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Articles 1 - 30 of 144
Full-Text Articles in Mathematics
The Problems Of Contemporariness And Voice: Review Of Literacy & Mathematics: A Contemporary Approach To Quantitative Literacy By Jay P. Abramson And Matthew A. Isom (2005), Gizem Karaali
Pomona Faculty Publications and Research
The book under review covers the traditional content of a typical mathematical literacy text. After a brief overview of the book contents, the review then focuses on two specific challenges that QL textbooks have to meet: the timeliness of the contexts used and the subjective author voice that inevitably colors any contextualized discussion. Both issues noticeably arise in the text reviewed. Nonetheless instructors may find it a helpful resource.
Math Education: A Messy Problem, Gizem Karaali
Math Education: A Messy Problem, Gizem Karaali
Pomona Faculty Publications and Research
The current state of math education in America is certainly not ideal, writes Gizem Karaali, but mathematicians, researchers, policy makers and others are working on it -- and it is definitely a problem worth working on.
Collaboration And Creativity In Southern Califonia: An Offering, Gizem Karaali, Ami Radunskaya
Collaboration And Creativity In Southern Califonia: An Offering, Gizem Karaali, Ami Radunskaya
Pomona Faculty Publications and Research
WiMSoCal (Women in Math in Southern California) is a regional conference in its ninth incarnation. The conference is the result of the efforts of Professor Cymra Haskell (USC) to create a supportive local community for women mathematicians. At our first meeting in 2007, a confluence of Ami’s EDGE regional cluster and Cymra’s WISE group at USC, we socialized, got to know each other and brainstormed about what we, as a group, would like to see happen. It was clear that our younger colleagues wanted to meet as mathematicians, sharing intellectual ideas as well as anecdotes from the trenches.
The Power Of Two: Two Tips For Mathematicians, Gizem Karaali
The Power Of Two: Two Tips For Mathematicians, Gizem Karaali
Pomona Faculty Publications and Research
This post is about two great tips involving the number 2 that I learned along the way. They will perhaps not double your happiness or fortune, but I promise you that you will not regret it if you do decide to take them along for the ride.
Review: On Complex Symmetric Toeplitz Operators, Stephan Ramon Garcia
Review: On Complex Symmetric Toeplitz Operators, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.
Review: On Rank One Perturbations Of Complex Symmetric Operators, Stephan Ramon Garcia
Review: On Rank One Perturbations Of Complex Symmetric Operators, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.
Review: A C*-Algebra Approach To Complex Symmetric Operators, Stephan Ramon Garcia
Review: A C*-Algebra Approach To Complex Symmetric Operators, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.
Review: Transitivity And Bundle Shifts, Stephan Ramon Garcia
Review: Transitivity And Bundle Shifts, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.
On The Similarity Of Ab And Ba For Normal And Other Matrices, Stephan Ramon Garcia, David Sherman, Gary Weiss
On The Similarity Of Ab And Ba For Normal And Other Matrices, Stephan Ramon Garcia, David Sherman, Gary Weiss
Pomona Faculty Publications and Research
It is known that AB and BA are similar when A and B are Hermitian matrices. In this note we answer a question of F. Zhang by demonstrating that similarity can fail if A is Hermitian and B is normal. Perhaps surprisingly, similarity does hold when A is positive semidefinite and B is normal.
