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Articles 121 - 150 of 2640
Full-Text Articles in Physical Sciences and Mathematics
Synthesis Of 2-Arylpyridines By The Suzuki–Miyaura Cross-Coupling Of Pyfluor With Hetero (Aryl) Boronic Acids And Esters, Juan Rueda-Espinosa, Dewni Ramanayake, Nicholas Ball, Jennifer A. Love
Synthesis Of 2-Arylpyridines By The Suzuki–Miyaura Cross-Coupling Of Pyfluor With Hetero (Aryl) Boronic Acids And Esters, Juan Rueda-Espinosa, Dewni Ramanayake, Nicholas Ball, Jennifer A. Love
Pomona Faculty Publications and Research
The Suzuki–Miyaura cross-coupling of pyridine-2-sulfonyl fluoride (PyFluor) with hetero(aryl) boronic acids and pinacol boronic esters is reported. The reactions can be performed using Pd(dppf)Cl2 as the catalyst, at temperatures between 65 and 100 °C and in the presence of water and oxygen. This transformation generates 2-arylpyridines in modest to good yields (5%–89%).
Undetermined Coefficients With Hyperbolic Sines And Cosines, Laurie A. Florio, George L. Fischer
Undetermined Coefficients With Hyperbolic Sines And Cosines, Laurie A. Florio, George L. Fischer
CODEE Journal
The method of undetermined coefficients is commonly applied to solve linear, constant coefficient, non-homogeneous ordinary differential equations when the forcing function is from a selected class of functions. Often the hyperbolic sine and cosine functions are not explicitly included in this list of functions. Through a set of guided examples, this work argues that the hyperbolic sine and cosine ought to be included in the select class of functions. Careful explanation is provided for the necessary treatment of the cases where the argument of the hyperbolic sine and/or cosine functions matches one or both of the roots of the characteristic …
Cookie(X) = 1/2, Lawrence M. Lesser
Cookie(X) = 1/2, Lawrence M. Lesser
Journal of Humanistic Mathematics
This poem applies the concept of expected value, denoted E(X), to the context of any limited resources two parties desire. Usually, "you divide, I choose" keeps pieces equal enough to preempt charges of unfairness. But if one piece is much larger, many distrust the unbiased (in expected value) process of a coin flip giving each person the same chance at the bigger piece and the same cookie amount on average: E(X) = (1/2)p + (1/2)(1-p) = 1/2
Ahab's Mercy, David Sheskin
Ahab's Mercy, David Sheskin
Journal of Humanistic Mathematics
A tale in which Captain Ahab and his chief mate Starbuck confront a classic problem in probability theory: the Monty Hall Problem.
Zeno Of Elea: A Dichotomy, Joseph Chaney
Zeno Of Elea: A Dichotomy, Joseph Chaney
Journal of Humanistic Mathematics
This two-part poem interprets Zeno's paradoxes as dimensions of a paradoxical view of reality.
I Am A Math Professor, Cacey L. Wells
I Am A Math Professor, Cacey L. Wells
Journal of Humanistic Mathematics
Original poem depicting the life of a math professor.
Elephant In The Room, Sabrina Sixta
Elephant In The Room, Sabrina Sixta
Journal of Humanistic Mathematics
This poem tries to express the difficulty of staying focused on one's research when there is so much turmoil in the world.
Infinity, Holly Wilson
Ultrafilters, Klaas Pieter Hart
Ultrafilters, Klaas Pieter Hart
Journal of Humanistic Mathematics
5-7-5 musings on ultrafilters.
Her X'S And Y'S: Limericks About Women Mathematicians, Marion D. Cohen
Her X'S And Y'S: Limericks About Women Mathematicians, Marion D. Cohen
Journal of Humanistic Mathematics
This poetry folder is just what its title says, limericks about women mathematicians. A few of them I’ve known personally, most not. There are, of course, many many many other women mathematicians; even though I write limericks prolifically, I could never finish writing about them all!
Towards Ethical Ai: Mathematics Influences Human Behavior, Dioneia M. Monte-Serrat, Carlo Cattani
Towards Ethical Ai: Mathematics Influences Human Behavior, Dioneia M. Monte-Serrat, Carlo Cattani
Journal of Humanistic Mathematics
Mathematics plays an important role in the linguistic structure of artificial in- telligence (AI). We describe the linguistic process as a unique structure present both in human cognition and in cognitive computing. The close relationship with both AI and human cognition is due to this unique structure, which paves the way for AI to interfere with the behavior of those who interact with it. We highlight the role of mathematicians in designing algorithms—the core of the AI linguistic process—and in defining steps and instructions for AI. Because al- gorithms, through AI, interfere with the thought of those who interact with …
May Graduation, Samuel Coskey
May Graduation, Samuel Coskey
Journal of Humanistic Mathematics
Here I narrate the story of the last few days of my graduate program in mathematics. After the completion of the thesis and the delivery of the defense, several twists and turns await in the hours and even minutes before the last deadline.
