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Cutting the Mobius Strip
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| Pengarang | : | Cooper Young |
| Nama Majalah/Jurnal | : | The College Mathematics Journal |
| Volume / Edisi | : | 55 (No. 2) |
| Halaman | : | 126-133 |
| Abstrak | : | Summary Using tools from algebraic topology and algebraic geometry (fundamental polygons and blowups, respectively), we prove that cutting along the center of a Möbius strip yields a cylinder. Acknowledgment I would like to thank Tadashi Tokieda for his talk, along with my friends Niven Achenjang and Nik Castro, whose conversations with me inspired this paper. I also want to thank Bailey Ray Jones and Daniel Halmrast for their help with diagrams. |
The Luckiest Strategy on Earth A Better Way to Buy Lottery Scratch-off Tickets
| Pengarang | : | Skip Garibaldi |
| Nama Majalah/Jurnal | : | The College Mathematics Journal |
| Volume / Edisi | : | 55 (No. 2) |
| Halaman | : | 117-125 |
| Abstrak | : | Lottery winner Dr. Joan Ginther, sometimes called “the luckiest woman on earth,” appeared to be pursuing a deliberate strategy in her lottery wins. Journalist Peter Mucha made a conjecture as to what her strategy might have been, and we analyze his proposal here. Using calculus, we show that the strategy proposed by Mucha is indeed better than the naive strategy. We give formulas showing how much a gambler pursuing this strategy can expect to make. |
The Weight of a Ten-Pound Bag of Potatoes
| Pengarang | : | Rus May |
| Nama Majalah/Jurnal | : | The College Mathematics Journal |
| Volume / Edisi | : | 55 (No. 2) |
| Halaman | : | 109-116 |
| Abstrak | : | The weight of a ten-pound bag of potatoes is almost certainly not exactly ten pounds. Rather, it is a random variable with a minimum of ten pounds. We investigate the distribution of these weights in the context of a renewal theorem from the theory of stochastic processes and provide a straightforward demonstration of this theorem using basic tools from calculus. |
We Can Differentiate Numbers, Too
| Pengarang | : | Timo Tossavainen, Pentti Haukkanen, Jorma K. Merikoski & Mika Mattila |
| Nama Majalah/Jurnal | : | The College Mathematics Journal |
| Volume / Edisi | : | 55 (No. 2) |
| Halaman | : | 100-108 |
| Abstrak | : | We survey the history of the arithmetic derivative and more recent advances in research on this topic. Among other things, we discuss a few generalizations of the original arithmetic derivative and some arithmetic differential equations that are related to Goldbach’s conjecture and the twin prime conjecture. Our primary purpose is to give an overview of this field, but we also aim at providing supplementary material for an introductory course on discrete mathematics or number theory. Therefore, our survey contains ten exercises. |
Extracting Pi from Chaos
| Pengarang | : | Milton F. Maritz |
| Nama Majalah/Jurnal | : | The College Mathematics Journal |
| Volume / Edisi | : | 55 (No. 2) |
| Halaman | : | 86-99 |
| Abstrak | : | We present an experimental method to find some digits of π, by extracting it from chaos generated by a quadratic polynomial. In fact, we iterate the logistic map in its chaotic regime, and show how to extract the digits of π out of those chaotic numbers. |
The Will Rogers Phenomenon and Sequential Migration
| Pengarang | : | Michael A. Jones, Allison Mocny & Jennifer Wilson |
| Nama Majalah/Jurnal | : | The College Mathematics Journal |
| Volume / Edisi | : | 55 (No. 3) |
| Halaman | : | 234-244 |
| Abstrak | : | The Will Rogers phenomenon describes when elements are moved or migrate from one set to another and the averages in both sets increase. We provide a mathematical condition for when the phenomenon occurs and when sequential migration results in the phenomenon occurring at each step for any permutation of the migrating elements. We use an example to explore other questions, including the likelihood of the phenomenon occurring and its relationship to Simpson’s paradox. |
A Guide to the Risk-Averse Gambler and Resolving the St. Petersburg Paradox Once and For All
| Pengarang | : | Amal Ibourk |
| Nama Majalah/Jurnal | : | The College Mathematics Journal |
| Volume / Edisi | : | 55 (No. 3) |
| Halaman | : | 226-234 |
| Abstrak | : | We use three kinds of computations: simulation, numeric, and symbolic, to guide risk-averse gamblers in general, and we offer particular advice on how to resolve the famous St. Petersburg paradox. |
On a Particular Particular Solution
| Pengarang | : | R. Travis Kowalski |
| Nama Majalah/Jurnal | : | The College Mathematics Journal |
| Volume / Edisi | : | 55 (No. 3) |
| Halaman | : | 215-225 |
| Abstrak | : | The usual process for solving a nonhomogeneous system of linear differential equations is to find the general complementary homogeneous solution first and then construct a particular solution from it. When can we flip the script on this process and compute a particular solution first? This paper argues this is possible when the nonhomogeneous forcing function is analytic. It presents two different series expansions for this particular particular solution using power series methods, and reveals a surprising connection to the more familiar variation of parameters formula. |
A Continuous-Time Markov Chain Model for the Spread of COVID-19
| Pengarang | : | Tim Departemen Ekonomi CSIS |
| Nama Majalah/Jurnal | : | The College Mathematics Journal |
| Volume / Edisi | : | 55 (No. 3) |
| Halaman | : | 210-214 |
| Abstrak | : | Since late 2019 the novel coronavirus, also known as COVID-19, has caused a pandemic that persists. This paper shows how a continuous-time Markov chain model for the spread of COVID-19 can be used to explain, and justify to undergraduate students, strategies now being used in attempts to control the virus. The material in the paper is written at the level of students who are taking an introductory course on the theory and applications of stochastic processes. |
Knots with Composite Colors
| Pengarang | : | Sandy Ganzell & Caroline VanBlargan |
| Nama Majalah/Jurnal | : | The College Mathematics Journal |
| Volume / Edisi | : | 55 (No. 3) |
| Halaman | : | 205-209 |
| Abstrak | : | The technique of distinguishing one knot from another by coloring arcs and applying some basic modular arithmetic is part of most standard undergraduate knot theory classes. When we study n-colorability, we are usually only interested when n is a prime number. But what if n is composite? What can we say then? |