Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Discipline
-
- Mathematics (52)
- Arts and Humanities (12)
- Environmental Sciences (12)
- Education (9)
- Social and Behavioral Sciences (9)
-
- Science and Mathematics Education (8)
- Other Mathematics (7)
- Discrete Mathematics and Combinatorics (5)
- Natural Resources Management and Policy (5)
- Sustainability (5)
- Algebra (4)
- Applied Mathematics (4)
- Chemistry (4)
- Creative Writing (4)
- Geometry and Topology (4)
- Water Resource Management (4)
- Art Education (3)
- Computer Sciences (3)
- Economics (3)
- Environmental Education (3)
- Environmental Indicators and Impact Assessment (3)
- Higher Education (3)
- Life Sciences (3)
- Number Theory (3)
- Poetry (3)
- Statistics and Probability (3)
- Architecture (2)
- Art and Design (2)
- Econometrics (2)
- Keyword
-
- Compressive sensing (3)
- Mathematics (3)
- 05A15 Exact enumeration problems (2)
- Archimedes (2)
- Automorphism groups of lattices (2)
-
- Computer Science (2)
- Counting (2)
- Cyclic lattices (2)
- Elliptic curve (2)
- Fiction (2)
- Hilbert space (2)
- Information theory (2)
- Music (2)
- Number theory (2)
- Numerical analysis (2)
- Sustainability (2)
- Toeplitz determinant (2)
- Water (2)
- Well-rounded lattices (2)
- 05-02 Combinatorics Research exposition (1)
- 05B45 Tessellation and tiling problems (1)
- 1) (1)
- 3-D Modeling (1)
- 3D printing (1)
- 68P25 Data encryption (1)
- 94A60 Cryptography (1)
- Abelian groups (1)
- Absolute Diophantine results (1)
- Active Learning (1)
- Activism (1)
- Publication
- Publication Type
Articles 1 - 30 of 85
Full-Text Articles in Physical Sciences and Mathematics
Review: A Short Introduction To De Branges-Rovnyak Spaces, Stephan Ramon Garcia
Review: A Short Introduction To De Branges-Rovnyak Spaces, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.
A Note On Practical Approximate Projection Schemes In Signal Space Methods, Xiaoyi Gu, Deanna Needell, Shenyinying Tu
A Note On Practical Approximate Projection Schemes In Signal Space Methods, Xiaoyi Gu, Deanna Needell, Shenyinying Tu
CMC Faculty Publications and Research
Compressive sensing (CS) is a new technology which allows the acquisition of signals directly in compressed form, using far fewer measurements than traditional theory dictates. Recently, many socalled signal space methods have been developed to extend this body of work to signals sparse in arbitrary dictionaries rather than orthonormal bases. In doing so, CS can be utilized in a much broader array of practical settings. Often, such approaches often rely on the ability to optimally project a signal onto a small number of dictionary atoms. Such optimal, or even approximate, projections have been difficult to derive theoretically. Nonetheless, it has …
Convergence Properties Of The Randomized Extended Gauss-Seidel And Kaczmarz Methods, Anna Ma, Deanna Needell, Aaditya Ramdas
Convergence Properties Of The Randomized Extended Gauss-Seidel And Kaczmarz Methods, Anna Ma, Deanna Needell, Aaditya Ramdas
CMC Faculty Publications and Research
The Kaczmarz and Gauss-Seidel methods both solve a linear system Xβ=y by iteratively refining the solution estimate. Recent interest in these methods has been sparked by a proof of Strohmer and Vershynin which shows the randomized Kaczmarz method converges linearly in expectation to the solution. Lewis and Leventhal then proved a similar result for the randomized Gauss-Seidel algorithm. However, the behavior of both methods depends heavily on whether the system is under or overdetermined, and whether it is consistent or not. Here we provide a unified theory of both methods, their variants for these different settings, and draw connections between …
Review: The Classical Hom-Yang-Baxter Equation And Hom-Lie Bialgebras, Gizem Karaali
Review: The Classical Hom-Yang-Baxter Equation And Hom-Lie Bialgebras, Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
Small Molecule Inhibitor Design For Anaplastic Lymphoma Kinase Inhibition, Theodore D. Hansel, David J. Grabovsky
Small Molecule Inhibitor Design For Anaplastic Lymphoma Kinase Inhibition, Theodore D. Hansel, David J. Grabovsky
Interface Compendium of Student Work
The Anaplastic Lymphoma Kinase (ALK) gene has been linked to tumorigenesis in a number of human cancers, including anaplastic large cell lymphoma (ALCL) and neuroblastoma. While ALK mutations in ALCL and many other cancers occur as a result of gene fusions with wild type kinase domains, those in neuroblastoma stem from single nucleotide polymorphisms (SNPs) in the kinase domain. These lead to autophosphorylation and constitutive signaling by ALK for cell growth and division, ultimately causing cancer. Crizotinib, an ATP-competitive ALK inhibitor, has proven to be an effective inhibitor of both ALKWT and ALKMutant kinase domains, and is in the middle …
On Montel And Montel–Popoviciu Theorems In Several Variables, Asuman Güven Aksoy, Jose M. Almira
On Montel And Montel–Popoviciu Theorems In Several Variables, Asuman Güven Aksoy, Jose M. Almira
CMC Faculty Publications and Research
We present an elementary proof of a general version of Montel’s theorem in several variables which is based on the use of tensor product polynomial interpolation. We also prove a Montel-Popoviciu’s type theorem for functions f:Rd→Rf:Rd→R for d > 1. Furthermore, our proof of this result is also valid for the case d = 1, differing in several points from Popoviciu’s original proof. Finally, we demonstrate that our results are optimal.