Beauty Of Life In Dynamical Systems: Philosophical Musings And Resources For Students, Soumya Banerjee, Joyeeta Ghose, Tarakeswar Banerjee, Kalyani Banerjee
Beauty Of Life In Dynamical Systems: Philosophical Musings And Resources For Students, Soumya Banerjee, Joyeeta Ghose, Tarakeswar Banerjee, Kalyani Banerjee
Journal of Humanistic Mathematics
Information plays a key role in life and in complex biological systems, and dynamical systems underlie and can be used to represent many complex systems. Indeed, dynamical systems and information processing capabilities may be the hallmarks of life-like systems. In this paper we combine dynamical systems with a computational framework to generate art. The framework can be used to generate aesthetically appealing forms of life-like systems. Our work suggests that we may need an ``aesthetic sense'' to recognize life that we have not seen before. We also provide teaching resources for students in schools and undergraduate institutions.
The Number Systems Tower, Bill Bauldry, Michael J. Bossé, William J. Cook, Trina Palmer, Jaehee K. Post
The Number Systems Tower, Bill Bauldry, Michael J. Bossé, William J. Cook, Trina Palmer, Jaehee K. Post
Journal of Humanistic Mathematics
For high school and college instructors and students, this paper connects number systems, field axioms, and polynomials. It also considers other properties such as cardinality, density, subset, and superset relationships. Additional aspects of this paper include gains and losses through sequences of number systems. The paper ends with a great number of activities for classroom use.
The "Benfordness" Of Bach Music, Chadrack Bantange, Darby Burgett, Luke Haws, Sybil Prince Nelson
The "Benfordness" Of Bach Music, Chadrack Bantange, Darby Burgett, Luke Haws, Sybil Prince Nelson
Journal of Humanistic Mathematics
In this paper we analyze the distribution of musical note frequencies in Hertz to see whether they follow the logarithmic Benford distribution. Our results show that the music of Johann Sebastian Bach and Johann Christian Bach is Benford distributed while the computer-generated music is not. We also find that computer-generated music is statistically less Benford distributed than human- composed music.
Synesthesia: 3.1415... Orange.Whiteperiwinklewhiteblue..., Shelly Sheats Harkness, Bethany A. Noblitt, Nicole Giesbers
Synesthesia: 3.1415... Orange.Whiteperiwinklewhiteblue..., Shelly Sheats Harkness, Bethany A. Noblitt, Nicole Giesbers
Journal of Humanistic Mathematics
In this paper we address the questions: What is synesthesia? What support(s) can teachers provide for their students who have synesthesia? Nicole, a future mathematics teacher who possesses this synesthesia “superpower”, describes how it impacted her learning. We collected data for this case study through an audio-recorded and transcribed interview, as well as from subsequent email correspondence between the three authors. We asked Nicole three kinds of questions: questions she is frequently asked, questions she would like to be asked, and questions teachers (like Shelly and Beth) might ask. Results indicate that synesthesia may have helped Nicole learn English as …
“I Got You”: Centering Identities And Humanness In Collaborations Between Mathematics Educators And Mathematicians, Anne M. Marshall, Sarah Sword, Mollie Applegate, Steven Greenstein, Terrance Pendleton, Kamuela E. Yong, Michael Young, Jennifer A. Wolfe, Theodore Chao, Pamela E. Harris
“I Got You”: Centering Identities And Humanness In Collaborations Between Mathematics Educators And Mathematicians, Anne M. Marshall, Sarah Sword, Mollie Applegate, Steven Greenstein, Terrance Pendleton, Kamuela E. Yong, Michael Young, Jennifer A. Wolfe, Theodore Chao, Pamela E. Harris
Journal of Humanistic Mathematics
Existing literature widely reports on the value of collaborations between mathematicians and mathematics educators, and also how complex those collaborations can be. In this paper, we report on four collaborations that sought to address what mathematics is and who gets to do it. Drawing on the literature and from the careful and intentional work of the collaborators, we offer a framework to capture the richness of those collaborations – one that acknowledges the importance of acknowledging and welcoming the extensive personal and professional experience of each person involved in the collaboration – and a look at how collaborations built with …
One Theorem, Two Ways: A Case Study In Geometric Techniques, John B. Little
One Theorem, Two Ways: A Case Study In Geometric Techniques, John B. Little
Journal of Humanistic Mathematics
If the three sides of a triangle ABΓ in the Euclidean plane are cut by points H on AB, Θ on BΓ, and K on ΓA cutting those sides in same ratios:
AH : HB = BΘ : ΘΓ = ΓK : KA,
then Pappus of Alexandria proved that the triangles ABΓ and HΘK have the same centroid (center of mass). We present two proofs of this result: an English translation of Pappus's original synthetic proof and a modern algebraic proof making use of Cartesian coordinates and vector concepts. Comparing the two methods, we can see that while the algebraic …
Teaching Mathematics With Poetry: Some Activities, Alexis E. Langellier
Teaching Mathematics With Poetry: Some Activities, Alexis E. Langellier
Journal of Humanistic Mathematics
During the summer of 2021, I experimented with a new way of getting children excited about mathematics: math poetry. Math can be a trigger word for some children and many adults. I wanted to find a way to make learning math fun—without the students knowing they’re doing math. In this paper I describe some activities I used with students ranging from grades K-12 to the college level and share several poem examples, from students in grades two to eight.
