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Articles 1 - 6 of 6
Full-Text Articles in Other Mathematics
Math And Democracy, Kimberly A. Roth, Erika L. Ward
Math And Democracy, Kimberly A. Roth, Erika L. Ward
Journal of Humanistic Mathematics
Math and Democracy is a math class containing topics such as voting theory, weighted voting, apportionment, and gerrymandering. It was first designed by Erika Ward for math master’s students, mostly educators, but then adapted separately by both Erika Ward and Kim Roth for a general audience of undergraduates. The course contains materials that can be explored in mathematics classes from those for non-majors through graduate students. As such, it serves students from all majors and allows for discussion of fairness, racial justice, and politics while exploring mathematics that non-major students might not otherwise encounter. This article serves as a guide …
Beginner's Analysis Of Financial Stochastic Process Models, David Garcia
Beginner's Analysis Of Financial Stochastic Process Models, David Garcia
HMC Senior Theses
This thesis explores the use of geometric Brownian motion (GBM) as a financial model for predicting stock prices. The model is first introduced and its assumptions and limitations are discussed. Then, it is shown how to simulate GBM in order to predict stock price values. The performance of the GBM model is then evaluated in two different periods of time to determine whether it's accuracy has changed before and after March 23, 2020.
Teiresias, Proportions, And Sexual Pleasure, Spyros Missiakoulis
Teiresias, Proportions, And Sexual Pleasure, Spyros Missiakoulis
Journal of Humanistic Mathematics
In this short article, I claim that Teiresias, the blind prophet of Apollo, in order to answer the question of whether “in sexual intercourse the woman had a larger share of pleasure than the man did”, measured the abstract concept of sexual pleasure and acted as a present-day scholar. With the help of numerical, not geometrical, proportions, he ended up with the conclusion “a man enjoyed one-tenth of the pleasure and a woman nine-tenths”.
Mathematics Versus Statistics, Mindy B. Capaldi
Mathematics Versus Statistics, Mindy B. Capaldi
Journal of Humanistic Mathematics
Mathematics and statistics are both important and useful subjects, but the former has maintained prominence in the American education system. On the other hand, statistics is more prevalent in daily life and is an increasingly marketable subject to know. This article gives a personal history of one mathematician’s bumpy road to learning and teaching statistics. Additionally, arguments for how and why to include statistics in the K-12 and college curricula are provided.
The Document Similarity Network: A Novel Technique For Visualizing Relationships In Text Corpora, Dylan Baker
The Document Similarity Network: A Novel Technique For Visualizing Relationships In Text Corpora, Dylan Baker
HMC Senior Theses
With the abundance of written information available online, it is useful to be able to automatically synthesize and extract meaningful information from text corpora. We present a unique method for visualizing relationships between documents in a text corpus. By using Latent Dirichlet Allocation to extract topics from the corpus, we create a graph whose nodes represent individual documents and whose edge weights indicate the distance between topic distributions in documents. These edge lengths are then scaled using multidimensional scaling techniques, such that more similar documents are clustered together. Applying this method to several datasets, we demonstrate that these graphs are …
Monte Carlo Approx. Methods For Stochastic Optimization, John Fowler
Monte Carlo Approx. Methods For Stochastic Optimization, John Fowler
Pomona Senior Theses
This thesis provides an overview of stochastic optimization (SP) problems and looks at how the Sample Average Approximation (SAA) method is used to solve them. We review several applications of this problem-solving technique that have been published in papers over the last few years. The number and variety of the examples should give an indication of the usefulness of this technique. The examples also provide opportunities to discuss important aspects of SPs and the SAA method including model assumptions, optimality gaps, the use of deterministic methods for finite sample sizes, and the accelerated Benders decomposition algorithm. We also give a …