L.A. River Project, Erin Payne
L.A. River Project, Erin Payne
The STEAM Journal
A field note that reflected the artists' experience of the city and the making of art through an activity at the L.A. River.
Unseen Minutia, Sara Kapadia
Art, Math, And Physics; All About For, Chris Brownell, Steve Pauls
Art, Math, And Physics; All About For, Chris Brownell, Steve Pauls
The STEAM Journal
Anish Kapoor’s public sculpture “Cloud Gate” and Frame of Reference.
Relationships, Michael Goodman
The Threshold Of Hearing, Mike Wereski
Ecoscience + Art Initiative: Designing A New Paradigm For College Education, Scholarship, And Service, Changwoo Ahn
Ecoscience + Art Initiative: Designing A New Paradigm For College Education, Scholarship, And Service, Changwoo Ahn
The STEAM Journal
The paper presents a new initiative, EcoScience + Art, which blooms at George Mason University. The creator explains the background, history, and recent activities of the initiative, and also introduces an on-going special project called “The Rain Project”, a student participatory project to design, construct, and monitor a green infrastructure (i.e., floating wetland) for sustainable stormwater management on campus. The special project is geared to design and present a new paradigm to integrate college education, scholarship, and service. The relevance of the initiative and the special project to STEAM education is discussed.
Putting The Team In Steam: The Art Of Robot Making, Teresa Walker, David Thompson
Putting The Team In Steam: The Art Of Robot Making, Teresa Walker, David Thompson
The STEAM Journal
What began as a life partnership has evolved into an early learning STEAM team. Artist, David Thompson, uses science, technology, engineering and math, on a daily basis, to create robots and much more. Teresa Day Walker is an assistant professor of early childhood education. Through necessity they discovered their combined talents could be used to promote STEAM in early childhood. David and Teri teamed up to provide a nearly impromptu robot making demonstration for 100 kindergarten students. After reading their co-authored book, Robot Hide and Seek, both, clay based and 3-D modeled images were used to generate interest and …
Guidelines For Good Mathematical Writing, Francis Su
Guidelines For Good Mathematical Writing, Francis Su
All HMC Faculty Publications and Research
Communicating mathematics well is an important part of doing mathematics. Many of us know from writing papers or giving talks that communicating effectively not only serves our audience but also clarifies and structures our own thinking. There is an art and elegance to good writing that every writer should strive for. And writing, as a work of art, can bring a person great personal satisfaction.
Within the MAA, we value exposition and mathematical communication. In this column, I’m sharing the advice I give my students to help them write well. There are more extensive treatments (e.g., see Paul Halmos’s How …
Extended Book Review: Really Big Numbers, By Richard Evan Schwartz; The Boy Who Loved Math: The Improbable Life Of Paul Erdös, By Deborah Heiligman; The Short Seller, By Elissa Brent Weissman, Gizem Karaali
Pomona Faculty Publications and Research
The genre of math lit for children is not huge, but it is growing. My kid loves the early reader books by my friend and colleague Julie Glass (A Dollar for Penny (1998), The Fly On the Ceiling (2000)). I found Izolda Fotiyeva’s Math with Mom (2003) too late for my daughter but will definitely read it with my son. For a neat twist on the traditional alphabet book, I recommend The Technical Alphabet (2014) by the engineer sisters Lavanya and Melissa Jawaharlal. More recently a colleague introduced me to Laura Overdeck’s Bedtime Math series; these will soon join …
The Topology Of Absence, Nora E. Culik
The Topology Of Absence, Nora E. Culik
Journal of Humanistic Mathematics
“The Topology of Absence” literalizes triangulations, hyperbeloids, and the concept of the limit in the story of “locating” a lost mother. This story, like “The Physicist’s Basement” in the July 2014 issue, is part of a series that worries about competing notions of mathematics, i.e., mathematics as some sort of disembodied configuration or as emergent in the material reality of human life.
Music And Mathematics, Robert J. Boucher
Music And Mathematics, Robert J. Boucher
Journal of Humanistic Mathematics
Mathematics has forever been.
Geometry Of Life, Janice Dykacz
Geometry Of Life, Janice Dykacz
Journal of Humanistic Mathematics
Relationships in life can be expressed through geometric curves
Mathematical Double Dactyls, Tristan Miller
Mathematical Double Dactyls, Tristan Miller
Journal of Humanistic Mathematics
No abstract provided.
Robin Chapman On (Her) Mathematics Education, Robin Chapman
Robin Chapman On (Her) Mathematics Education, Robin Chapman
Journal of Humanistic Mathematics
No abstract provided.
