Open Access. Powered by Scholars. Published by Universities.®
- Institution
-
- Georgia Southern University (28)
- Claremont Colleges (11)
- Ursinus College (8)
- Illinois Math and Science Academy (7)
- Illinois Wesleyan University (7)
-
- Dordt University (4)
- Walden University (4)
- City University of New York (CUNY) (3)
- Gettysburg College (3)
- Morehead State University (3)
- University of Nebraska - Lincoln (3)
- Boise State University (2)
- Governors State University (2)
- Illinois State University (2)
- Montclair State University (2)
- Sacred Heart University (2)
- Western Michigan University (2)
- Assumption University (1)
- Ateneo de Manila University (1)
- Bryant University (1)
- George Fox University (1)
- Hope College (1)
- Kansas State University Libraries (1)
- Kennesaw State University (1)
- Lawrence University (1)
- Loyola University Chicago (1)
- Marshall University (1)
- Missouri University of Science and Technology (1)
- Old Dominion University (1)
- Purdue University (1)
- Keyword
-
- Mathematics (14)
- Education (4)
- Applications (3)
- Chaos (3)
- Mathematics education (3)
-
- Algebra (2)
- Derived set (2)
- Developmental math (2)
- High school mathematics (2)
- Lifetime Data (2)
- Limit point (2)
- Linear programming (2)
- Lorenz Equations (2)
- Manipulatives (2)
- Math (2)
- Maximum likelihood estimation (2)
- Moments (2)
- Paradox (2)
- Pascal Matrix (2)
- Professional development (2)
- Proper Connection (2)
- Remedial math (2)
- Routh-Hurwitz Theorem (2)
- Stability (2)
- Submatrices (2)
- Teaching (2)
- Topology (2)
- 8th Grade (1)
- <p>Poisson processes.</p> <p>Poisson distribution.</p> <p>Sex differences in education.</p> (1)
- Abstract algebra (1)
- Publication
-
- Department of Mathematical Sciences Faculty Publications (27)
- John Wesley Powell Student Research Conference (7)
- Professional Learning Day (7)
- Journal of Humanistic Mathematics (6)
- Faculty Work Comprehensive List (4)
-
- Walden Dissertations and Doctoral Studies (4)
- Celebration of Student Scholarship Poster Sessions Archive (3)
- Math Faculty Publications (3)
- Pomona Faculty Publications and Research (3)
- Topology (3)
- All HMC Faculty Publications and Research (2)
- Analysis (2)
- Annual Symposium on Biomathematics and Ecology Education and Research (2)
- Geometry (2)
- Honors Theses (2)
- Mathematics Faculty Publications and Presentations (2)
- Publications and Research (2)
- Abstract Algebra (1)
- Academic Chairpersons Conference Proceedings (1)
- All Capstone Projects (1)
- All Student Theses (1)
- Articles (1)
- Communication Disorders & Special Education Faculty Publications (1)
- Computer Science: Faculty Publications and Other Works (1)
- DBER Speaker Series (1)
- Department of Mathematics Facuty Scholarship and Creative Works (1)
- Department of Mathematics: Faculty Publications (1)
- Dissertations (1)
- Dissertations, Theses, and Capstone Projects (1)
- Doctor of Education (EdD) (1)
Articles 1 - 30 of 117
Full-Text Articles in Education
Minimization And Eulerian Formulation Of Differential Geometry Based Nonpolar Multiscale Solvation Models, Zhan Chen
Department of Mathematical Sciences Faculty Publications
In this work, the existence of a global minimizer for the previous Lagrangian formulation of nonpolar solvation model proposed in [1] has been proved. One of the proofs involves a construction of a phase field model that converges to the Lagrangian formulation. Moreover, an Eulerian formulation of nonpolar solvation model is proposed and implemented under a similar parameterization scheme to that in [1]. By doing so, the connection, similarity and difference between the Eulerian formulation and its Lagrangian counterpart can be analyzed. It turns out that both of them have a great potential in solvation prediction for nonpolar molecules, while …
Extension Groups For Dg Modules, Saeed Nasseh, Sean Sather-Wagstaff
Extension Groups For Dg Modules, Saeed Nasseh, Sean Sather-Wagstaff
Department of Mathematical Sciences Faculty Publications
Let M and N be differential graded (DG) modules over a positively graded commutative DG algebra A. We show that the Ext-groups ExtiA(M,N) defined in terms of semi-projective resolutions are not in general isomorphic to the Yoneda Ext-groups YExtiA(M,N) given in terms of equivalence classes of extensions. On the other hand, we show that these groups are isomorphic when the first DG module is semi-projective.
