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Articles 1 - 30 of 501
Full-Text Articles in Mathematics
Infinite Line, Infinite Knowledge: The 'Spera' And Organized Chaos In Lambert's Encyclopedia, The 'Liber Floridus', Ava Romano
Theses and Dissertations
The Liber Floridus is a medieval encyclopedia renowned for its program of circular diagrams, or sperae. Inside this manuscript of 190 chapters, these diagrams frame and embody written knowledge, revealing a connection between encyclopedism and life in the Benedictine monastery by creating a coherent visual organization of chapters.
Mathematics And Political Ideology: A Historical Argument Against The Cultural Understanding Of Mathematics As An Apolitical Field, And A Journalistic Report On The Impact Of The Trump Administration On American Mathematics In 2026, Philo Judson
Pitzer Senior Theses
The interplay between political ideology and mathematics is a recurring theme throughout the history of the academic field. Mathematics has been used as a tool of empire, while mathematicians have been elevated by states as symbols of national genius for political prestige. Political ideologies have also shaped the field from within, both through the suppression of mathematical thought and the enforcement of mathematical authority. Since 2025, the Trump administration has launched large-scale political attacks on American institutions of higher education, which include lawsuits, discrimination investigations, and the removal of federal funding from certain institutions that don’t adhere to the administration’s …
Early Theories On Fluid Resistance And Translation Of Euler’S “Dilucidationes De Resistentia Fluidorum”, Sylvio R. Bistafa
Early Theories On Fluid Resistance And Translation Of Euler’S “Dilucidationes De Resistentia Fluidorum”, Sylvio R. Bistafa
Euleriana
In 1763, Euler published Dilucidationes de resistentia fluidorum (Explanations on the resistance of fluids), a memoir that challenges the fluid resistance theories proposed by Isaac Newton and d’Alembert. Euler's work explores the resistance experienced by solid bodies moving through fluids, critiquing both Newton's "common rule" and d’Alembert's paradox, which predicted zero resistance for non-viscous fluids. Euler's treatise is divided into two parts: the first focuses on the mathematical modeling of fluid flow patterns, while the second addresses the calculation of fluid resistance on surfaces. Despite significant advancements, Euler's work remains constrained by the limitations of non-viscous fluid assumptions, ultimately grappling …
Let’S Teach More Accurate And Inclusive History! The Case Of Islamic Contributions To Mathematics And Science, Nuh Aydin
Journal of Humanistic Mathematics
Schools commonly teach a history of mathematics and science that is Eurocentric. This selective version of the history of science, called Classical Narrative by some, is rooted in colonial times and mindset, and has reinforced certain negative opinions about other cultures. It ignores or downplays contributions to mathematics and sciences from non-western civilizations, and falsely attributes many scientific discoveries to European scholars. Medieval Islamic Civilization, which had strong connections to Renaissance Europe, serves as a clear example of how this narrative is distorted. Based on research on primary sources since the middle of the 20th century, we now know that …
A Practical Rule Of Divisibility By 7 In Uqlīdisī’S Kitāb Al-Fuṣūl Fī Al-Ḥisāb Al-Hindī, Müjdat Takıcak, Mertkan Şimşek
A Practical Rule Of Divisibility By 7 In Uqlīdisī’S Kitāb Al-Fuṣūl Fī Al-Ḥisāb Al-Hindī, Müjdat Takıcak, Mertkan Şimşek
Journal of Humanistic Mathematics
There are many known examples of divisibility rules in modern mathematics. However, some of these rules are far from being practical, such as the current divisibility rule by 7. A far more useful method can be found in the work of the tenth-century Islamic mathematician Abū al-Ḥasan al-Uqlīdisī (d. 980), who proposed a divisibility rule for 7 in his treatise Kitāb al-Fuṣūl fī al-Ḥisāb al-Hindī. Compared to modern techniques, Uqlīdisī’s rule is both simpler and more practical. This article (re)introduces this rule, and provides an exposition of the mathematical reasoning that underpins it.
The Other Side Of The Equation: De-Simplification, A Prerequisite For Calculus, Stephen L. Brown
The Other Side Of The Equation: De-Simplification, A Prerequisite For Calculus, Stephen L. Brown
ACMS Conference Proceedings 2005
No abstract provided.