What's In A Name? A Critical Review Of Definitions Of Quantitative Literacy, Numeracy, And Quantitative Reasoning, Gizem Karaali, Edwin H Villafane Hernandez '18, Jeremy Alexander Taylor '18
What's In A Name? A Critical Review Of Definitions Of Quantitative Literacy, Numeracy, And Quantitative Reasoning, Gizem Karaali, Edwin H Villafane Hernandez '18, Jeremy Alexander Taylor '18
Pomona Faculty Publications and Research
This article aims to bring together various threads in the eclectic literature that make up the scholarship around the theme of Quantitative Literacy. In investigating the meanings of terms like "quantitative literacy," "quantitative reasoning," and "numeracy," we seek common ground, common themes, common goals and aspirations of a community of practitioners. A decade ago, these terms were relatively new in the public sphere; today policy makers and accrediting agencies are routinely inserting them into general education conversations. Having good, representative, and perhaps even compact and easily digestible definitions of these terms might come in handy in public relations contexts as …
Visual Properties Of Generalized Kloosterman Sums, Paula Burkhardt '16, Alice Zhuo-Yu Chan '14, Gabriel Currier '16, Stephan Ramon Garcia, Florian Luca, Hong Suh '16
Visual Properties Of Generalized Kloosterman Sums, Paula Burkhardt '16, Alice Zhuo-Yu Chan '14, Gabriel Currier '16, Stephan Ramon Garcia, Florian Luca, Hong Suh '16
Pomona Faculty Publications and Research
For a positive integer m and a subgroup A of the unit group (Z/mZ)x, the corresponding generalized Kloosterman sum is the function K(a, b, m, A) = ΣuEA e(au+bu-1/m). Unlike classical Kloosterman sums, which are real valued, generalized Kloosterman sums display a surprising array of visual features when their values are plotted in the complex plane. In a variety of instances, we identify the precise number-theoretic conditions that give rise to particular phenomena.
Lattices From Hermitian Function Fields, Albrecht Böttcher, Lenny Fukshansky, Stephan Ramon Garcia, Hiren Maharaj
Lattices From Hermitian Function Fields, Albrecht Böttcher, Lenny Fukshansky, Stephan Ramon Garcia, Hiren Maharaj
Pomona Faculty Publications and Research
We consider the well-known Rosenbloom-Tsfasman function field lattices in the special case of Hermitian function fields. We show that in this case the resulting lattices are generated by their minimal vectors, provide an estimate on the total number of minimal vectors, and derive properties of the automorphism groups of these lattices. Our study continues previous investigations of lattices coming from elliptic curves and finite Abelian groups. The lattices we are faced with here are more subtle than those considered previously, and the proofs of the main results require the replacement of the existing linear algebra approaches by deep results of …
Lattices From Tight Equiangular Frames, Albrecht Böttcher, Lenny Fukshansky, Stephan Ramon Garcia, Hiren Maharaj, Deanna Needell
Lattices From Tight Equiangular Frames, Albrecht Böttcher, Lenny Fukshansky, Stephan Ramon Garcia, Hiren Maharaj, Deanna Needell
Pomona Faculty Publications and Research
We consider the set of all linear combinations with integer coefficients of the vectors of a unit tight equiangular (k,n) frame and are interested in the question whether this set is a lattice, that is, a discrete additive subgroup of the k-dimensional Euclidean space. We show that this is not the case if the cosine of the angle of the frame is irrational. We also prove that the set is a lattice for n = k + 1 and that there are infinitely many k such that a lattice emerges for n = 2k …
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.
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.
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 …
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.
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!
Review: On Pairs Of Generalized And Hypergeneralized Projections In A Hilbert Space, Stephan Ramon Garcia
Review: On Pairs Of Generalized And Hypergeneralized Projections In A Hilbert Space, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.
