Physical Sciences and Mathematics Commons^™

Seen With Other Eyes: A Service Learning Project For High School Mathematicians Working With Visually Impaired Learners, Özgür Akas

Journal of Humanistic Mathematics

Seen With Other Eyes (SWOE) is a community involvement project that focuses on mathematics education for the visually impaired. In this essay I describe this project, which I developed together with my students at Robert College, a private high school in Turkey, and share some of our story. In the past few years, our work was welcomed by the global mathematics education community, as a testimony to the power of social media to connect like-minded educators with one another.

Balancing Entertainment And Learning In The Popularization Of Mathematics: The Seven Light Bulbs Problem, Man Keung Siu

Journal of Humanistic Mathematics

Popularization of mathematics plays a significant role in drawing more “friends of mathematics” from the public, which is important for the healthy and prosperous development of the discipline. The issue of a suitable balance between entertainment and learning is constantly on the minds of those who put effort into this task. This article discusses this issue in the context of mathematical museums and describes a simple problem involving seven light bulbs to illustrate its main points.

To Fall In Love With Math, Do This, Susan D'Agostino

Journal of Humanistic Mathematics

In the viral New York Times essay, “To Fall in Love with Anyone, Do This,” Mandy Len Catron details an experience she and an acquaintance had as they shared responses to psychologist Arthur Aron’s thirty-six questions intended to make participants fall in love. She notes that, “we all have a narrative of ourselves that we offer up to strangers and acquaintances, but Dr. Aron’s questions make it impossible to rely on that narrative.” In this paper, we claim that we also have narratives of our relationship to mathematics that we offer up to ourselves and others. Following, we offer a …

The Humanistic Mathematics Network Journal: A Bibliographic Report, Nurullah E. Goren, Tiffany Zhu

Journal of Humanistic Mathematics

The content of the Humanistic Mathematics Network Newsletter was reviewed by Claire Skrivanos and Qingcheng Zhang in [1]. This report reviews the content of the Humanistic Mathematics Network Journal (1992-2004).

A Survey Of The Math Blogosphere, Katherine Thompson

Journal of Humanistic Mathematics

This article provides an overview of different types of mathematical blogs currently available. There are over twenty blogs highlighted, ranging from the technical to the recreational, from those sponsored by national mathematical organizations to those run by individuals--including students.

Rolling Dice On A Date, Francesca Raphael, Jennifer Switkes

Journal of Humanistic Mathematics

When a young mathematician faces the prospect of a date, all kinds of mathematics ensue. Here we explore her innovative way to keep the conversation going through rolling dice to decide which conversation starter to utilize. In the course of our exploration, we solve an interesting generating function problem.

What Makes A Theory Of Infinitesimals Useful? A View By Klein And Fraenkel, Vladimir Kanovei, Karin Katz, Mikhail Katz, Thomas Mormann

Journal of Humanistic Mathematics

Felix Klein and Abraham Fraenkel each formulated a criterion for a theory of infinitesimals to be successful, in terms of the feasibility of implementation of the Mean Value Theorem. We explore the evolution of the idea over the past century, and the role of Abraham Robinson's framework therein.

Mathematical Arguments In Favor Of Risk In Andy Weir's The Martian, Sarah C. Cobb, Jeff B. Hood

Journal of Humanistic Mathematics

In Andy Weir’s novel The Martian, the characters encounter high-stakes, life-or-death situations, in which they must make choices based on their assessment of risk and likely outcomes. They have different reactions to risky situations, based on their approaches to assessing risk and their perspectives on the stakes involved. In this paper, we examine the ways that characters in The Martian intuitively assess risk and compare them to mathematical analysis of the situations in the book.