Euler Archive Spotlight: Translations Of Euler's Works To Languages Other Than English, Michael P. Saclolo
Euler Archive Spotlight: Translations Of Euler's Works To Languages Other Than English, Michael P. Saclolo
Euleriana
The Euler Archive is home to almost all of Euler’s original publications and roughly a quarter of them have accompanying translations to English. A small number of Euler’s works also have translations to a handful of other languages, namely, Dutch, French, German, Italian, Portuguese, and Turkish that are available in the archive. We put a spotlight on these non-English translations in this issue.
On The Motion Of The Nodes Of The Moon And The Variation Of Its Inclination To The Ecliptic (An English Translation Of De Motu Nodorum Lunae Eiusque Inclinationis Ad Eclipticam Variatione), Patrick T. Headley
Euleriana
In this paper Euler attempts to explain some features of the motion of the Moon using Newton’s inverse-square law of gravity. He describes the evidence in favor of Newton’s theory but also the lack of progress in the study of lunar motion due to the difficulty of the three-body problem, arising here since both the Sun and the Earth have large effects on the Moon. He proceeds to investigate the line of intersection between the planes of the Earth's orbit and the Moon's orbit, as well as the angle between the two planes.
The Merchant And The Mathematician: Commerce And Accounting, Graziano Gentili, Luisa Simonutti, Daniele C. Struppa
The Merchant And The Mathematician: Commerce And Accounting, Graziano Gentili, Luisa Simonutti, Daniele C. Struppa
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this article we describe the invention of double-entry bookkeeping (or partita doppiaas it was called in Italian), as a fertile intersection between mathematics and early commerce. We focus our attention on this seemingly simple technique that requires only minimal mathematical expertise, but whose discovery is clearly the result of a mathematical way of thinking, in order to make a conceptual point about the role of mathematics as the humus from which disciplines as different as operations research, computer science, and data science have evolved.
Unknowable Truths: The Incompleteness Theorems And The Rise Of Modernism, Caroline Tvardy
Unknowable Truths: The Incompleteness Theorems And The Rise Of Modernism, Caroline Tvardy
Honors Scholars Collaborative Projects
This thesis evaluates the function of the current history of mathematics methodologies and explores ways in which historiographical methodologies could be successfully implemented in the field. Traditional approaches to the history of mathematics often lack either an accurate portrayal of the social and cultural influences of the time, or they lack an effective usage of mathematics discussed. This paper applies a holistic methodology in a case study of Kurt Gödel’s influential work in logic during the Interwar period and the parallel rise of intellectual modernism. In doing so, the proofs for Gödel’s Completeness and Incompleteness theorems will be discussed as …
“All Of These Political Questions”: Anticommunism, Racism, And The Origin Of The Notices Of The American Mathematical Society, Michael J. Barany
“All Of These Political Questions”: Anticommunism, Racism, And The Origin Of The Notices Of The American Mathematical Society, Michael J. Barany
Journal of Humanistic Mathematics
A recent controversy involving the Notices of the American Mathematical Society and questions of politics, racism, and the appropriate role of a professional mathematical organization began with a comparison to events the American Mathematical Society confronted in 1950. A close look at the AMS’s own archives for that period shows that the controversies that vexed the society around 1950 do indeed resonate strongly with those of today, but not in the ways recently suggested. Then, as now, the AMS confronted allegations of political and viewpoint discrimination in universities, the challenges of structural racism in American education and society, and the …
The Infinite Is The Chasm In Which Our Thoughts Are Lost: Reflections On Sophie Germain's Essays, Adam Glesser, Bogdan D. Suceavă, Mihaela Vajiac
The Infinite Is The Chasm In Which Our Thoughts Are Lost: Reflections On Sophie Germain's Essays, Adam Glesser, Bogdan D. Suceavă, Mihaela Vajiac
Mathematics, Physics, and Computer Science Faculty Articles and Research