The Creation Of A Video Review Guide For The Free-Response Section Of The Advanced Placement Calculus Exam, Jeffrey Brown
The Creation Of A Video Review Guide For The Free-Response Section Of The Advanced Placement Calculus Exam, Jeffrey Brown
Honors Theses
The Creation of a Video Review Guide for the Free-Response Section of the Advanced Placement Calculus Exam follows the creation of a resource to help students prepare for the College Board’s Advanced Placement Calculus Exam. This project originated out of the authors personal experiences in preparing for this exam. The goal of the project was to create an accessible resource that reviews content, provides insights into the Advanced Placement exam, and creates successful habits in student responses. This paper, chronologically, details the development of the resource and a reflection on the final product and future uses.
Going For Gold In The International Math Olympiad, Queena N. Lee-Chua
Going For Gold In The International Math Olympiad, Queena N. Lee-Chua
Mathematics Faculty Publications
In July 2016, two high school students in the Philippine team garnered gold at the 57th International Mathematics Olympiad (IMO) in Hong Kong, capping a three-decade long quest for the top prize in the most prestigious high school math competition in the world. The four other team members also brought home honors, boosting our country to its highest rank ever, 17th out of 109 countries. This article discusses the history of the Philippine participation in the IMO, and examines the critical factors that have led to the victory. For Philippine team participants in general, these include: institutionalized and refined search …
Pedagogical Moves As Characteristics Of One Instructor’S Instrumental Orchestrations With Tinkerplots And The Ti-73 Explorer: A Case Study, James L. Kratky
Pedagogical Moves As Characteristics Of One Instructor’S Instrumental Orchestrations With Tinkerplots And The Ti-73 Explorer: A Case Study, James L. Kratky
Dissertations
Those supporting contemporary reform efforts for mathematics education in the United States have called for increased use of technologies to support student-centered learning of mathematical concepts and skills. There is a need for more research and professional development to support teachers in transitioning their instruction to better meet the goals of such reform efforts.
Instrumental approaches to conceptualizing technology use in mathematics education, arising out of the theoretical and empirical work in France and other European nations, show promise for use to frame studies on school mathematics in the United States. Instrumental genesis is used to describe the bidirectional and …
Race, Space, And The Conflict Inside Us, Francis Su
Race, Space, And The Conflict Inside Us, Francis Su
All HMC Faculty Publications and Research
Talking about race is hard. Our nation is wrestling with some open wounds about race. These sores have been around a while, but they have been brought to light recently by technology, politics, and an increasingly diverse population. And regardless of the outcome of the U.S. presidential election, we will all need to work at healing these sores, not just in our personal lives, but in our classrooms and in our profession.
Exploring Connections Between Advanced And Secondary Mathematics, Erin E. Baldinger, Eileen Murray, Diana White, Shawn Broderick, Nicholas Wasserman
Exploring Connections Between Advanced And Secondary Mathematics, Erin E. Baldinger, Eileen Murray, Diana White, Shawn Broderick, Nicholas Wasserman
Department of Mathematics Facuty Scholarship and Creative Works
The second meeting of this Working Group continues to explore questions about the connections between abstract algebra and school mathematics. Our goal is to focus in on questions around the way in which teachers’ practice might be influenced based on their understanding of such connections. In particular, we will gather interested individuals in an effort to deepen our understanding of existing connections between abstract algebra and secondary mathematics and which of these connections are important for secondary teachers to know and understand. Moreover, we aim to further research in this area by first considering connections between abstract algebra and school …
Life After Calculus: 20 Years Later, Darren B. Glass
Life After Calculus: 20 Years Later, Darren B. Glass
Math Faculty Publications
In 1996 Math Horizons interviewed a group of students at the Joint Mathematics Meetings; now, 20 years later, one of those students, Darren Glass, interviews another group of students.
