Open Access. Powered by Scholars. Published by Universities.®
- Discipline
-
- Arts and Humanities (586)
- Education (141)
- Science and Mathematics Education (74)
- Other Mathematics (46)
- Creative Writing (39)
-
- Social and Behavioral Sciences (35)
- Poetry (24)
- Teacher Education and Professional Development (23)
- Philosophy (20)
- Higher Education (18)
- Statistics and Probability (17)
- History (16)
- Curriculum and Instruction (14)
- Fiction (13)
- Geometry and Topology (13)
- Logic and Foundations (13)
- Applied Mathematics (12)
- Number Theory (12)
- History of Science, Technology, and Medicine (11)
- Life Sciences (11)
- Music (11)
- Social Justice (10)
- Analysis (9)
- Art and Design (9)
- Educational Methods (9)
- Logic and Foundations of Mathematics (9)
- Algebra (8)
- Computer Sciences (8)
- Keyword
-
- Mathematics (63)
- Poetry (44)
- Mathematics education (29)
- Creativity (16)
- Math (15)
-
- Motherhood (15)
- Teaching (15)
- Geometry (13)
- Ethics (12)
- Statistics (12)
- Poem (11)
- Education (9)
- History of mathematics (9)
- Fiction (8)
- Proof (8)
- Social justice (8)
- Art (7)
- COVID-19 (7)
- Equity (7)
- Humanistic mathematics (7)
- Mathematical poetry (7)
- Music (7)
- Outreach (7)
- Problem solving (7)
- Data science (6)
- Philosophy (6)
- Pi (6)
- STEM (6)
- Calculus (5)
- Euclid (5)
Articles 661 - 690 of 708
Full-Text Articles in Mathematics
Prisoner's Dilemma, Raymond N. Greenwell
Prisoner's Dilemma, Raymond N. Greenwell
Journal of Humanistic Mathematics
No abstract provided.
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 …
The Physicist's Basement, Nora Culik
The Physicist's Basement, Nora Culik
Journal of Humanistic Mathematics
No abstract provided.
The Discipline Of History And The “Modern Consensus In The Historiography Of Mathematics”, Michael N. Fried
The Discipline Of History And The “Modern Consensus In The Historiography Of Mathematics”, Michael N. Fried
Journal of Humanistic Mathematics
Teachers and students of mathematics often view history of mathematics as just mathematics as they know it, but in another form. This view is based on a misunderstanding of the nature of history of mathematics and the kind of knowledge it attempts to acquire. Unfortunately, it can also lead to a deep sense of disappointment with the history of mathematics itself, and, ultimately, a misunderstanding of the historical nature of mathematics. This kind of misunderstanding and the disappointment following from it--both raised to the level of resentment--run through the paper "A Critique of the Modern Consensus in the Historiography of …
A Critique Of The Modern Consensus In The Historiography Of Mathematics, Viktor Blåsjö
A Critique Of The Modern Consensus In The Historiography Of Mathematics, Viktor Blåsjö
Journal of Humanistic Mathematics
The history of mathematics is nowadays practiced primarily by professional historians rather than mathematicians, as was the norm a few decades ago. There is a strong consensus among these historians that the old-fashioned style of history is “obsolete,” and that “the gains in historical understanding are incomparably greater” in the more “historically sensitive” works of today. I maintain that this self-congratulatory attitude is ill-founded, and that the alleged superiority of modern historiographical standards ultimately rests on a dubious redefinition of the purpose of history rather than intrinsic merit.
How Do I Love Thee? Let Me Count The Ways For Syllabic Variation In Certain Poetic Forms, Mike Pinter
How Do I Love Thee? Let Me Count The Ways For Syllabic Variation In Certain Poetic Forms, Mike Pinter
Journal of Humanistic Mathematics
The Dekaaz poetic form, similar to haiku with its constrained syllable counts per line, invites a connection between poetry and mathematics. Determining the number of possible Dekaaz variations leads to some interesting counting observations. We discuss two different ways to count the number of possible Dekaaz variations, one using a binary framework and the other approaching the count as an occupancy problem. The counting methods described are generalized to also count variations of other poetic forms with syllable counts specified, including haiku. We include Dekaaz examples and suggest a method that can be used to randomly generate a Dekaaz variation.