On Mathematicians' Eccentricity, Robert Haas
On Mathematicians' Eccentricity, Robert Haas
Journal of Humanistic Mathematics
Eccentricity, though not inevitable, happens. Lightheartedly classifying examples, the author traces it back to factors, like creativity and absorption, essential to mathematical success, and recommends an attitude of amused tolerance towards others as well as to ourselves.
A System Of Equations: Mathematics Lessons In Classical Literature, Valery F. Ochkov, Andreas Look
A System Of Equations: Mathematics Lessons In Classical Literature, Valery F. Ochkov, Andreas Look
Journal of Humanistic Mathematics
The aim of this paper is to showcase a handful of mathematical challenges found in classical literature and to offer possible ways of integrating classical literature in mathematics lessons. We analyze works from a range of authors such as Jules Verne, Anton Chekhov, and others. We also propose ideas for further tasks. Most of the problems can be restated in terms of simple mathematical equations, and they can often be solved without a computer. Nevertheless, we use the computer program Mathcad to solve the problems and to illustrate the solutions to enhance the reader’s mathematical experience.
Mathematics: What Has It To Do With Me?, Man Keung Siu
Mathematics: What Has It To Do With Me?, Man Keung Siu
Journal of Humanistic Mathematics
Mathematics teachers must have encountered the following question raised by students: “What is the use of mathematics?” Although the value of mathematics is not to be determined solely by its applications, to the general public this is a more important and more convincing facet of the subject. Nevertheless, this also brings up the corresponding query: is this subject being properly used? Does mathematics play a role in moral education?
On Similarities And Differences Between Proving And Problem Solving, Milos Savic
On Similarities And Differences Between Proving And Problem Solving, Milos Savic
Journal of Humanistic Mathematics
A link between proving and problem solving has been established in the literature [5, 21]. In this paper, I discuss similarities and differences between proving and problem solving using the Multidimensional Problem-Solving Framework created by Carlson and Bloom [2] with Livescribepen data from a previous study [13]. I focus on two participants’ proving processes: Dr. G, a topologist, and L, a mathematics graduate student. Many similarities between the framework and the proving processes of Dr. G and L were revealed, but there were also some differences. In addition, there were some distinct differences between the proving actions of the …
Counting The Angels And Devils In Escher's Circle Limit Iv, John Choi, Nicholas Pippenger
Counting The Angels And Devils In Escher's Circle Limit Iv, John Choi, Nicholas Pippenger
Journal of Humanistic Mathematics
We derive the rational generating function that enumerates the angels and devils in M. C. Escher's Circle Limit IV according to their combinatorial distance from the six creatures whose feet meet at the center of the disk. This result shows that the base of the exponential rate of growth is 1.582... (the largest root of the polynomial 1 - z^2 - 2z^3 - z^4 + z^6).
Rows Vs. Columns: Randomized Kaczmarz Or Gauss-Seidel For Ridge Regression, Ahmed Hefny, Deanna Needell, Aaditya Ramdas
Rows Vs. Columns: Randomized Kaczmarz Or Gauss-Seidel For Ridge Regression, Ahmed Hefny, Deanna Needell, Aaditya Ramdas
CMC Faculty Publications and Research
The Kaczmarz and Gauss-Seidel methods aim to solve a linear m × n system Xβ = y by iteratively refining the solution estimate; the former uses random rows of X to update β given the corresponding equations and the latter uses random columns of X to update corresponding coordinates in β. Interest in these methods was recently revitalized by a proof of Strohmer and Vershynin showing linear convergence in expectation for a randomized Kaczmarz method variant (RK), and a similar result for the randomized Gauss-Seidel algorithm (RGS) was later proved by Lewis and Leventhal. Recent work unified the analysis of …
Review: Nevanlinna-Pick Spaces With Hyponormal Multiplication Operators, Stephan Ramon Garcia
Review: Nevanlinna-Pick Spaces With Hyponormal Multiplication Operators, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.
Review: On Symplectic Self-Adjointness Of Hamiltonian Operator Matrices, Stephan Ramon Garcia
Review: On Symplectic Self-Adjointness Of Hamiltonian Operator Matrices, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.
To The Mathematical Beach, Francis Su
To The Mathematical Beach, Francis Su
All HMC Faculty Publications and Research
What context am I missing that hinders my connection with my students? How often do I take the time to get to know their backgrounds? What are the primary experiences that shaped them, and do those present obstacles or opportunities for learning? And in what ways does the mathematical beach say “open to all” but still feel restricted?
These questions appear unrelated to mathematics, but if we ignore their effects, some of our students will not flourish.
Summer Cleaning: (Digital) Organizing Basics For Mathematicians, Gizem Karaali
Summer Cleaning: (Digital) Organizing Basics For Mathematicians, Gizem Karaali
Pomona Faculty Publications and Research
At the beginning of last summer I wrote about a neat trick to make your summer a productive one. And I heard from some of you who took me up on this suggestion; it seems that this actually works for many people! So, this year, for those who are willing to experiment with new ideas, I have another summer recommendation: Let us clean!