A Framework For The Teaching Of Modeling For Biologists, M. Drew Lamar, Carrie Diaz Eaton
A Framework For The Teaching Of Modeling For Biologists, M. Drew Lamar, Carrie Diaz Eaton
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Designing And Mentoring In A Research Experience For Undergraduates, Alex Capaldi
Designing And Mentoring In A Research Experience For Undergraduates, Alex Capaldi
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Longitudinal Success Of Calculus I Reform, Doug Bullock, Kathrine E. Johnson, Janet Callahan
Longitudinal Success Of Calculus I Reform, Doug Bullock, Kathrine E. Johnson, Janet Callahan
Janet M. Callahan
This paper describes the second year of an ongoing project to transform calculus instruction at Boise State University. Over the past several years, Calculus I has undergone a complete overhaul that has involved a movement from a collection of independent, uncoordinated, personalized, lecture-based sections, into a single coherent multi-section course with an activelearning pedagogical approach. The overhaul also significantly impacted the course content and learning objectives. The project is now in its fifth semester and has reached a steady state where the reformed practices are normative within the subset of instructors who might be called upon to teach Calculus I. …
Rank Of Submatrices Of The Pascal Matrix, Scott N. Kersey
Rank Of Submatrices Of The Pascal Matrix, Scott N. Kersey
Department of Mathematical Sciences Faculty Publications
In a previous paper, we derived necessary and sufficient conditions for the invertibility of square submatrices of the Pascal upper triangular matrix. To do so, we established a connection with the two-point Birkhoff interpolation problem. In this paper, we extend this result by deriving a formula for the rank of submatrices of the Pascal matrix. Our formula works for both square and non-square submatrices. We also provide bases for the row and column spaces of these submatrices. Further, we apply our result to one-point lacunary polynomial approximation.
Faith Connections In The Math Classroom, Valorie L. Zonnefeld, Ryan G. Zonnefeld
Faith Connections In The Math Classroom, Valorie L. Zonnefeld, Ryan G. Zonnefeld
Faculty Work Comprehensive List
Looking for ways to make faith connections in your math classroom? The Zonnefelds present a framework, developed in collaboration with local teachers, that synthesizes faith connections, the TfT framework, and Common Core standards.
Standards-Based Assessment In A Developmental Math Course, Valorie L. Zonnefeld, Michal Huizenga, Aaron Van Beek, Kate Van Weelden
Standards-Based Assessment In A Developmental Math Course, Valorie L. Zonnefeld, Michal Huizenga, Aaron Van Beek, Kate Van Weelden
Faculty Work Comprehensive List
Learn why we decided to try standards-based instruction in an undergraduate, developmental algebra course and what we learned in the process.
A Generalized Class Of Exponentiated Modified Weibull Distribution With Applications, Shusen Pu, Broderick O. Oluyede, Yuqi Qui, Daniel F. Linder
A Generalized Class Of Exponentiated Modified Weibull Distribution With Applications, Shusen Pu, Broderick O. Oluyede, Yuqi Qui, Daniel F. Linder
Department of Mathematical Sciences Faculty Publications
In this paper, a new class of five parameter gamma-exponentiated or generalized modified Weibull (GEMW) distribution which includes exponential, Rayleigh, Weibull, modified Weibull, exponentiated Weibull, exponentiated exponential, exponentiated modified Weibull, exponentiated modified exponential, gamma-exponentiated exponential, gamma-exponentiated Rayleigh, gamma-modified Weibull, gamma-modified exponential, gamma-Weibull, gamma-Rayleigh and gamma-exponential distributions as special cases is proposed and studied. Mathematical properties of this new class of distributions including moments, mean deviations, Bonferroni and Lorenz curves, distribution of order statistics and Renyi entropy are presented. Maximum likelihood estimation technique is used to estimate the model parameters and applications to real data sets presented in order to illustrate …
Equivariant Formality Of Transversely Symplectic Foliations And Frobenius Manifolds, Yi Lin, Xiangdong Yang
Equivariant Formality Of Transversely Symplectic Foliations And Frobenius Manifolds, Yi Lin, Xiangdong Yang
Department of Mathematical Sciences Faculty Publications
Consider the Hamiltonian action of a compact connected Lie group on a transversely symplectic foliation whose basic cohomology satisfies the Hard Lefschetz property. We establish an equivariant formality theorem and an equivariant symplectic dδ-lemma in this setting. As an application, we show that there exists a natural Frobenius manifold structure on the equivariant basic cohomology of the given foliation. In particular, this result provides a class of new examples of dGBV-algebras whose cohomology carries a Frobenius manifold structure.