"Sophie Germain (1776–1831) is quite well-known to the mathematical community for her contributions to number theory [17] and elasticity theory (e.g., see [2, 5]). On the other hand, there have been few attempts to understand Sophie Germain as an intellectual of her time, as an independent thinker outside of academia, and as a female mathematician in France, facing the prejudice of the time of the First Empire and of the Bourbon Restoration, while pursuing her thoughts and interests and writing on them. Sophie Germain had to face a double challenge: the mathematical difficulty of the problems she approached and the …
Quantitative Literacy And The Mathematical Association Of America In The 2000’S: Ql Subcommittee Of Cupm , Sigmaa Ql, And Maa Notes #70, Rick Gillman
Numeracy
This Roots and Seeds article is a partial history of the quantitative literacy movement in the Mathematical Association of America in the first decade of the 21st century. It focuses on the inclusion of QL in the MAA Committee on the Undergraduate Program in Mathematics’ CUPM Curriculum Guidelines (2004), the creation of the special interest group for MAA members (SIGMAA QL, 2004), and the work of that body in subsequent years, in particular, the MAA Notes #70, Current Practices in Quantitative Literacy (2006). I discuss some issues that were problematic in the QL movement in the MAA in those years …
Closing Banquet Eulogies, Russell Howell, C. Ray Rosentrater
Closing Banquet Eulogies, Russell Howell, C. Ray Rosentrater
ACMS Conference Proceedings 2019
A tribute to David Lay; A tribute to John Roe
Developing Mathematicians: The Benefits Of Weaving Spiritual And Disciplinary Discipleship, Patrick Eggleton
Developing Mathematicians: The Benefits Of Weaving Spiritual And Disciplinary Discipleship, Patrick Eggleton
ACMS Conference Proceedings 2019
Part of the goal of discipleship at the Christian university is for faith development to seep into the hearts of the students. Similarly, the goal of the development of future mathematicians is for the mathematical proficiencies, the practices like problem solving and analytical reasoning that permeate each of the courses, to seep into the hearts of our majors. This presentation shares how the weaving of our spiritual and disciplinary discipleship efforts benefits the faith development of our students while also helping them to think like a mathematician.
From Perfect Shuffles To Landau's Function, Brian D. Beasley
From Perfect Shuffles To Landau's Function, Brian D. Beasley
ACMS Conference Proceedings 2019
If we view a given shuffle of a deck of cards as a permutation, then repeatedly applying this same shuffle will eventually return the deck to its original order. In general, how many steps will that take? What happens in the case of so-called perfect shuffles? What type of shuffle will require the greatest number of applications before restoring the original deck? This talk will address those questions and provide a brief history of the work of Edmund Landau on the maximal order of a permutation in the symmetric group on n objects. It will also note some recent progress …
Replacing Remedial Mathematics With Corequisites In General Education Mathematics Courses, Alana Unfried
Replacing Remedial Mathematics With Corequisites In General Education Mathematics Courses, Alana Unfried
ACMS Conference Proceedings 2019
Many colleges and universities offer courses, such as Remedial Mathematics or Elementary Algebra, that underprepared students must complete before they can take a college-level mathematics course. However, nationally there is a push to replace remedial mathematics courses with corequisite courses instead. This design allows students to enter directly into their general education mathematics course instead of first overcoming the barrier of a remedial course. Corequisite mathematics courses were implemented across the 23-campus California State University system during the 2018-19 academic year. I will discuss the design and implementation of a corequisite structure at California State University, Monterey Bay, in particular …
Charles Babbage And Mathematical Aspects Of The Miraculous, Courtney K. Taylor
Charles Babbage And Mathematical Aspects Of The Miraculous, Courtney K. Taylor
ACMS Conference Proceedings 2019
Charles Babbage is widely known as the father of the computer, but he is lesser known for his contributions to natural theology and apologetics. In 1837 Babbage wrote the Ninth Bridgewater Treatise in response to a series of writings concerning faith and science that had been commissioned by the Royal Society. Among the remarkable features of the Ninth Bridgewater are mathematical analogies concerning the miraculous. We will explore these ideas, which range from the difference engine to a family of fourth degree curves, illustrating that for Babbage, miracles are not exceptions to natural law, but rather instances of a larger …