Predicting The Next Us President By Simulating The Electoral College, Boyan Kostadinov

Journal of Humanistic Mathematics

We develop a simulation model for predicting the outcome of the US Presidential election based on simulating the distribution of the Electoral College. The simulation model has two parts: (a) estimating the probabilities for a given candidate to win each state and DC, based on state polls, and (b) estimating the probability that a given candidate will win at least 270 electoral votes, and thus win the White House. All simulations are coded using the high-level, open-source programming language R. One of the goals of this paper is to promote computational thinking in any STEM field by illustrating how probabilistic …

Mathematics, Writing, And Rhetoric: Deep Thinking In First-Year Learning Communities, Christine Von Renesse, Jennifer Digrazia

Journal of Humanistic Mathematics

Through the process of combining two seemingly unlikely bedfellows, mathematics and composition, two instructors explain how rhetoric connects the art of writing and the art of doing mathematics in an inquiry-based learning community. Combining these two courses in a learning community enables students and instructors to practice the deep thinking valued by each instructor and by a traditional liberal arts education while challenging both our and our students’ individual, disciplinary, and rhetorical conventions and beliefs. Using student writing from our course, our assignments from mathematics and composition, and survey evaluation results, we demonstrate how engaging in inquiry-based education provides unconventional …

Ways Of Relating To The Mathematics Of The Past, Michael N. Fried

Journal of Humanistic Mathematics

Historians of mathematics, by definition, look at mathematics of the past. But mathematicians, too, often look at mathematics of the past; mathematicians of the past themselves often looked very closely at mathematics of their own past. Is their relationship to the past the same as that of the historians? Is every view of the past an historical view? Indeed, is every historical view historical in the same way? Or is it possible that there are different kinds of relationships to the mathematics of the past? This paper will suggest that there are in fact a variety of such relationships. It …

Communicating Mathematics Across Time, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

Numerical Approximation Of Diffusive Capture Rates By Planar And Spherical Surfaces With Absorbing Pores, Andrew J. Bernoff, Alan E. Lindsay

All HMC Faculty Publications and Research

In 1977 Berg and Purcell published a landmark paper entitled Physics of Chemore- ception, which examined how a bacterium can sense a chemical attractant in the fluid surrounding it [H. C. Berg and E. M. Purcell, Biophys J, 20 (1977), pp. 193–219]. At small scales the attrac- tant molecules move by Brownian motion and diffusive processes dominate. This example is the archetype of diffusive signaling problems where an agent moves via a random walk until it either strikes or eludes a target. Berg and Purcell modeled the target as a sphere with a set of small circular targets (pores) that …

Decoding Book Barcode Images, Yizhou Tao

CMC Senior Theses

This thesis investigated a method of barcode reconstruction to address the recovery of a blurred and convoluted one-dimensional barcode. There are a lot of types of barcodes used today, such as Code 39, Code 93, Code 128, etc. Our algorithm applies to the universal barcode, EAN 13. We extend the methodologies proposed by Iwen et al. (2013) in the journal article "A Symbol-Based Algorithm for Decoding barcodes." The algorithm proposed in the paper requires a signal measured by a laser scanner as an input. The observed signal is modeled as a true signal corrupted by a Gaussian convolution, additional noises, …

Stormwater Capture In The Built Watershed: Fostering Public Awareness Of Water Conservation Through A Parcel-Level Approach To Stormwater Management, Benjamin Rigby

Pitzer Senior Theses

As California contends with climate change and more extreme cycles of drought and deluge, water management agencies and conservation groups are looking towards solutions to the decreasing reliability of imported water supplies. Stormwater has historically been perceived as a threat to development but when captured properly, it presents a resource that can augment local water supplies. Solutions to water supply issues in California have traditionally employed technical and centrally controlled methods for importing water, but there is a growing understanding that parcel-level capture through vegetated swales presents an opportunity for reducing the impact that development has on California’s hydrology. Vegetated …

Sustainability-Efficiency Paradox: The Efficacy Of State Energy Plans In Building A More Sustainable Energy Future, Austin Zimmerman

Pitzer Senior Theses

State energy plans are created at the request of a sitting governor or State Legislature in order to provide guidance set goals for the state’s energy sector. These plans will be critical indicators of energy trends such as the future market share of coal, natural gas, and renewables. If the future of energy in the United States is to be remotely sustainable, low-carbon policies must headline state plans. The strength of a state’s energy plan in terms of sustainability is directly related to that state’s willingness to prioritize and commit to incorporating energy sources that produce negligible carbon emissions. Questions …

Pollinator Power: Supporting Bees Through Ecoregion Specific Planting Guides, Maya Thomas

