Physical Sciences and Mathematics Commons^™

The Frankensteinian Nature Of Mathematics, Ali Barahmand

Journal of Humanistic Mathematics

Frankenstein is a story about a scientist who creates a sapient creature that gets out of control and horrifies its creator by its unexpected behavior. In this note, we show that this type of undesirable behavior can reflect a part of the nature of mathematics, and that its origin is related to the ontological question of whether mathematics is invented or discovered. Based on a review of the relationship be- tween discovery and invention, we demonstrate that mathematics has similarities and differences with both discovery and invention. In the natural sciences, new instruments have to be invented to discover new …

Seating Groups And 'What A Coincidence!': Mathematics In The Making And How It Gets Presented, Peter J. Rowlett

Journal of Humanistic Mathematics

Mathematics is often presented as a neatly polished finished product, yet its development is messy and often full of mis-steps that could have been avoided with hindsight. An experience with a puzzle illustrates this conflict. The puzzle asks for the probability that a group of four and a group of two are seated adjacently within a hundred seats, and is solved using combinatorics techniques.

Logical Or Epistemological? A Study On Kepler’S 3m Cosmological Model, Po-Hung Liu

Journal of Humanistic Mathematics

Kepler published Mysterium Cosmographicum in 1597 constructing his cosmo- logical model based on the five regular polyhedra. Such a creative but weird idea was almost consistent with empirical evidence. Furthermore, following the Pythagorean belief about the connection between music and astronomy, Kepler delved into looking for what things having to do with the planetary movements have the harmonic consonances. This article claims that Kepler’s model is a 3M (mathematical, musical, and metaphysical) model and demonstrates how it had been constructed. Furthermore, I explore the reasons behind Kepler’s departure from the 3M model and his subsequent consideration of a non-circular orbit, …

On Parallels Between Words And Music, Will Turner

Journal of Humanistic Mathematics

A generalised song is a means of drawing parallels between words and music. The parallels are encoded in a mathematical structure, which is interpreted in a verbal structure and a musical structure. Here we develop a number of new techniques for drawing such parallels, in giving two examples of generalised songs, `Relation', and `Merge/Split'.

The first five partials of a note played on a piano are roughly 0,12,19,24,28 semitones above the fundamental.`Relation' is a generalised song, whose musical part is played on a piano, constructed from the mathematical relation 4.28 = 3.12 + 4.19.

`Merge/Split' is a generalised song whose …

Undergraduate Mathematics Students Question And Critique Society Through Mathematical Modeling, Will Tidwell, Amy Bennett

Journal of Humanistic Mathematics

Mathematics can be used as a tool to question and critique society and, in doing so, give us more information about the world around us and how it operates. This however, is not a common perspective that is conveyed to students during their undergraduate mathematics coursework. This paper contributes to the understanding of how undergraduate mathematics students question and critique society via mathematical modeling tasks. In two courses at two universities, 27 mathematics majors and secondary preservice teachers engaged in the modeling process situated in authentic contexts to learn specific concepts and make mathematical connections across domains and disciplines. Both …

Aesthetic Approaches To Symmetric Functions, John M. Campbell

Journal of Humanistic Mathematics

Symmetry is often regarded as an integral aspect about aesthetics. This motivates the pursuit of interdisciplinary studies based on the use of subjects in mathematics concerned with symmetry in conjunction with aesthetics. What is referred to as a symmetric function in the field of algebraic combinatorics is an abstraction based on polynomials that exhibit a symmetric property, and this leads us to pursue an algebraic combinatorics-inspired exploration based on aesthetics. In particular, we use different bases and transitions between them to create aesthetically pleasing visualizations of symmetric functions. We see that these visualizations in turn raise new and interesting questions.

Mathematicians Going East, Pasha Zusmanovich

Journal of Humanistic Mathematics

I survey emigration of mathematicians from Europe, before and during WWII, to Russia. The emigration started at the end of 1920s, the time of “Great Break”, and accelerated in 1930s, after the introduction in Germany of the “non-Aryan laws”. Not everyone who wanted to emigrate managed to do so, and most of those who did spent a relatively short time in Russia, being murdered or deported, or fleeing the Russian regime. After 1937, the year of “Great Purge”, only a handful of emigrant mathematicians remained, and even fewer managed to leave a trace in the scientific milieu of their new …

Sharing Four Biscuits Between Three People: An Illustrative Example Of How Mathematics Is Intertwined With Human Values, Lovisa Sumpter, David Sumpter