The Applicability Of Mathematics And The Naturalist Die, Ricardo J. Cordero-Soto
The Applicability Of Mathematics And The Naturalist Die, Ricardo J. Cordero-Soto
ACMS Conference Proceedings 2019
Philosopher and Christian apologist William Lane Craig has proposed a valid deductive argument for God’s existence that is rooted in the applicability of mathematics to the physical universe. This argument was presented by Craig during a debate with philosopher and atheist Alex Rosenberg. During the debate, Rosenberg presented a rebuttal to the soundness of this argument by appealing to chance as an explanation to the applicability of mathematics to the physical universe. In this talk, the presenter will discuss how the naturalist die is unable to produce “chance application” of mathematics while defending the soundness of the argument in light …
Faith, Mathematics, And Science: The Priority Of Scripture In The Pursuit And Acquisition Of Truth, Bob Mallison
Faith, Mathematics, And Science: The Priority Of Scripture In The Pursuit And Acquisition Of Truth, Bob Mallison
ACMS Conference Proceedings 2019
This research will examine some approaches for identifying truth as well as some issues involved in recognizing reliable sources of information. We will proceed from a decidedly Christian perspective including the conviction that God created an orderly universe (and that studying nature provides valuable information about Him) and that His Word, the Bible, even more clearly expresses in- formation about Him. We will discuss some of the essential tools used by mathematicians and scientists for the discovery of truth – namely, models. We will examine some valuable models from history, and briefly discuss that as additional scientific information became available, …
Teaching Mathematics At An African University -- My Experience, Kathleen Lewis
Teaching Mathematics At An African University -- My Experience, Kathleen Lewis
ACMS Conference Proceedings 2019
For eight years (2010-2018), I was the head of the math department at The University of The Gambia, a small, new (started in 1999) university in a very small, mostly Muslim, West African country that most Americans have never heard of. During that time, a number of other Americans and Europeans came to teach for shorter periods of time. I will talk about what this experience was like for us, both the good and the bad. I will describe the possibilities for others to spend either a sabbatical or an extended period of time at such a university and suggest …
Lagrange's Interpolation, Chinese Remainder, And Linear Equations, Jesús Jiménez
Lagrange's Interpolation, Chinese Remainder, And Linear Equations, Jesús Jiménez
ACMS Conference Proceedings 2019
Consider a finite set of points {(x1, y1), (x2, y2), . . . , (xk , yk )} in R2. The Lagrange’s interpolation problem is to find a polynomial p(x) of degree k − 1 satisfying p(xi) = yi for 1 ≤ i ≤ k. We will recall the solution to Lagrange’s interpolation problems as an instance of the Chinese Remainder Theorem. Next, we will show that a similar approach can be used to construct solutions to a system of linear equations.
Addressing Challenges In Creating Math Presentations, David Schweitzer
Addressing Challenges In Creating Math Presentations, David Schweitzer
ACMS Conference Proceedings 2019
When it comes to composing presentation slides with extensive mathematical content, each of the slide creation platforms has at least one significant drawback. Whether it is Beamer and its steep learning curve, PowerPoint and its relative inefficiency with math, Google Slides and its complete lack of math capabilities, or some other platform, no one tool single-handedly offers an ideal solution. Additionally, if users desire creative flexibility, such as the ability to easily change fonts or colors, the platforms’ respective limitations can become even more pronounced. In a project that has been well suited for undergraduate research, the presenter and his …
Overcoming Stereotypes Through A Liberal Arts Math Course, Jessica Hamm
Overcoming Stereotypes Through A Liberal Arts Math Course, Jessica Hamm
ACMS Conference Proceedings 2019
"I'm just not a math person.” We’ve heard this comment countless times from our students. It is a mentality that both paralyzes and strangely comforts them. In this talk I will describe how I use my liberal arts Joy of Mathematics course to help students address and overcome stereotypes. In particular, I will discuss a specific assignment as well as share some student comments and perspectives on how this course helped change their viewpoint on more than just math.