Ekstasen: Love Poetry By Felix Hausdorff, Kimberly Gladman
Ekstasen: Love Poetry By Felix Hausdorff, Kimberly Gladman
Journal of Humanistic Mathematics
Four poems by the mathematician Felix Hausdorff are presented in English translation, together with their German originals and commentary about Hausdorff’s multidisciplinary achievements.
Could Raphael’S School Of Athens Contain Hidden Geometry?, Frode S. Larsen, Harald E. Moe
Could Raphael’S School Of Athens Contain Hidden Geometry?, Frode S. Larsen, Harald E. Moe
Journal of Humanistic Mathematics
In this article we argue that Raphael has hidden a geometric shape called a vesica piscis in his fresco The School of Athens (1510-1511). The vesica piscis, and several findings which can be interpreted as suggesting the presence of a vesica piscis in the fresco, are presented. Several of these suggestions relate to the vesica piscis drawn in the construction of an equilateral triangle in the first proposition of Euclid’s Elements. Based on findings in the fresco, we suggest that the vesica piscis should be interpreted in light of a philosophical and theological controversy which took place in Italy …
The Long Search For Collatz Counterexamples, Oliver K. Clay
The Long Search For Collatz Counterexamples, Oliver K. Clay
Journal of Humanistic Mathematics
Despite decades of effort, the Collatz conjecture remains neither proved, nor refuted by a counterexample, nor formally shown to be undecidable. This note introduces the Collatz problem and probes its logical depth with a test question: can the search space for counterexamples be iteratively reduced, and when would it help?
Exploring Set-Theoretic Practices Of Youth Engagement In Connective Journalism: What We Lose In School-Mathematical Descriptions, Alexandra R. Aguilar, Emma C. Gargroetzi, Lynne M. Zummo, Emma P. Bene
Exploring Set-Theoretic Practices Of Youth Engagement In Connective Journalism: What We Lose In School-Mathematical Descriptions, Alexandra R. Aguilar, Emma C. Gargroetzi, Lynne M. Zummo, Emma P. Bene
Journal of Humanistic Mathematics
Analyzing youth video submissions regarding COVID-19 to KQED’s ‘Let’s Talk About the Election’ website, we explore the mathematics these youth engaged in through their submissions without creating any explicit connection to school mathematical concepts or standards. Our focus is the students’ construction of sets (e.g. sets of nurses, doctors, American workers), as a means of creating connection with voters and other media authors through Marchi and Clark’s (2021) construct of connective journalism. We observe these youth constructing sets of varying sizes and reflecting on how these sets are contextualized within a larger political dialogue. We also attempt to rewrite part …
Students’ Mathematical Learning During The Covid-19 Pandemic, Jessica Mean, Shilpa Dasgupta
Students’ Mathematical Learning During The Covid-19 Pandemic, Jessica Mean, Shilpa Dasgupta
Journal of Humanistic Mathematics
This paper discusses our new approach to assessing students’ learning. This approach includes the use of a final project rather than a final cumulative exam. We suggest that students taking a deep dive into one particular math concept and being able to make connections between that concept and the real world are educational achievements during this pandemic. We also argue that there is value in online learning because students who learn online choose to use library resources and develop their own interests by attending office hours, all of which benefit their learning.