Scripps Senior Theses

The pollination of flowering crops by bees is an invaluable ecosystem service that supports biodiversity and much of the global agricultural system. Pollinators move pollen between the male structures of a plant to the female structures of a plant of the same species. This fertilizes the female plant, which then produces the next generation. This process also provides the pollinator with the nectar or pollen it needs to survive. While some plants transfer pollen through different means, the majority of plants need help from pollinators to reproduce. Depending on the means of pollination, pollination can be classified as abiotic or …

Green Looks Good On You: The Rhetoric And Moral Identity Of Conscious Consumption Blogs, Abigail O'Brien

Scripps Senior Theses

Conscious consumption blogs are at the center of a particular online community where eco-friendly products are popularized. Through the lens of these blogs, this paper analyzes discourse around identity, purchasing, sustainability, lifestyle, community, and activism, to investigate the forces at work in the conscious consumption movement and identify where there is a need for a shift towards a more political environmentalism. As an environmentalist strategy, conscious consumption disproportionately centers the consumer angle, constructing personal possessions as symbols of sustainability. Language analysis reveals strong individualistic messages about personal belief, preference, and benefit which overwhelm any sense of communal good. Instead, motivation …

Colonialism And Its Aftermaths In Vieques, Puerto Rico: How U.S. Hegemony Led To Contamination, A Superfund Site, And Local Mistrust, Kaya Mark

Scripps Senior Theses

After sixty-two years of U.S. military testing, the small Puerto Rican island of Vieques and its residents continue to fight against ongoing environmental and social effects of U.S. hegemony. Starting with the arrival of the Spanish, then with U.S. occupation and use of Vieques as a military stopover, Viequense residents are used to U.S. governmental presence on their land. Despite the military’s removal from Vieques in 2003, many local residents have a fundamental lack of trust for the U.S. government. Because of this lack of trust and transparency with U.S. governmental actions in the post- World War II period, residents …

Iterative Matrix Factorization Method For Social Media Data Location Prediction, Natchanon Suaysom

HMC Senior Theses

Since some of the location of where the users posted their tweets collected by social media company have varied accuracy, and some are missing. We want to use those tweets with highest accuracy to help fill in the data of those tweets with incomplete information. To test our algorithm, we used the sets of social media data from a city, we separated them into training sets, where we know all the information, and the testing sets, where we intentionally pretend to not know the location. One prediction method that was used in (Dukler, Han and Wang, 2016) requires appending one-hot …

Self Regulation In College-Level Mathematics Classes, Jenny Lee

HMC Senior Theses

This thesis investigates the need for improvement in mathematics education at the college level in the US regarding equitable practices in instruction. In particular, it focuses on understanding the role self-regulation can play in the classroom dynamics, and how self-regulation can be a way to empower students. Also included is a case study in an introductory linear algebra class at a liberal arts college and is meant to provide a investigation into a way of incorporating self-regulation by using self-paced assessments. Results of this study suggest a possible question to consider in reforming mathematics education for a more equitable environment …

On The Landscape Of Random Tropical Polynomials, Christopher Hoyt

HMC Senior Theses

Tropical polynomials are similar to classical polynomials, however addition and multiplication are replaced with tropical addition (minimums) and tropical multiplication (addition). Within this new construction, polynomials become piecewise linear curves with interesting behavior. All tropical polynomials are piecewise linear curves, and each linear component uniquely corresponds to a particular monomial. In addition, certain monomial in the tropical polynomial can be trivial due to the fact that tropical addition is the minimum operator. Therefore, it makes sense to consider a graph of connectivity of the monomials for any given tropical polynomial. We investigate tropical polynomials where all coefficients are chosen from …

Sequential Probing With A Random Start, Joshua Miller

HMC Senior Theses

Processing user requests quickly requires not only fast servers, but also demands methods to quickly locate idle servers to process those requests. Methods of finding idle servers are analogous to open addressing in hash tables, but with the key difference that servers may return to an idle state after having been busy rather than staying busy. Probing sequences for open addressing are well-studied, but algorithms for locating idle servers are less understood. We investigate sequential probing with a random start as a method for finding idle servers, especially in cases of heavy traffic. We present a procedure for finding the …