Fields In Math And Farming, Susan D'Agostino
Fields In Math And Farming, Susan D'Agostino
Journal of Humanistic Mathematics
A young woman’s search for a a contemplative, insightful experience leads her from farming to mathematics.
Being Reasonable: Using Brainteasers To Develop Reasoning Ability In Humanistic Mathematics Courses, Gary Stogsdill
Being Reasonable: Using Brainteasers To Develop Reasoning Ability In Humanistic Mathematics Courses, Gary Stogsdill
Journal of Humanistic Mathematics
Developing reasoning ability is often cited as one of the principal justifications of a mathematics requirement for liberal arts undergraduates. Humanistic math courses have become recognized as a paradigm for liberal arts mathematics, but such courses may not provide the opportunity to develop reasoning ability. The author describes his procedure for using brainteasers to promote reasoning in a humanistic math course for liberal arts undergraduates.
Joining ``The Mathematician's Delirium To The Poet's Logic'': Mathematical Literature And Literary Mathematics, Rita Capezzi, Christine Kinsey
Joining ``The Mathematician's Delirium To The Poet's Logic'': Mathematical Literature And Literary Mathematics, Rita Capezzi, Christine Kinsey
Journal of Humanistic Mathematics
This paper describes our team-taught interdisciplinary mathematics and literature course, Mathematical Literature and Literary Mathematics, which invites students to consider Raymond Queneau's challenge: "Why shouldn't one demand a certain effort on the reader's part? Everything is always explained to him. He must eventually tire of being treated with such contempt.'' We study works by Berge, Borges, Calvino, Perec, Queneau, Robbe-Grillet and Stoppard, among others. From a literary critical perspective, the course highlights the play of language rather than the primacy of meaning. We choose texts where mathematical concepts are subjects or structuring elements of the literature, and ideally both. …
Some Effects Of The Human Genome Project On The Erdős Collaboration Graph, Chris Fields
Some Effects Of The Human Genome Project On The Erdős Collaboration Graph, Chris Fields
Journal of Humanistic Mathematics
The Human Genome Project introduced large-scale collaborations involving dozens to hundreds of scientists into biology. It also created a pressing need to solve discrete mathematics problems involving tens of thousands of elements. In this paper, we use minimal path lengths in the Erdős Collaboration Graph between prominent individual researchers as a measure of the distance between disciplines, and we show that the Human Genome Project brought laboratory biology as a whole closer to mathematics. We also define a novel graph reduction method and a metric that emphasizes the robustness of collaborative connections between researchers; these can facilitate the analysis of …
Game Theory Meets The Humanities And Both Win Or Book Review: Game Theory And The Humanities: Bridging Two Worlds, By Steven J. Brams, Karl-Dieter Crisman
Game Theory Meets The Humanities And Both Win Or Book Review: Game Theory And The Humanities: Bridging Two Worlds, By Steven J. Brams, Karl-Dieter Crisman
Journal of Humanistic Mathematics
This review discusses Brams' wide-ranging book Game Theory and the Humanities and gives some basic examples of the methodology and style, including how the Theory of Moves contributes to understanding such games.
Promoting Active Studying: The Study Challenge, Christopher K. Storm, Salvatore Petrilli, Susan Petry
Promoting Active Studying: The Study Challenge, Christopher K. Storm, Salvatore Petrilli, Susan Petry
Journal of Humanistic Mathematics
We explore using a “Study Challenge” to help students become active studiers in mathematics courses. We describe how a Study Challenge works and how we implemented it in calculus and differential equations courses. We discuss qualitative reactions from students who accepted the Study Challenge, which suggest that this might be a useful tool for students’ to add to their examination preparation toolbox. Finally, we offer some suggestions for implementing a Study Challenge within the mathematics classroom.