No Simple Formula: Navigating Tensions In Teaching Postsecondary Social Justice Mathematics, Alexa W. C. Lee-Hassan
No Simple Formula: Navigating Tensions In Teaching Postsecondary Social Justice Mathematics, Alexa W. C. Lee-Hassan
Journal of Humanistic Mathematics
Instructors of Social Justice Mathematics (SJM) have shared important insights into the powerful potential of connecting classroom mathematics with authentic data about social justice topics, but they have also warned about the harm such teaching can cause when done poorly. In this article, I consider what is necessary to teach SJM at the postsecondary level. I share research that has supported me in learning to teach SJM and highlight challenges that are particular to doing this work in postsecondary contexts. I then describe my experiences navigating the central tensions of this work while honoring its complexity.
Critical Co-Investigators Of Math Trails: Reflections From A Student And Teacher, Benjamin Dickman, Julia Feinberg
Critical Co-Investigators Of Math Trails: Reflections From A Student And Teacher, Benjamin Dickman, Julia Feinberg
Journal of Humanistic Mathematics
In this article, a K-12 mathematics educator and a recent (2020) high school graduate discuss curricular work related to math trails, which are based around the idea of mathematizing potential discoveries along a physical walk. The intersection of math trails with the realities of schooling amid the COVID pandemic is described, along with ways in which math trail learning has ramified beyond classroom walls. This collaboration serves not only to draw attention to the under-researched topic of math trails, but also to exhibit how students and teachers can, in the language of Freire, work together as critical co-investigators.
Math And Democracy, Kimberly A. Roth, Erika L. Ward
Math And Democracy, Kimberly A. Roth, Erika L. Ward
Journal of Humanistic Mathematics
Math and Democracy is a math class containing topics such as voting theory, weighted voting, apportionment, and gerrymandering. It was first designed by Erika Ward for math master’s students, mostly educators, but then adapted separately by both Erika Ward and Kim Roth for a general audience of undergraduates. The course contains materials that can be explored in mathematics classes from those for non-majors through graduate students. As such, it serves students from all majors and allows for discussion of fairness, racial justice, and politics while exploring mathematics that non-major students might not otherwise encounter. This article serves as a guide …
Responsible Data Science For Genocide Prevention, Victor Piercey
Responsible Data Science For Genocide Prevention, Victor Piercey
Journal of Humanistic Mathematics
The term "genocide" emerged out of an effort to describe mass atrocities committed in the first half of the 20th century. Despite a convention of the United Nations outlawing genocide as a matter of international law, the problem persists. Some organizations (including the United Nations) are developing indicator frameworks and “early-warning” systems that leverage data science to produce risk assessments of countries where conflict is present. These tools raise questions about responsible data use, specifically regarding the data sources and social biases built into algorithms through their training data. This essay seeks to engage mathematicians in discussing these concerns.
#Disruptjmm: Online Social Justice Advocacy And Community Building In Mathematics, Rachel Roca, Carrie Diaz Eaton, Drew Lewis, Joseph Hibdon, Stefanie Marshall
#Disruptjmm: Online Social Justice Advocacy And Community Building In Mathematics, Rachel Roca, Carrie Diaz Eaton, Drew Lewis, Joseph Hibdon, Stefanie Marshall
Journal of Humanistic Mathematics
In 2019, \#DisruptJMM, a Twitter hashtag, began circulating after an Inclusion/Exclusion blog by Dr. Piper H pointing to the need to make commonplace conversations about human suffering in the Joint Mathematics Meetings (JMM). While the \#DisruptJMM hashtag has been used since 2019, the vast majority of use was in the JMM 2020 meetings. Twitter hashtags are used by activists to push forward conversations, join communities around a single idea, and create change. In this article, we draw on frameworks from community building seen in other equity and inclusion advocacy hashtags such as \#GirlsLikeUs [7] to qualitatively code and analyze tweets …
On Definitions Of "Mathematician", Ron Buckmire, Carrie Diaz Eaton, Joseph Hibdon, Katherine M. Kinnaird, Drew Lewis, Jessica Libertini, Omayra Ortega, Rachel Roca, Andrés R. Vindas Meléndez
On Definitions Of "Mathematician", Ron Buckmire, Carrie Diaz Eaton, Joseph Hibdon, Katherine M. Kinnaird, Drew Lewis, Jessica Libertini, Omayra Ortega, Rachel Roca, Andrés R. Vindas Meléndez
Journal of Humanistic Mathematics
The definition of who is or what makes a “mathematician” is an important issue to be addressed in the mathematics community. Too often, a narrower definition of who is considered a mathematician (and what is considered mathematics) is used to exclude people from the discipline—both explicitly and implicitly. However, using a narrow definition of a mathematician allows us to highlight, examine, and challenge systemic barriers that exist in certain spaces of the community. This paper analyzes and illuminates tensions between narrow and broad definitions and how they can be used to promote both inclusion and exclusion simultaneously. In this article, …