Journal of Humanistic Mathematics

Despite convincing arguments by mathematicians, philosophers, sociologists and machine learning practitioners to the contrary, there remains a widespread notion amongst many members of the general public (and some practitioners) that mathematics is neutral, that it is free from human values. One reason why this notion persists is that we lack clear-cut examples that demonstrate how mathematics and values are intertwined. In this paper, we offer one such example. In particular, we show that when sharing four biscuits between three people, several possible mathematical and ethical frameworks can be used. We demonstrate that different solutions—hiding one biscuit, arbitrarily sharing the extra …

The Automathography: A Humanistic Autobiographical Writing Assignment For Mathematics Courses, Colton Sawyer, Ron Buckmire

Journal of Humanistic Mathematics

In this article, we discuss an autobiographical writing assignment that we call an “automathography” which can be used in different types of mathematics and mathematics education courses, and by extension, in other disciplines as well. This assignment can enhance student-instructor interactions, develop student communication skills, and provide outlets for student creativity by leveraging the lived experiences of students. We have deployed the assignment in different kinds of classes (general education [service] courses and major-only seminars) at different kinds of institutions (a private, open-admission, large university on the East Coast and a private, highly selective, small liberal arts college on the …

Finding Your Mathematical Roots: Inclusion And Identity Development In Mathematics, Linda Mcguire

Journal of Humanistic Mathematics

This paper details a semester-long course project that has been successfully adapted for use in mathematics courses ranging from introductory level, general-education classes to advanced courses in the mathematics major. Through creating aspirational mathematical family trees and writing mathematical autobiographies, this assignment is designed to help battle belonging uncertainty, to challenge students to self-situate in relation to the history of mathematical and scientific knowledge, and to make visible a student’s developing identity in mathematics and, more broadly, in STEM.

The construction and scaffolding of the project, assignments, examples of student work, foundational readings, assessment and outcomes, and adaptation strategies for …

Gödel's Theorem In The Continuing Education Of Mathematics Teachers, Ana J. Lemes

Journal of Humanistic Mathematics

The notion of dépaysement épistémologique (epistemological disorientation) aims to capture the sense of disorientation when a learner is led to question their prior assumptions and understandings, generating uncertainty in a context in which they thought they had certain knowledge. This article describes an activity used with a group of practicing mathematics teachers in Uruguay that integrates elements of the history of mathematics related to Gödel’s incompleteness theorem, with the aim of provoking in the participants the experience of dépaysement épistémologique. Results show that several of the teachers participating in the activity felt dépaysement épistémologique, and this feeling triggered …

Our Histories, Our Values, Our Mathematics, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

Life Beyond The Horizon: The Universe Was Born In A Black Hole, Zahria Patrick

Undergraduate Research Symposium

It is a widely accepted fact that obtaining information about a black hole is a near-impossible task without being stretched like a spaghetti noodle and trapped in one due to its strong gravitational pull. If the universe exists in a black hole, however, it will mean that it could be possible to survive after crossing its inescapable borders. As surprising as all of this may seem, this theory has existed for quite a while amongst a few different physicists. One person that has shed light on and expanded people’s knowledge of this frightening theory is theoretical physicist, Nikodem Poplawski. The …

The Effect Of Variation Of N-Substituents On Oxidopyridinium Ions In (4+3) Cycloadditions, Zahria Patrick, Madison Clark

Undergraduate Research Symposium

The aim of this research project is to expand the scope of 4 + 3 cycloadduct chemistry by varying functional groups attached to the prerequisite oxidopyridinium ion for each respective cycloadduct product. While N-substitution of the pyridinium precursor is known to proceed smoothly if alkylated by a lone methyl group, we evaluated the effect a larger alkyl group would have on the overall yield of the 4 + 3 cycloadduct product.

Isobutyl triflate, generated from the known reaction between isobutyl alcohol and triflic anhydride, was reacted with ethyl 5-hydroxy-nicotinate to generate the respective N-isobutyl oxidopyridinium ion in quantitative …

Total Variation Flow In R^N Dimensions With Examples Relating To Perimeters Of Level Sets, Luis Schneegans, Victoria Shumakovich

Undergraduate Research Symposium

In this project, we explore radial solutions to the Total Variation Flow (TVF) equation with the help of the Sign Fast Diffusion Equation (SFDE) and prior results in the 1-dimensional case. Specifically for radial solutions, we derive equations and explicit solutions relating to the n-dimensional case. Lastly, we look at how level sets and (time) profiles change.

