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Problems and Solutions
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| Pengarang | : | Daniel H. Ullman, Daniel J. Velleman, Stan Wagon & Douglas B. West |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 132 (No. 1) |
| Halaman | : | 89-99 |
| Abstrak | : | Proposed problems, solutions, and classics should be submitted online at americanmathematicalmonthly.submittable.com/submit. Proposed problems must not be under consideration concurrently at any other journal, nor should they be posted to the internet before the deadline date for solutions. Proposed solutions to the problems below must be submitted by May 31, 2025. Proposed classics should include the problem statement, solution, and references. More detailed instructions are available online. An asterisk (*) after the number of a problem or a part of a problem indicates that no solution is currently available. |
100 Years Ago This Month in The American Mathematical Monthly
| Pengarang | : | Vadim Ponomarenko |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 132 (No. 1) |
| Halaman | : | 88 |
| Abstrak | : | Abstrak tidak tersedia. |
Launching a Data Analytics Major: How Collaboration and Agility Built a Successful Program
| Pengarang | : | Richard Forrester, Emily Marshall, Je?rey Forrester, David Richeson & Jennifer Schaefer |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 132 (No. 1) |
| Halaman | : | 77-88 |
| Abstrak | : | In this article, we share the details of Dickinson College’s journey to establish a data analytics major. Designed to provide students with the technical pro?ciency required to become a data scientist, Dickinson’s data analytics major also incorporates values of a liberal arts education, including interdisciplinary learning, critical thinking, thoughtful analysis, ef-fective communication, and ethical considerations. We describe how sustained collaboration, a detailed plan to engage the campus community, partnerships with alumni, and support from senior leaders were essential to this achievement. We also discuss the challenges and successes encountered before and after the approval of the major. |
Sports Analytics Double Take: The Need for Multiple Perspectives on Data
| Pengarang | : | Tim Chartier |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 132 (No. 1) |
| Halaman | : | 63-76 |
| Abstrak | : | The intricacies of our world often lead to nuanced data, which has signi?cant im-plications for data analysis. Data analysts must be wary of moving too quickly to ?nal con-clusions. Behind an insight might lurk initially misleading results. In the context of sports analytics, speci?cally basketball, this article demonstrates the intrinsic need for the sports an-alyst to pose a question and then prod and investigate the insights offered by the data. The article analyzes public datasets with less than a dozen data points and more than 400,000 rows of data. Further, the article offers an entryway to the ?eld of data analytics via sports. |
The Matrix Equation
| Pengarang | : | Stephan Ramon Garcia, Juganta Rajkhowa & Kuldeep Sarma |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 132 (No. 1) |
| Halaman | : | 62 |
| Abstrak | : | Abstrak tidak tersedia. |
Modeling & Optimization for Streaming Li?ening Demand
| Pengarang | : | Kobi Abayomi |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 132 (No. 1) |
| Halaman | : | 48-61 |
| Abstrak | : | Digital delivery of songs has radically changed the way people can enjoy music, the sort of music available for listening, and the manner by which rights holders are compensated for their contributions to songs. Subscribers can enjoy an unlimited potpourri of songs and sounds, uniquely free of incremental acquisition or switching costs. This shift reveals listen-ing patterns governed by af?nity, boredom, attention budgets, etc. Listening patterns can be driven instantaneously, dynamically, organically or programmatically (playlists, for example). Listening demand is in a new paradigm, with a commensurate change in revenue implications. These new listening phenomena deprecate past orthodoxy around content curation in which a listener made a single purchase of a song. This point-of-sale model is now insuf?cient: de-mand revenue is proportional to song af?nity—e.g., by how often a song is listened to within a time interval—and can be modeled as a time dependent process. We explore modeling digital on-demand demand and employ a fully Bayesian probabilistic model that: (1) yields estima-tors for multi-level effects on song demand and (2) naturally joins with multi-stage Linear Optimization scheme to optimize the same. |
Diversity, Identity, and Data
| Pengarang | : | Chad M. Topaz, Heather Z. Brooks, Unchitta Kan, Bjorn Sandstede, Christian Michael Smith |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 132 (No. 1) |
| Halaman | : | 36-47 |
| Abstrak | : | While quantitative approaches cannot replace disciplinary insights from the social sciences and humanities, they can sometimes provide new perspectives. Building on research from psychology and organizational theory, we use a mathematical framework to study the in-terplay of two group-level characteristics: diversity, de?ned as the distribution of identity char-acteristics, and shared identity, denoting the extent to which these characteristics are shared amongst individuals. Although these quantities are theoretically independent, we ?nd a strong negative correlation between them in two sample data sets, namely, principal creative contrib-utors to Hollywood hit movies and American Community Survey data on state populations. |
Yet the Riemann Zeta Function at Positive Even Integers
| Pengarang | : | Wagner Costa Filho |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 132 (No. 1) |
| Halaman | : | 35 |
| Abstrak | : | Abstrak tidak tersedia. |
Uncovering the Euclidean Geometry of Data
| Pengarang | : | Badde, Paul |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 132 (No. 1) |
| Halaman | : | 26-34 |
| Abstrak | : | Suppose you have a collection of objects in some exotic metric space and you’d like to see what they would look like if they were instead in Euclidean space. Or suppose these ob-jects aren’t even points in a metric space, they are just entities for which you have some rough, intuitive notion of distance between each pair of them—one that need not satisfy any of?cial mathematical properties like the triangle inequality. There is a linear algebraic optimization procedure called multidimensional scaling that embeds these objects in Euclidean space in a manner that approximates their original distances. This uncovers the Euclidean geometry hid-den in data. This article explores how it works and what it’s useful for, particularly in a data science context. |
An Invitation to the Euler Characteritic Transform
| Pengarang | : | Elizabeth Munch |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 132 (No. 1) |
| Halaman | : | 15-25 |
| Abstrak | : | The Euler characteristic transform (ECT) is a simple to de?ne yet powerful rep-resentation of shape. The idea is to encode an embedded shape by tracking how the Euler characteristic, a simple integer-valued topological invariant, changes as the shape is built up in a particular direction. Because the ECT has been shown to be injective on the space of embed-ded simplicial complexes, it has been used for applications spanning a range of disciplines, including plant morphology and protein structural analysis. In this survey article, we present a comprehensive overview of the Euler characteristic transform, highlighting the main idea on a simple leaf example, and surveying its key concepts, theoretical foundations, and available applications. |