Evaluating Flexibility Metrics On Simple Temporal Networks With Reinforcement Learning, Hamzah I. Khan

HMC Senior Theses

Simple Temporal Networks (STNs) were introduced by Tsamardinos (2002) as a means of describing graphically the temporal constraints for scheduling problems. Since then, many variations on the concept have been used to develop and analyze algorithms for multi-agent robotic scheduling problems. Many of these algorithms for STNs utilize a flexibility metric, which measures the slack remaining in an STN under execution. Various metrics have been proposed by Hunsberger (2002); Wilson et al. (2014); Lloyd et al. (2018). This thesis explores how adequately these metrics convey the desired information by using them to build a reward function in a reinforcement learning …

An Incidence Approach To The Distinct Distances Problem, Bryce Mclaughlin

HMC Senior Theses

In 1946, Erdös posed the distinct distances problem, which asks for the minimum number of distinct distances that any set of n points in the real plane must realize. Erdös showed that any point set must realize at least &Omega(n^1/2) distances, but could only provide a construction which offered &Omega(n/&radic(log(n)))$ distances. He conjectured that the actual minimum number of distances was &Omega(n^1-&epsilon) for any &epsilon > 0, but that sublinear constructions were possible. This lower bound has been improved over the years, but Erdös' conjecture seemed to hold until in 2010 Larry Guth and Nets Hawk Katz …

Hyperthermia As A Cancer Treatment- From Theory To Practice, Graham Fullerton

CMC Senior Theses

Using iron super-paramagnetic and ferromagnetic nanoparticles composed of Fe₃O₄ molecules, scientists analyze the effectiveness and practicality of this new treatment theory, hyperthermia. The problems of magnetic particle density, isothermal barriers/cellular cooling thresholds, and nanoparticle specific targeting are addressed in this review.

Iron magnetic nanoparticles were chosen due to their relatively low biological reactivates and lack of subsequent cellular toxicity. However, there are significant heating problems associated with these magnetic nanoparticles due to their relative size and short thermal time constants or thermal half-lives. Effectively, these aforementioned issues create a phenomenon where cancerous cells, surrounded by unheated healthy …

Can A Comprehensive Transition Plan To Barefoot Running Be The Solution To The Injury Epidemic In American Endurance Runners?, Michael A. Scarlett

CMC Senior Theses

Fossils belonging to the genus Homo, dating as far back as two million years ago, exhibit uniquely efficient features suggesting that early humans had evolved to become exceptional endurance runners. Although they did not have the cushion or stability-control features provided in our modern day running shoes, our early human ancestors experienced far less of the running-related injuries we experience today. The injury rate has been estimated as high as 90% annually for Americans training for a marathon and as high as 79% annually for all American endurance runners. There is an injury epidemic in conventionally shod populations that …

The Boundedness Of The Hardy-Littlewood Maximal Function And The Strong Maximal Function On The Space Bmo, Wenhao Zhang

CMC Senior Theses

In this thesis, we present the space BMO, the one-parameter Hardy-Littlewood maximal function, and the two-parameter strong maximal function. We use the John-Nirenberg inequality, the relation between Muckenhoupt weights and BMO, and the Coifman-Rochberg proposition on constructing A₁ weights with the Hardy- Littlewood maximal function to show the boundedness of the Hardy-Littlewood maximal function on BMO. The analogous statement for the strong maximal function is not yet understood. We begin our exploration of this problem by discussing an equivalence between the boundedness of the strong maximal function on rectangular BMO and the fact that the strong maximal function maps …

Step-Selection Functions For Modeling Animal Movement -- Case Study: African Buffalo, Maia Adar

CMC Senior Theses

Understanding what factors influence wildlife movement allows landscape planners to make informed decisions that benefit both animals and humans. New quantitative methods, such as step-selection functions, provide valuable objective analyses of wildlife connectivity. This paper provides a framework for creating a step-selection function and demonstrates its use in a case study. The first section provides a general introduction about wildlife connectivity research. The second section explains the math behind the step-selection function using a simple example. The last section gives the results of a step-selection model for African buffalo in the Kavango Zambezi Transfrontier Conservation Area. Buffalo were found to …