Lefschetz Contact Manifolds And Odd Dimensional Symplectic Geometry, Yi Lin
Lefschetz Contact Manifolds And Odd Dimensional Symplectic Geometry, Yi Lin
Department of Mathematical Sciences Faculty Publications
In the literature, there are two different versions of Hard Lefschetz theorems for a compact Sasakian manifold. The first version, due to Kacimi-Alaoui, asserts that the basic cohomology groups of a compact Sasakian manifold satisfies the transverse Lefschetz property. The second version, established far more recently by Cappelletti-Montano, De Nicola, and Yudin, holds for the De Rham cohomology groups of a compact Sasakian manifold. In the current paper, using the formalism of odd dimensional symplectic geometry, we prove a Hard Lefschetz theorem for compact K-contact manifolds, which implies immediately that the two existing versions of Hard Lefschetz theorems are mathematically …
The Log-Logistic Weibull Distribution With Applications To Lifetime Data, Broderick O. Oluyede, Susan Foya, Gayan Warahena-Liyanage, Shujiao Huang
The Log-Logistic Weibull Distribution With Applications To Lifetime Data, Broderick O. Oluyede, Susan Foya, Gayan Warahena-Liyanage, Shujiao Huang
Department of Mathematical Sciences Faculty Publications
In this paper, a new generalized distribution called the log-logistic Weibull (LLoGW) distribution is developed and presented. This distribution contain the log-logistic Rayleigh (LLoGR), log-logistic exponential (LLoGE) and log-logistic (LLoG) distributions as special cases. The structural properties of the distribution including the hazard function, reverse hazard function, quantile function, probability weighted moments, moments, conditional moments, mean deviations, Bonferroni and Lorenz curves, distribution of order statistics, L-moments and Renyi entropy are derived. Method of maximum likelihood is used to estimate the parameters of this new distribution. A simulation study to examine the bias, mean square error of the maximum likelihood estimators …
Stabilizing The Lorenz Flows Using A Closed Loop Quotient Controller, James P. Braselton, Yan Wu
Stabilizing The Lorenz Flows Using A Closed Loop Quotient Controller, James P. Braselton, Yan Wu
Department of Mathematical Sciences Faculty Publications
In this study, we introduce a closed loop quotient controller into the three-dimensional Lorenz system. We then compute the equilibrium points and analyze their local stability. We use several examples to illustrate how cross-sections of the basins of attraction for the equilibrium points look for various parameter values. We then provided numerical evidence that with the controller, the controlled Lorenz system cannot exhibit chaos if the equilibrium points are locally stable.
On The Expression Of Higher Mathematics In American Sign Language, John Tabak
On The Expression Of Higher Mathematics In American Sign Language, John Tabak
Journal of Interpretation
Abstract
The grammar and vocabulary of higher mathematics are different from the grammar and vocabulary of conversational English and conversational American Sign Language (ASL). Consequently, mathematical language presents interpreters with a unique set of challenges. This article characterizes those aspects of mathematical grammar that are peculiar to the subject. (A discussion of mathematical vocabulary and its expression in ASL can be found elsewhere (Tabak, 2014).) An increased awareness of the grammar of mathematical language will prove useful to those interpreters for the deaf and deaf mathematics professionals seeking to express higher mathematics in ASL.
In this article one will, for …
Invertibility Of Submatrices Of The Pascal Matrix And Birkhoff Interpolation, Scott N. Kersey
Invertibility Of Submatrices Of The Pascal Matrix And Birkhoff Interpolation, Scott N. Kersey
Department of Mathematical Sciences Faculty Publications
The infinite upper triangular Pascal matrix is T = [( j )i] for 0 ≤ i, j. It is easy to see that any leading principle square submatrix is triangular with determinant 1, hence invertible. In this paper, we investigate the invertibility of arbitrary square submatrices Tr, c comprised of rows r = [r0, … , rm ] and columns c = c0 , … , cm[] of T. We show that Tr, c is invertible r ≤ c i.e., ri ≤ ci for i = 0, …, m(), or equivalently, iff all diagonal entries are nonzero. To prove this …
Fast Cycles Detecting In Non-Linear Discrete Systems, Dmitriy Dmitrishin, Elena Franzheva, Alexander M. Stokolos
Fast Cycles Detecting In Non-Linear Discrete Systems, Dmitriy Dmitrishin, Elena Franzheva, Alexander M. Stokolos
Department of Mathematical Sciences Faculty Publications
In the paper below we consider a problem of stabilization of a priori unknown unstable periodic orbits in non-linear autonomous discrete dynamical systems. We suggest a generalization of a non-linear DFC scheme to improve the rate of detecting T-cycles. Some numerical simulations are presented.
From Chaos To Order Through Mixing, Dmitriy Dmitrishin, I. M. Skrinnik, Alexander M. Stokolos
From Chaos To Order Through Mixing, Dmitriy Dmitrishin, I. M. Skrinnik, Alexander M. Stokolos
Department of Mathematical Sciences Faculty Publications
In this article we consider the possibility of controlling the dynamics of nonlinear discrete systems. A new method of control is by mixing states of the system (or the functions of these states) calculated on previous steps. This approach allows us to locally stabilize a priori unknown cycles of a given length. As a special case, we have a cycle stabilization using nonlinear feedback. Several examples are considered.