The Roaring Lion Of Berlin: The Life, Thought, And Influence Of Eugen Dühring, Arden Roy

Undergraduate Research Symposium

The life and influence of 19th-century German polymath Eugen Dühring remain but a mere footnote in the history of ideas, being primarily relegated to the status of little more than a theoretical rival to Marxism in the German socialist movement and the occasional object of Freidrich Nietzsche's rhetorical flogging. Despite the current consensus on the subject, Eugen Dühring was a scholar of vast, remarkable learnedness, contributing greatly to philosophy, economics, and the natural sciences. The aim of this talk will be to clear the fog surrounding the life and work of the controversial blind scholar and give an account of …

Etherification Of Propargylic Alcohol Using Ferrocenium Ions, Cody Amann, Sai Anvesh Bezawada, Eike B. Bauer

Undergraduate Research Symposium

Etherification of Propargylic Alcohol using Ferrocenium Ions

Cody Amann, Sai Anvesh Bezawada and Eike B. Bauer*

Department of Chemistry and Biochemistry, University of Missouri-St.Louis, MO 63121

Our research efforts are directed toward the improvement of iron-based catalyst systems. The Bauer research group recently found that the ferrocenium cation is a catalytically active in the etherification of propargylic alcohols. My research was to compare the effect of two different counteranions of the ferrocenium cation on the catalytic activity. Etherification test reactions were performed using 2-methyl-2-phenol-propargylic alcohol and n-butanol to afford the corresponding propargylic ether substitution products. The complexes used …

Determination Of Antibody Affinity For The Alzheimer’S Amyloid-Β Protein, Bree Carlton

Undergraduate Research Symposium

Alzheimer's Disease (AD) is a common form of dementia that is characterized by inflammation, loss of brain mass, and loss of motor function and memory. One of the pathological hallmarks of AD is the accumulation of Amyloid-β (Aβ) in the brain as senile plaques. Aβ is formed from a large protein called Amyloid Precursor Protein (APP) when specific enzymes cut a segment of the protein into a shorter polypeptide chain, Aβ. Different aggregation species were used in this project, specifically monomers and protofibrils. Monomers are naturally occurring and nontoxic, while protofibrils are neurotoxic and neuroinflammatory. One way that Aβ can …

Effect Of Methane Mitigation On Global Temperature Under A Permafrost Feedback, Hannah Bäck, Riley May, Divya Sree Naidu, Steffen Eikenberry

Mathematics and Statistics Student Research and Class Projects

Earth systems may fall into an undesirable system state if 1.5°C of warming is exceeded. Carbon release from substantial permafrost stocks vulnerable to near-term warming represents a positive climate feedback that may increase the risk of 1.5°C warming or greater. Methane (CH₄) is a short-lived but powerful greenhouse gas with a global warming potential 28.5 times that of carbon dioxide (CO₂) over a 100 year time span. Because permafrost thaw in the coming centuries is partly determined by the warming in the 21st century, rapid reductions in methane emissions early in the 21st century could have …

Rewilding Our Story: Using Storytelling To Combat Climate Change, Calli Lambard

Sustainability Research & Practice Seminar Presentations

Calli Lambard, WCU Office of Sustainability, Rewilding Our Story: Using Storytelling to Combat Climate Change

Analyzing The Effects Of Data Variability & Volume On Predicting Particulate Matter (Pm2.5): Insights From A Machine Learning Approach, Jada A. Macharie

Theses and Dissertations

Accurately predicting PM_2.5 concentrations are imperative to the future of public health and environmental policies. Machine learning models incorporating spatial and temporal datasets to predict PM_2.5 are often limited by data availability constraints and poor resolution satellite imagery.

On The Qualitative Analysis Of Nonlinear Q-Fractional Delay Descriptor Systems, Abdullah Yi̇ği̇t

Turkish Journal of Mathematics

In this manuscript, we obtain some sufficient conditions for a nonlinear q fractional integro singular system with constant delays to be asymptotically admissible and a nonlinear q fractional non-singular system to be asymptotically stable. We use Lyapunov-Krasovskii functionals and some inequalities to obtain these conditions. At the same time, we present some numerical examples that confirm the sufficient conditions we obtained theoretically, with their annotated solutions and graphs.

On Lyapunov-Type Inequalities For Five Different Types Of Higher Order Boundary Value Problems, Mustafa Fahri̇ Aktaş, Bariş Berkay Erçikti

Turkish Journal of Mathematics

In this paper, we establish the uniqueness and existence of the classical solution to higher-order boundary value problems. Then, we give a new Lyapunov-type inequalities for higher order boundary value problems. Our study is based on Green’s functions corresponding to the five different types of two-point boundary value problems. In addition, some applications of the obtained inequalities are given.