Maximum Elements Of Ordered Sets And Anselm's Ontological Argument, Doug Ward
Maximum Elements Of Ordered Sets And Anselm's Ontological Argument, Doug Ward
ACMS Conference Proceedings 2019
I will present a simple theorem concerning maximal elements of a set T endowed with an ordering “>” that is antisymmetric, i.e., if A and B are elements of T , we cannot have both A > B and B > A. A special case of this theorem is a simple version of the ontological argument, one of the classical proofs for the existence of God.
Numerical Range Of Toeplitz Matrices Over Finite Fields, Derek Thompson, Maddison Guillaume Baker, Amish Mishra
Numerical Range Of Toeplitz Matrices Over Finite Fields, Derek Thompson, Maddison Guillaume Baker, Amish Mishra
ACMS Conference Proceedings 2019
We characterize the kth numerical range of all n×n Toeplitz matrices with a constant main diagonal and another single, non-zero diagonal, where the matrices are over the field Zp[i], with p a prime congruent to 3 mod 4. We find that, for k ∈ Z∗, the kth numerical range is always equal to Zp[i] with the exception of the scaled identity. We also use similar techniques to discover a general connection between the 0th numerical range and the kth numerical range. Lastly, we conclude with a conjecture regarding the general numerical range of all triangular Toeplitz matrices.
Is Mathematical Truth Time Dependent? Comments From A Paper By Judith Grabiner, Richard Stout
Is Mathematical Truth Time Dependent? Comments From A Paper By Judith Grabiner, Richard Stout
ACMS Conference Proceedings 2019
Judith Grabiner, a renowned historian of mathematics, has written many papers related to signifi- cant changes in the content and nature of analysis, from the 17th through the 19th century. In her paper “Is Mathematical Truth Time Dependent?” Professor Grabiner gives several reasons for the changing nature and requirements in rigor that occurred over this period of two hundred years. In this talk I will briefly summarize her conclusions, particularly in light of how they might influence a Christian perspective on mathematics.
Models, Values, And Disasters, Michael H. Veatch
Models, Values, And Disasters, Michael H. Veatch
ACMS Conference Proceedings 2019
Decision-support models have values embedded in them and are subjective to varying degrees. Philosophical and ethical perspectives on operations research models are used to describe this subjectivity. Approaches to model building are then suggested that take into account subjectivity and values. For the decisions to reflect the right values, the model must align with the decision-maker’s values. I argue that it is appropriate and important for Christians applying mathematical models to be keenly aware of decision-maker’s values and seek to reflect them in the model. Disaster response planning is presented as an example where incorporating values is challenging. The responding …
Factors That Motivate Students To Learn Mathematics, Dave Klanderman, Sarah Klanderman, Benjamin Gliesmann, Josh Wilkerson, Patrick Eggleton
Factors That Motivate Students To Learn Mathematics, Dave Klanderman, Sarah Klanderman, Benjamin Gliesmann, Josh Wilkerson, Patrick Eggleton
ACMS Conference Proceedings 2019
What motivates some students to want to learn mathematics while others do not share similar motivation? Are these factors intrinsic, extrinsic, or a combination of both? To answer these questions, we adapted a survey originally developed by Tapia (1996) and later shortened by Lim and Chapman (2015). We administered the survey in multiple middle schools, a high school, and multiple colleges and universities. We obtained over 100 completed surveys for each of these educational levels. This presentation offers an analysis of these data, including descriptive statistics and confidence intervals for each educational level. For the college and university sample, we …
Thinking Beautifully About Mathematics: A View Of Mathematics As The Science Of Measurable Orders, James M. Turner
Thinking Beautifully About Mathematics: A View Of Mathematics As The Science Of Measurable Orders, James M. Turner
ACMS Conference Proceedings 2019
At Calvin College, First Year Students are required to take a section of our Discovering the Christian Mind course during our January term. For the past 3 years, I have taught a section of this course titled Thinking Beautiful ly about Mathematics. In it, I explored, with the students, various areas of mathematics, as well as how mathematicians have explored them, while addressing such questions as “Is mathematics invented or discovered?” and “Why is mathematics unreasonably effective?” Ultimately, we look to identify ways and characterizations for how beauty displays itself in mathematics and how and it what ways beauty is …