What Is So Negative About Negative Exponents?, Geoffrey D. Dietz
What Is So Negative About Negative Exponents?, Geoffrey D. Dietz
Journal of Humanistic Mathematics
While teaching college-level mathematics (from College Algebra to Calculus to Abstract Algebra), I have observed that students are often uncomfortable using negative exponents in calculations. I believe the fault partially lies in the manner in which negative exponents are taught in Algebra 1 or Algebra 2 courses, especially in rigid instructions always to write answers using only positive exponents. After reviewing a sample of algebra texts used in the United States over the last two centuries, it appears that while attitudes toward negative exponents have varied from author to author over time, the current trend is to declare explicitly that …
Benjamin Banneker's Original Handwritten Document: Observations And Study Of The Cicada, Janet E. Barber, Asamoah Nkwanta
Benjamin Banneker's Original Handwritten Document: Observations And Study Of The Cicada, Janet E. Barber, Asamoah Nkwanta
Journal of Humanistic Mathematics
Benjamin Banneker, farmer, mathematician, astronomer, and scientist, is known for his mathematical puzzles, ephemeris calculations, almanacs, his wooden clock, land surveying work, and famous letter on human rights. However, as a naturalist, his scientific and systematic observations of the cicadas are less known. In this paper we publicize Banneker’s naturalistic study of the seventeen-year periodic cycle of the cicada and make available the original handwritten document of his observations. We also introduce the audience of this journal to an intriguing natural problem involving prime numbers.
Improving Equity And Education: Why And How, Patricia Clark Kenschaft
Improving Equity And Education: Why And How, Patricia Clark Kenschaft
Journal of Humanistic Mathematics
Progress is possible. When I graduated from college, only 5\% of the new U.S. doctorates in mathematics went to women; now it is about 30\%. There is of course room (and need) for more progress. This paper begins with an account of my research about women and black mathematicians. The latter group claimed that racial equality can be achieved only when better elementary school mathematics education is available to all children in this country. That motivated me to lead a seven-year, grant-supported program to work with elementary school teachers and children in nine New Jersey districts, including Newark, Paterson, and …
Liberal Arts Inspired Mathematics: A Report Or How To Bring Cultural And Humanistic Aspects Of Mathematics To The Classroom As Effective Teaching And Learning Tools, Anders K H Bengtsson
Liberal Arts Inspired Mathematics: A Report Or How To Bring Cultural And Humanistic Aspects Of Mathematics To The Classroom As Effective Teaching And Learning Tools, Anders K H Bengtsson
Journal of Humanistic Mathematics
This is the report of a project on ways of teaching university-level mathematics in a humanistic way. The main part of the project recounted here involved a journey to the United States during the fall term of 2012 to visit several liberal arts colleges in order to study and discuss mathematics teaching. Several themes that came up during my conversations at these colleges are discussed in the text: the invisibility of mathematics in everyday life, the role of calculus in American mathematics curricula, the "is algebra necessary?'' discussion, teaching mathematics as a language, the transfer problem in learning, and the …
Galileo And Aristotle's Wheel, Olympia Nicodemi
Galileo And Aristotle's Wheel, Olympia Nicodemi
Journal of Humanistic Mathematics
At the beginning of his last major work, Galileo tackles an old paradox, Aristotle's Wheel, in order to produce a model of the continuum that explains (at least to him) how line segments of different length could be put into a one-to-one correspondence. His argument seems like a playful digression. However, it is precisely this type of a one-to-one correspondence that he needs to support his work on free fall. In this article, we investigate how Galileo's model for the wheel paradox informs his work on free fall. We also examine some of the reasons his results on free fall---results …
Harmonics In The Library, Charles Coppin
Harmonics In The Library, Charles Coppin
Journal of Humanistic Mathematics
Students of traditional calculus courses can discover significant mathematics original to themselves, especially if these courses are taught in a way that allows shafts of mathematical light to shine through. We tell a story of such an incident in the form of a dialogue between two fictional students. Our students, on their own, discover (or rediscover) a well-known problem based on the harmonic series. We believe opportunities for such discoveries are greater if students have had some experience with inquiry-based learning prior to entering a traditional course. More broadly, we aim to demonstrate what can occur when students feel no …
A Math Therapy Exercise, Gary Stogsdill
A Math Therapy Exercise, Gary Stogsdill
Journal of Humanistic Mathematics
Math anxiety prevents many liberal arts undergraduates from appreciating mathematics and realizing their potential in math courses and math-related endeavors. The author describes his development and use of a "math therapy exercise" that enables students to move beyond the paralyzing grip of math anxiety and cultivate a more positive relationship with mathematics.
