization of the family of polynomials Pa(z) =zd−1(z−da/(d−1)), the family fλ=λtanpzq. These functions have a super-attractive fixed point, and, depending on p, one or two asymptotic values. Although many of the dynamical properties generalize, the existence of an essential singularity and of poles of multiplicity greater than one implies that significantly different techniques are required here. Adding transcendental methods to standard …
Interdisciplinary Thinking: Financial Literacy Crosses Disciplinary Boundaries, Marla A. Sole
Interdisciplinary Thinking: Financial Literacy Crosses Disciplinary Boundaries, Marla A. Sole
Publications and Research
Financial literacy is ideally suited to be integrated into mathematics courses and taught in an interdisciplinary manner. Students learn best and are motivated when tackling real-world meaningful questions. This article shares how elementary mathematics was applied to better understand the debate about raising the minimum wage and the United States National Debt. To serve as a guide for other teachers who wish to incorporate financial literacy into their mathematics courses and take an interdisciplinary approach, this article suggests readings, data sets, and pedagogical practices. Students were engaged and enthusiastic to work on problems that challenged their thinking about financial issues.
Three Imprimitive Character Sums, Brad Isaacson
Three Imprimitive Character Sums, Brad Isaacson
Publications and Research
We express three imprimitive character sums in terms of generalized Bernoulli numbers. These sums are generalizations of sums introduced and studied by Arakawa, Berndt, Ibukiyama, Kaneko and Ramanujan in the context of modular forms and theta function identities. As a corollary, we obtain a formula for cotangent power sums considered by Apostol.
Amm Problem #12219, Brad Isaacson
A Twisted Generalization Of The Classical Dedekind Sum, Brad Isaacson
A Twisted Generalization Of The Classical Dedekind Sum, Brad Isaacson
Publications and Research
In this paper, we express three different, yet related, character sums in terms of generalized Bernoulli numbers. Two of these sums are generalizations of sums introduced and studied by Berndt and Arakawa–Ibukiyama–Kaneko in the context of the theory of modular forms. A third sum generalizes a sum already studied by Ramanujan in the context of theta function identities. Our methods are elementary, relying only on basic facts from algebra and number theory.
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
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
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
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
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
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
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
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
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
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
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
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
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.
Graded Quivers, Generalized Dimer Models And Toric Geometry, Sebastián Franco, Azeem Hasan
Graded Quivers, Generalized Dimer Models And Toric Geometry, Sebastián Franco, Azeem Hasan
Publications and Research
The open string sector of the topological B-model on CY (m+2)-folds is described by m-graded quivers with superpotentials. This correspondence extends to general m the well known connection between CY (m+2)-folds and gauge theories on the world-volume of D(5-2m)-branes for m = 0, ..., 3. We introduce m-dimers, which fully encode the m-graded quivers and their superpotentials, in the case in which the CY (m+2)-folds are toric. Generalizing the well known m = 1,2 cases, m-dimers significantly simplify the connection between geometry and m-graded quivers. A key …
A Concise Workbook For College Algebra 2nd Edition, Fei Ye
A Concise Workbook For College Algebra 2nd Edition, Fei Ye
Open Educational Resources
This is the second edition of the book "A Concise Workbook for College Algebra". In this new edition, some tips and notes, more exercises and examples were added.
Arecibo Message, Joshua P. Tan
Arecibo Message, Joshua P. Tan
Open Educational Resources
This two week assignment asks students to interpret and analyze the 1974 Arecibo Message sent by Drake and Sagan. Week 1 introduces the concepts behind the construction of the message and engages with a critical analysis of the architecture and the contents of the message. Week 2 asks students to develop software in a Jupyter Notebook (available for free from the Anaconda Python Distribution) to interpret messages that were similar to those produced by Drake and Sagan.
Understanding The Impact Of Peer-Led Workshops On Student Learning, Afolabi Ibitoye, Nadia Kennedy, Armando Cosme
Understanding The Impact Of Peer-Led Workshops On Student Learning, Afolabi Ibitoye, Nadia Kennedy, Armando Cosme
Publications and Research
As students we often wonder why some subjects are easy to understand and requires not much effort in terms of re-reading the material, for us to grasp what it entails. One subject seems to remain elusive and uneasy for a vast majority of learners at all levels of education; that subject is Mathematics, it is one subject that most learners finds difficult even after doubling the amount of time spent on studying the material. My intention is to explore ways to make Mathematics easier for other students using feedback from students enrolled in NSF mathematics peer leading workshops, and use …
A Comparative Study Of Incidence Of Domestic Violence Between Immigrant And Non-Immigrant Women In The United States Of America, Nadia A. Gordon, Urmi Ghosh-Dastidar, Janet Liou-Mark, Shamita Dasgupta
A Comparative Study Of Incidence Of Domestic Violence Between Immigrant And Non-Immigrant Women In The United States Of America, Nadia A. Gordon, Urmi Ghosh-Dastidar, Janet Liou-Mark, Shamita Dasgupta
Publications and Research
Immigrant women in the USA come from various socio-economic, cultural, and religious backgrounds. Some of these women suffer from domestic violence; however, due to their strict cultural or social structure, they often stay quiet and rarely report these incidents to the authorities. Additionally, since these immigrant women face more challenges than their non-immigrant peers, they are more reluctant or unlikely to leave their abusive partners. An analysis was completed using published data as an attempt to establish if any statistically significant differences exist between reported incidences among immigrant women and non-immigrant women. A chi-square analysis (χ2 = 14.53; p-value …
Simulation As A Predictor In Probability, Xiaona Zhou
Simulation As A Predictor In Probability, Xiaona Zhou
Publications and Research
In this study, we simulate bivariate normal data. We gain intuition about the bivariate normal distribution by comparing the generated data to the associated bivariate normal density surface. We also get results about covariance and correlation. We will use tools from linear algebra to discuss transformations of random normal vectors, and the use of contours.
Validation Of A Lottery, Xiaona Zhou
Validation Of A Lottery, Xiaona Zhou
Publications and Research
The NY Pick 4 lottery consists of four "randomly" chosen digits from 0 to 9. For this to be fair, each digit should be equally likely to occur. To determine whether this is the case, a Chi-squared goodness of fit test will be applied to historical data. This provides a quantitative way of measuring how well the observed frequency of digits matches our expectations of a fair lottery. We also explore the "Lucky Sum", which is also a part of the Pick 4. We determine which sum is most likely to occur, and what the odds of winning are if …
An Invitation To Linear Algebra, David N. Pham, Jonathon Funk, Wenjian Liu
An Invitation To Linear Algebra, David N. Pham, Jonathon Funk, Wenjian Liu
Open Educational Resources
This is an OER textbook on linear algebra.