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Jeffrey Ehme – PRIMUS, 2024
The Miller-Rabin test is a useful probabilistic method for finding large primes. In this paper, we explain the method in detail and give three variations on this test. These variations were originally developed as student projects to supplement a course in error correcting codes and cryptography.
Descriptors: Probability, Numbers, Coding, Algorithms
Keith Brandt – PRIMUS, 2024
This paper describes a project assigned in a multivariable calculus course. The project showcases many fundamental concepts studied in a typical course, including the distance formula, equations of lines and planes, intersection of planes, Lagrange multipliers, integrals in both Cartesian and polar coordinates, parametric equations, and arc length.
Descriptors: Mathematics Instruction, Calculus, Equations (Mathematics), Design
Atmai, Rachid; Kizer-Pugh, Curtis; Shipman, Barbara A. – PRIMUS, 2023
This article is a discovery-based instructional resource for faculty to use as a capstone course or exploratory project for undergraduates who are familiar with (but not necessarily fluent in) calculus, linear algebra, complex variables, and geometry. The explorations flow from a simple change in sign: in the complex numbers a + bi, where…
Descriptors: Capstone Experiences, Mathematics Education, Majors (Students), Discovery Learning
Kirsten Doehler; Laura Taylor – PRIMUS, 2024
A project involving data related to socioeconomic indicators was administered in an introductory statistics course. As part of this project, student groups investigated a data set from the United States Department of Agriculture Food and Nutrition Service website with information on recipients of Supplemental Nutrition Assistance Program (SNAP)…
Descriptors: College Students, Statistics Education, Introductory Courses, Mathematics Education
Holley Friedlander; Jennifer Schaefer – PRIMUS, 2024
Though posters have been used as a pedagogical tool in a variety of fields, the literature suggests that the use of posters as an educational assessment tool by the mathematics community has been limited. This is unfortunate given the numerous potential benefits of a poster, including the development of oral communication skills and the ability to…
Descriptors: Student Projects, Visual Aids, Student Evaluation, Algebra
Deka, Lipika; Shereen, Peri; Wand, Jeffrey – PRIMUS, 2023
Course-based Undergraduate Research Experiences (CUREs) were originally developed by biologists to answer the call for undergraduate curriculum reform and expose more students to authentic research experiences [Wei and Woodin. 2011. Undergraduate research experiences in biology: Alternatives to the apprenticeship model. "CBE Life Sciences…
Descriptors: Undergraduate Students, Student Research, Mathematics Education, Models
Savitz, Ryan; Savitz, Fred; DiMarco, David; Hollingsworth, Blane – PRIMUS, 2020
This paper discusses a concept that we call "'m'-tile means," which are the arithmetic mean of data values that break a data set into "m"-1 equal parts. Studying "m"-tile means can engage students' critical thinking skills and demonstrate the concepts underlying commonly used measures of central tendency, and so they…
Descriptors: Mathematical Concepts, Statistics, Mathematics Instruction, Student Projects
Estabrooks, Chad; McArdle, David – PRIMUS, 2022
The design and initial implementation of a project-based directed study course in mathematical research and communication is described. The intention of the course is to expose students to the foundation of mathematical research through inquiry-based learning. Students are asked to approach an exercise in topology as though it is an open problem.…
Descriptors: Inquiry, Student Projects, Undergraduate Students, Student Research
Ethan Berkove; Ben Galluzzo – PRIMUS, 2024
This curated collection covers a selection of PRIMUS articles published over a roughly 12-year period that focus on modeling and applications. The collection includes sections on individual projects, courses with a significant modeling component, and modeling and applications in extracurricular settings and throughout the curriculum.
Descriptors: Mathematics Education, Undergraduate Study, Mathematical Models, Mathematical Applications
Matchett, Andrew – PRIMUS, 2023
This article describes five elementary statistics projects involving the COVID-19 data made available to the public in csv files by the Centers for Disease Control and Prevention. The first project examined data available at the beginning of the COVID surge in New York City in spring, 2020, and used the correlation coefficient to estimate the…
Descriptors: Statistics Education, Student Projects, COVID-19, Pandemics
Steven Greenstein; Bogdan G. Nita – PRIMUS, 2024
With this paper, we share an activity for the undergraduate mathematics classroom called "The Harp Project" that leverages the aesthetic nature of both the mathematical and the musical arts. This project was conceived as a STEAM/PBL project with the added feature that it was carried out in pieces by an entire class. Anecdotal evidence…
Descriptors: College Mathematics, Mathematics Instruction, Aesthetics, STEM Education
Oremland, Lucy S.; Szabo, Csilla – PRIMUS, 2022
In this paper, we present an overview of a series of 1-credit applied problem solving courses. The goal of these courses was to help students develop their oral and written communication skills, ability to work as a team, and general problem solving skills through preparation and participation in the Mathematical Contest in Modeling (MCM) and…
Descriptors: Interdisciplinary Approach, Problem Solving, Active Learning, Student Projects
Oremland, Lucy S. – PRIMUS, 2022
Transforming an observable phenomenon into a tractable model is a challenging process, from determining the appropriate modeling scale to making realistic simplifying assumptions. However, many modeling texts are anchored around problems that have already been synthesized into a digestible format, which inhibits an opportunity to engage students…
Descriptors: Mathematics Instruction, Mathematical Models, Biological Sciences, Interdisciplinary Approach
Koss, Lorelei – PRIMUS, 2022
In a recent article, Crider recommends ending a course with a memorable learning experience, called an epic finale, instead of a final exam. Here, we give the details of epic finales given in four mathematics courses: Discrete Mathematics, Information and Coding Theory, Real Analysis, and Complex Analysis. We describe how to reconfigure a course…
Descriptors: Mathematics Instruction, Learning Activities, Mathematics Tests, Teamwork
Jones, Leslie B.; Hopkins, Britney J. – PRIMUS, 2020
Computer programming and mathematical algorithms are natural partners in the development of programming skills, logical thought, and a deeper understanding of mathematical concepts. We present the details of a course which blends the two at the sophomore level. This course is required of our mathematics majors, but attracts mathematics minors from…
Descriptors: Mathematics Instruction, Programming, Teaching Methods, College Mathematics