Freedom Through Inquiry, Francis Su
Freedom Through Inquiry, Francis Su
All HMC Faculty Publications and Research
I delivered this speech at the Inquiry‐Based Learning Forum & 19th Annual Legacy of R.L. Moore Conference on August 4, 2016. It is partly an homage to an influential teacher, partly an excuse to articulate what makes some styles of teaching so effective, and partly an excuse to talk about difficult issues facing our nation and our classrooms today.
Definition Of A Method For The Formulation Of Problems To Be Solved With High Performance Computing, Ramya Peruri
Definition Of A Method For The Formulation Of Problems To Be Solved With High Performance Computing, Ramya Peruri
Master of Science in Computer Science Theses
Computational power made available by current technology has been continuously increasing, however today’s problems are larger and more complex and demand even more computational power. Interest in computational problems has also been increasing and is an important research area in computer science. These complex problems are solved with computational models that use an underlying mathematical model and are solved using computer resources, simulation, and are run with High Performance Computing. For such computations, parallel computing has been employed to achieve high performance. This thesis identifies families of problems that can best be solved using modelling and implementation techniques of parallel …
Note On Vertex And Total Proper Connection Numbers, Emily C. Chizmar, Colton Magnant, Pouria Salehi Nowbandegani
Note On Vertex And Total Proper Connection Numbers, Emily C. Chizmar, Colton Magnant, Pouria Salehi Nowbandegani
Department of Mathematical Sciences Faculty Publications
This note introduces the vertex proper connection number of a graph and provides a relationship to the chromatic number of minimally connected subgraphs. Also a notion of total proper connection is introduced and a question is asked about a possible relationship between the total proper connection number and the vertex and edge proper connection numbers.
Stop Ruining Math! Reasons And Remedies For The Maladies Of Mathematics Education, Rachel M. Steinig
Stop Ruining Math! Reasons And Remedies For The Maladies Of Mathematics Education, Rachel M. Steinig
Journal of Humanistic Mathematics
Did you love math as a kid? Or was it ruined for you? Sadly, many people have had math ruined for them for various reasons. Some might say that it was because of not understanding what was going on, being bored in class, parental or societal pressure to achieve in math, not seeing a point in learning math, wrong amount of homework, grades, curriculum, physical concerns, mean teachers, or any number of things. This article delves into the many common reasons why math is ruined for so many kids, and offers solutions so that math can be enjoyable for everyone. …
Spatiotemporal Interpolation Methods For The Application Of Estimating Population Exposure To Fine Particulate Matter In The Contiguous U.S. And A Real-Time Web Application, Lixin Li, Xiaolu Zhou, Marc Kalo, Reinhard E. Piltner
Spatiotemporal Interpolation Methods For The Application Of Estimating Population Exposure To Fine Particulate Matter In The Contiguous U.S. And A Real-Time Web Application, Lixin Li, Xiaolu Zhou, Marc Kalo, Reinhard E. Piltner
Department of Mathematical Sciences Faculty Publications
Appropriate spatiotemporal interpolation is critical to the assessment of relationships between environmental exposures and health outcomes. A powerful assessment of human exposure to environmental agents would incorporate spatial and temporal dimensions simultaneously. This paper compares shape function (SF)-based and inverse distance weighting (IDW)-based spatiotemporal interpolation methods on a data set of PM2.5 data in the contiguous U.S. Particle pollution, also known as particulate matter (PM), is composed of microscopic solids or liquid droplets that are so small that they can get deep into the lungs and cause serious health problems. PM2.5 refers to particles with a mean aerodynamic …
Partial Differential Equations And Function Spaces, Shijun Zheng, Simone Secchi, Huoxiong Wu, Nguyen Cong Phuc
Partial Differential Equations And Function Spaces, Shijun Zheng, Simone Secchi, Huoxiong Wu, Nguyen Cong Phuc
Department of Mathematical Sciences Faculty Publications
It is well known that PDEs and the theory of function spaces have played a central role in the mathematical analysis of problems arising from mathematical physics, biology, and other branches of modern applied sciences. This special issue addresses the current advances in these two broad areas; in particular it focuses on the connections and interactions between them. We are happy that this issue has received the attention of active researchers with interesting and valuable contributions in the field. Topics cover areas from existence and nonexistence theorems for degenerate differential operators to multilinear fractional singular integral operators on weighted function …
Example Of An Order 16 Non Symplectic Action On A K3 Surface, Jimmy J. Dillies
Example Of An Order 16 Non Symplectic Action On A K3 Surface, Jimmy J. Dillies
Department of Mathematical Sciences Faculty Publications
We exhibit an example of a K3 surface of Picard rank 14 with a non-symplectic automorphism of order 16 which fixes a rational curve and 10 isolated points. This settles the existence problem for the last case of Al Tabbaa, Sarti and Taki's classification.