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Articles 1021 - 1050 of 2640
Full-Text Articles in Physical Sciences and Mathematics
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!
Direct, Biomimetic Synthesis Of (+)-Artemone Via A Stereoselective, Organocatalytic Cyclization, Eric D. Nacsa, Brian C. Fielder, Shannon P. Wetzler, Veerasak Srisuknimit, Jonathan P. Litz, Mary J. Van Vleet, Kim Quach, David A. Vosburg
Direct, Biomimetic Synthesis Of (+)-Artemone Via A Stereoselective, Organocatalytic Cyclization, Eric D. Nacsa, Brian C. Fielder, Shannon P. Wetzler, Veerasak Srisuknimit, Jonathan P. Litz, Mary J. Van Vleet, Kim Quach, David A. Vosburg
All HMC Faculty Publications and Research
We present a four-step synthesis of (+)-artemone from (–)- linalool, featuring iminium organocatalysis of a doubly diastereoselective conjugate addition reaction. The strategy follows a proposed biosynthetic pathway, rapidly generates stereochemical complexity, uses no protecting groups, and minimizes redox manipulations.
Counting On R-Fibonacci Numbers, Arthur Benjamin, Curtis Heberle
Counting On R-Fibonacci Numbers, Arthur Benjamin, Curtis Heberle
All HMC Faculty Publications and Research
We prove the r-Fibonacci identities of Howard and Cooper using a combinatorial tiling approach.
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.
The Cantor Trilogy, Harun Šiljak
The Cantor Trilogy, Harun Šiljak
Journal of Humanistic Mathematics
The Cantor trilogy is a mathematical dystopia featuring JHM as an important part of that world... at least to humans.
My Finite Field, Matthew Schroeder
My Finite Field, Matthew Schroeder
Journal of Humanistic Mathematics
A love poem written in the language of mathematics.
Prisoner's Dilemma, Raymond N. Greenwell
Prisoner's Dilemma, Raymond N. Greenwell
Journal of Humanistic Mathematics
No abstract provided.
Book Review: Love And Math: The Heart Of Hidden Reality By Edward Frenkel, Emily R. Grosholz
Book Review: Love And Math: The Heart Of Hidden Reality By Edward Frenkel, Emily R. Grosholz
Journal of Humanistic Mathematics
This review traces Edward Frenkel’s attempt to convey the excitement of mathematical research to a popular audience. In his expositions and explanations of his own research program, he shows how processes of mathematical discovery depend on the juxtaposition of various iconic and symbolic modes of representation as disparate fields of research are brought together in the service of problem solving. And he shows how crucial the encouragement of various older mathematicians was to his own development, as they guided his choice of problems, and served as inspiration.
Abscissas And Ordinates, David Pierce
Abscissas And Ordinates, David Pierce
Journal of Humanistic Mathematics
In the manner of Apollonius of Perga, but hardly any modern book, we investigate conic sections as such. We thus discover why Apollonius calls a conic section a parabola, an hyperbola, or an ellipse; and we discover the meanings of the terms abscissa and ordinate. In an education that is liberating and not simply indoctrinating, the student of mathematics will learn these things.
The Symbolic And Mathematical Influence Of Diophantus's Arithmetica, Cyrus Hettle
The Symbolic And Mathematical Influence Of Diophantus's Arithmetica, Cyrus Hettle
Journal of Humanistic Mathematics
Though it was written in Greek in a center of ancient Greek learning, Diophantus's Arithmetica is a curious synthesis of Greek, Egyptian, and Mesopotamian mathematics. It was not only one of the first purely number-theoretic and algebraic texts, but the first to use the blend of rhetorical and symbolic exposition known as syncopated mathematics. The text was influential in the development of Arabic algebra and European number theory and notation, and its development of the theory of indeterminate, or Diophantine, equations inspired modern work in both abstract algebra and computer science. We present, in this article, a selection of problems …
Love Games: A Game-Theory Approach To Compatibility, Kerstin Bever, Julie Rowlett
Love Games: A Game-Theory Approach To Compatibility, Kerstin Bever, Julie Rowlett
Journal of Humanistic Mathematics
In this note, we present a compatibility test with a rigorous mathematical foundation in game theory. The test must be taken separately by both partners, making it difficult for either partner alone to control the outcome. To introduce basic notions of game theory we investigate a scene from the film "A Beautiful Mind" based on John Nash's life and Nobel-prize-winning theorem. We recall this result and reveal the mathematics behind our test. Readers may customize and modify the test for more accurate results or to evaluate interpersonal relationships in other settings, not only romantic. Finally, we apply Dyson's and Press's …
On The Persistence And Attrition Of Women In Mathematics, Katrina Piatek-Jimenez
On The Persistence And Attrition Of Women In Mathematics, Katrina Piatek-Jimenez
Journal of Humanistic Mathematics
The purpose of this study was to investigate what motivates women to choose mathematics as an undergraduate major and to further explore what shapes their future career goals, paying particular attention to their undergraduate experiences and their perceptions of the role of gender in these decisions. A series of semi-structured, individual interviews were conducted with twelve undergraduate women mathematics majors who were attending either a large public university or a small liberal arts college. This study found that strong mathematical identities and enjoyment of mathematics heavily influenced their decisions to major in mathematics. At the career selection stage, these women …
Probing The Inverted Classroom: A Study Of Teaching And Learning Outcomes In Engineering And Mathematics, Nancy K. Lape, Rachel Levy, Darryl Yong
Probing The Inverted Classroom: A Study Of Teaching And Learning Outcomes In Engineering And Mathematics, Nancy K. Lape, Rachel Levy, Darryl Yong
All HMC Faculty Publications and Research
Flipped classrooms have started to become commonplace on university campuses. Despite the growing number of flipped courses, however, quantitative information on their effectiveness remains sparse. Active learning is a mode of instruction that focuses the responsibility of learning on learners. Multiple studies have shown that active learning leads to better student outcomes. Given that instructors in flipped classrooms are generally able to create more opportunities for students to apply or practice course material, we hypothesized that students in a flipped classroom would exhibit more learning compared to students in an unflipped class. This case study describes our research comparing …
Acceptance-Rejection Sampling With Hierarchical Models, Christian A. Ayala
Acceptance-Rejection Sampling With Hierarchical Models, Christian A. Ayala
CMC Senior Theses
Hierarchical models provide a flexible way of modeling complex behavior. However, the complicated interdependencies among the parameters in the hierarchy make training such models difficult. MCMC methods have been widely used for this purpose, but can often only approximate the necessary distributions. Acceptance-rejection sampling allows for perfect simulation from these often unnormalized distributions by drawing from another distribution over the same support. The efficacy of acceptance-rejection sampling is explored through application to a small dataset which has been widely used for evaluating different methods for inference on hierarchical models. A particular algorithm is developed to draw variates from the posterior …