A Mathematician's Villanelle, Gizem Karaali
A Mathematician's Villanelle, Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
Topological Complexity In Protein Structures, Erica Flapan, Gabriella Heller '14
Topological Complexity In Protein Structures, Erica Flapan, Gabriella Heller '14
Pomona Faculty Publications and Research
For DNA molecules, topological complexity occurs exclusively as the result of knotting or linking of the polynucleotide backbone. By contrast, while a few knots and links have been found within the polypeptide backbones of some protein structures, non-planarity can also result from the connectivity between a polypeptide chain and inter- and intra-chain linking via cofactors and disulfide bonds. In this article, we survey the known types of knots, links, and non-planar graphs in protein structures with and without including such bonds and cofactors. Then we present new examples of protein structures containing Möbius ladders and other non-planar graphs as a …
Permutation Invariant Lattices, Lenny Fukshansky, Stephan Ramon Garcia, Xun Sun
Permutation Invariant Lattices, Lenny Fukshansky, Stephan Ramon Garcia, Xun Sun
Pomona Faculty Publications and Research
We say that a Euclidean lattice in Rn is permutation invariant if its automorphism group has non-trivial intersection with the symmetric group Sn, i.e., if the lattice is closed under the action of some non-identity elements of Sn. Given a fixed element T E Sn, we study properties of the set of all lattices closed under the action of T: we call such lattices T-invariant. These lattices naturally generalize cyclic lattices introduced by Micciancio in [7,8], which we previously studied in [1]. Continuing our investigation, we discuss some basic properties of …
Toeplitz Determinants With Perturbations In The Corners, Albrecht Böttcher, Lenny Fukshansky, Stephan Ramon Garcia, Hiren Maharaj
Toeplitz Determinants With Perturbations In The Corners, Albrecht Böttcher, Lenny Fukshansky, Stephan Ramon Garcia, Hiren Maharaj
Pomona Faculty Publications and Research
This paper is devoted to exact and asymptotic formulas for the determinants of Toeplitz matrices with perturbations by blocks of fixed size in the four corners. If the norms of the inverses of the unperturbed matrices remain bounded as the matrix dimension goes to infinity, then standard perturbation theory yields asymptotic expressions for the perturbed determinants. This premise is not satisfied for matrices generated by so-called Fisher-Hartwig symbols. In that case we establish formulas for pure single Fisher-Hartwig singularities and for the Hermitian matrices induced by general Fisher-Hartwig symbols.
An Exhibition Of Exponential Sums: Visualizing Supercharacters, Paula Burkhardt '16, Gabriel Currier '16, Stephan Ramon Garcia, Mathieu De Langis '15, Bob Lutz '13, Hong Suh '16
An Exhibition Of Exponential Sums: Visualizing Supercharacters, Paula Burkhardt '16, Gabriel Currier '16, Stephan Ramon Garcia, Mathieu De Langis '15, Bob Lutz '13, Hong Suh '16
Pomona Faculty Publications and Research
We discuss a simple mathematical mechanism that produces a variety of striking images of great complexity and subtlety. We briefly explain this approach and present a selection of attractive images obtained using this technique.
Model Spaces: A Survey, Stephan Ramon Garcia, William T. Ross
Model Spaces: A Survey, Stephan Ramon Garcia, William T. Ross
Pomona Faculty Publications and Research
This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.
Review: Crystal Bases Of Q-Deformed Kac Modules Over The Quantum Superalgebras Uq(Gl(Mln)), Gizem Karaali
Review: Crystal Bases Of Q-Deformed Kac Modules Over The Quantum Superalgebras Uq(Gl(Mln)), Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
Math Talk: Preparing Your Conference Presentation, Gizem Karaali
Math Talk: Preparing Your Conference Presentation, Gizem Karaali
Pomona Faculty Publications and Research
If you are a typical reader of this blog, then you recently wrapped up your finals week and then dutifully made a summer plan. And then came the summer. Your plan may have involved working on a manuscript, preparing for a qualifying exam or a new course coming up in the fall, drafting a grant proposal, learning a new language (human or machine), eating kale in four different forms, and perhaps some fun times under the sun. Some, like me, also made plans to travel to conferences and give talks. Gearing up to get ready for my first conference of …
Four Quotient Set Gems, Stephan Ramon Garcia, Michael Someck '14, Bob Lutz '13, Bryan Brown '15, Michael Dairyko '13
Four Quotient Set Gems, Stephan Ramon Garcia, Michael Someck '14, Bob Lutz '13, Bryan Brown '15, Michael Dairyko '13
Pomona Faculty Publications and Research
Our aim in this note is to present four remarkable facts about quotient sets. These observations seem to have been overlooked by the MONTHLY, despite its intense coverage of quotient sets over the years.
Why You Need A Summer Plan, Gizem Karaali
Why You Need A Summer Plan, Gizem Karaali
Pomona Faculty Publications and Research
In the last decade, for many times, I have tasted first-hand the end-of-summer blues I described above. I have spent many early spring months dreaming of all that I would be doing when the summer arrives, only to realize that it was already September and I had not much to show for for the months in between. I have also observed many of my peers going through similar things, and I just assumed for years that this was how it had to be. But then some time in the middle of the tenure track, I decided to try approaching my …