Rock Art Tallies: Mathematics On Stone In Western North America, James V. Rauff
Rock Art Tallies: Mathematics On Stone In Western North America, James V. Rauff
Journal of Humanistic Mathematics
Western North America abounds with rock art sites. From Alberta to New Mexico and from Minnesota to California one can find the enigmatic rock paintings and rock carvings left by the pre-Columbian inhabitants. The images left behind on the rocks of the American plains and deserts are those of humanoids and animals, arrows and spears, and a variety of geometric shapes and abstract designs. Also included, in great numbers, are sequences of repeated shapes and marks that scholars have termed "tallies." The tallies are presumed to be an ancient accounting of something or some things. This article examines rock art …
Some Contributions To The Sociology Of Numbers, Robert Dawson
Some Contributions To The Sociology Of Numbers, Robert Dawson
Journal of Humanistic Mathematics
Those who work with numbers eventually realize that they all have different personalities (the word "numbers" can of course be replaced by any number of other nouns here.) Here is one view of the issue.
How To Cook Up A Math Poem In N Easy Steps, Caleb Emmons
How To Cook Up A Math Poem In N Easy Steps, Caleb Emmons
Journal of Humanistic Mathematics
A mathematical poem attempts to distill a mathematical concept and present it in a literary or visually compelling way. This paper presents an outline of my own personal method of composing such poetry. The outline is elucidated via an extended meditation on the composition of one particular poem.
On Contemplation In Mathematics, Frank Lucas Wolcott
On Contemplation In Mathematics, Frank Lucas Wolcott
Journal of Humanistic Mathematics
In a section about research, we make the case that intentional, structured reflection on the mathematical research process, by mathematical researchers themselves, would result in better mathematicians doing better mathematics. As supporting evidence, we describe the Flavors and Seasons project. In a section about teaching, we describe the contemplative education movement and share personal experiences using meditation in the math classroom. We conclude with an explicit proposal for elucidating the experiential context of mathematics, in both research and teaching environments.
Teaching The Complex Numbers: What History And Philosophy Of Mathematics Suggest, Emily R. Grosholz
Teaching The Complex Numbers: What History And Philosophy Of Mathematics Suggest, Emily R. Grosholz
Journal of Humanistic Mathematics
The narrative about the nineteenth century favored by many philosophers of mathematics strongly influenced by either logic or algebra, is that geometric intuition led real and complex analysis astray until Cauchy and Kronecker in one sense and Dedekind in another guided mathematicians out of the labyrinth through the arithmetization of analysis. Yet the use of geometry in most cases in nineteenth century mathematics was not misleading and was often key to important developments. Thus the geometrization of complex numbers was essential to their acceptance and to the development of complex analysis; geometry provided the canonical examples that led to the …
On The Occasion Of Your Graduation, Robert Dawson
On The Occasion Of Your Graduation, Robert Dawson
Journal of Humanistic Mathematics
A letter from an absent supervisor to a doctoral student about to graduate reveals a terrible secret.
Math Moment, Paige S. Orland
Math Moment, Paige S. Orland
Journal of Humanistic Mathematics
A short poem comparing Exponential and Logistic functions.
Confidence Interval, Ursula Whitcher
Confidence Interval, Ursula Whitcher
Journal of Humanistic Mathematics
A poem about estimating probabilities.