Globally Generated Vector Bundles On The Del Pezzo Threefold Of Degree 6 With Picard Number 2, Takuya Nemoto

Turkish Journal of Mathematics

We classify globally generated vector bundles on a general hyperplane section of P2 × P2 embedded by the Segre embedding, considering small first Chern classes c1 = (1, 1) and c1 = (2, 1).

Extremal Functions For A Singular Super-Critical Trudinger-Moser Inequality, Juan Zhao

Turkish Journal of Mathematics

In this paper, we deal with a singular super-critical Trudinger-Moser inequality on a unit ball of Rn , n ≥ 3. For any p > 1, we set λp(B) = inf u∈W1,n 0 (B),u̸≡0 ∫ B |∇u|ndx ( ∫ B |u|pdx)n/p as an eigenvalue related to the n-Laplacian. Let S be a set of radially symmetric functions. Precisely, if β ≥ 0 and α < (1 + p nβ)n−1+n/pλp(B) , then there exists a positive constant ϵ0 such that when λ ≤ 1 + ϵ0 , sup u∈W1,n 0 (B)∩S, ∫ B |∇u|ndx−α( ∫ B |u|p|x|pβdx) np ≤1 ∫ B |x|pβ ( eαn(1+ p n β)|u| n n−1 − λ Σm k=0 |αn(1 + p nβ)u n n−1 |k k! ) dx is attained, where αn = nω1/(n−1) n−1 , ωn−1 is the surface area of the unit ball in Rn . The proof is based on the method of blow-up analysis. The case λ = 0 was studied by Yang-Zhu in [38]. de Figueiredo [11] considered the case p = 2, β ≥ 0, and α = 0 in two dimension. The case λ = 0, p = n,−1 < β < 0, and α = 0 was considered by Adimurthi-Sandeep [1]. Our results extend those of the above cases.

Bmfou Pilot Project Rfc - Request For Change, Nikia Greene, Daryl Reed

Silver Bow Creek/Butte Area Superfund Site

No abstract provided.

Bmfou Pilot Project Rfc - Request For Change, Wsp Environment & Infrastructure, Inc., Nikia Greene, Daryl Reed

Silver Bow Creek/Butte Area Superfund Site

No abstract provided.

Dynamic Prognosis Prediction For Patients On Dapt After Drug-Eluting Stent Implantation: Model Development And Validation, Fang Li, Laila Rasmy, Yang Xiang, Jingna Feng, Ahmed Abdelhameed, Xinyue Hu, Zenan Sun, David Aguilar, Abhijeet Dhoble, Jingcheng Du, Qing Wang, Shuteng Niu, Yifang Dang, Xinyuan Zhang, Ziqian Xie, Yi Nian, Jianping He, Yujia Zhou, Jianfu Li, Mattia Prosperi, Jiang Bian, Degui Zhi, Cui Tao

School of Medicine Faculty Publications

BACKGROUND: The rapid evolution of artificial intelligence (AI) in conjunction with recent updates in dual antiplatelet therapy (DAPT) management guidelines emphasizes the necessity for innovative models to predict ischemic or bleeding events after drug-eluting stent implantation. Leveraging AI for dynamic prediction has the potential to revolutionize risk stratification and provide personalized decision support for DAPT management. METHODS AND RESULTS: We developed and validated a new AI-based pipeline using retrospective data of drug-eluting stent-treated patients, sourced from the Cerner Health Facts data set (n=98 236) and Optum’s de-identified Clinformatics Data Mart Database (n=9978). The 36 months following drug-eluting stent implantation were …

Eocene (50–55 Ma) Greenhouse Climate Recorded In Nonmarine Rocks Of San Diego, Ca, Usa, Adrian P. Broz, Devin Pritchard-Peterson, Diogo Spinola, Sarah Schneider, Gregory Retallack, Lucas C.R. Silva

Purdue University Libraries Open Access Publishing Fund

Nonmarine rocks in sea cliffs of southern California store a detailed record of weathering under tropical conditions millions of years ago, where today the climate is much drier and cooler. This work examines early Eocene (~ 50–55 million-year-old) deeply weathered paleosols (ancient, buried soils) exposed in marine terraces of northern San Diego County, California, and uses their geochemistry and mineralogy to reconstruct climate and weathering intensity during early Eocene greenhouse climates. These Eocene warm spikes have been modeled as prequels for ongoing anthropogenic global warming driven by a spike in atmospheric CO2. Paleocene-Eocene thermal maximum (PETM, ~ 55 Ma) kaolinitic …