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Cody L. Patterson; Paul Christian Dawkins; Holly Zolt; Anthony Tucci; Kristen Lew; Kathleen Melhuish – PRIMUS, 2024
This article presents an inquiry-oriented lesson for teaching Lagrange's theorem in abstract algebra. This lesson was developed and refined as part of a larger grant project focused on how to "Orchestrate Discussions Around Proof" (ODAP, the name of the project). The lesson components were developed and refined with attention to how well…
Descriptors: Mathematics Instruction, Algebra, Validity, Mathematical Logic
Gabriel Gianni Cantanelli; Barbara A. Shipman – PRIMUS, 2024
Through galleries of graphs and short filmstrips, this paper aims to sharpen students' eyes for visually recognizing continuous functions. It seeks to develop intuition for what visual features of a graph continuity does and does not allow for. We have found that even students who can work correctly with rigorous definitions may not be able to…
Descriptors: Mathematics Instruction, College Mathematics, Undergraduate Study, Visual Aids
Ulrich A. Hoensch – PRIMUS, 2024
We present a concrete situation where there is a difference between the theoretical security of a cipher and its limitations when implemented in practice. Specifically, when entering a PIN, smudges on the keypad substantially reduce its security. We show how the number of possible keys in the presence of the "smudge attack" can be…
Descriptors: Information Security, Computer Security, Coding, Undergraduate Study
Melinda Lanius – PRIMUS, 2024
In this paper, I analyze the impact of culture and metaphor on cryptology education. I will compare and contrast the historically grounded metaphors of cryptology-is-warfare and encryption-is-security to a set of counter-metaphors: cryptology-is-privacy and encryption-is-communication. Using this explicit understanding of conceptual metaphor, I…
Descriptors: Figurative Language, Technology, Coding, Information Security
Joshua Holden – PRIMUS, 2024
This paper describes Alkaline, a size-reduced version of Kyber, which has recently been announced as a prototype NIST standard for post-quantum public-key cryptography. While not as simple as RSA, I believe that Alkaline can be used in an undergraduate classroom to effectively teach the techniques and principles behind Kyber and post-quantum…
Descriptors: Technology, Coding, Undergraduate Study, Algebra
Kalman, Dan – PRIMUS, 2023
In the precalculus curriculum, logistic growth generally appears in either a discrete or continuous setting. These actually feature distinct versions of logistic growth, and textbooks rarely provide exposure to both. In this paper, we show how each approach can be improved by incorporating an aspect of the other, based on a little known synthesis…
Descriptors: Mathematics Education, Calculus, Teaching Methods, Mathematical Models
T. Clark – PRIMUS, 2024
A standard element of the undergraduate ordinary differential equations course is the topic of separable equations. For instructors of those courses, we present here a series of novel modeling scenarios that prove to be a compelling motivation for the utility of differential equations. Furthermore, the growing complexity of the models leads to the…
Descriptors: Mathematics Instruction, Undergraduate Study, College Mathematics, Equations (Mathematics)
Diamond, Harvey – PRIMUS, 2023
This paper presents a series of basic computational problems that are mathematically and/or graphically appealing, and provides an idea of places one might go in trying to understand what is happening, integrating mathematics, computation, and graphics. The real point of this paper is to make a case, through those examples, for computation as an…
Descriptors: Mathematics Instruction, Computation, College Mathematics, Undergraduate Study
K. Lew; L. Guajardo; M. A. Gonzalez; K. Melhuish – PRIMUS, 2024
Proof comprehension is an important skill for students to develop in their proof-based courses, yet students are rarely afforded opportunities to develop this skill. In this paper, we describe two implementations of an activity structure that was developed to give students the opportunity to engage with complex proofs and to develop their proof…
Descriptors: Mathematical Logic, Validity, Mathematics Instruction, Mathematics Skills
George Ashline; Bret Findley; Mitchell Andrea; Dylan Wawruck – PRIMUS, 2024
We describe the components and implementation of an activity for multivariable calculus featuring applications to the field of chemistry. This activity focuses on the isobaric thermal expansion coefficient found using partial differentiation of the volume of an ideal gas with respect to temperature as pressure is held constant. Broader goals of…
Descriptors: Learning Activities, Mathematics Instruction, Calculus, Chemistry
Bagai, Shobha – PRIMUS, 2023
The article describes how to derive the equation of curves that are obtained from string art. Conversely, if the equation of a curve is given, one can find the relation between the intercepts either on a rectangular axes, skewed axis, or a circle to trace out these curves. Some of these curves can be easily traced out using the string art if they…
Descriptors: Undergraduate Study, College Mathematics, Art Activities, Mathematical Concepts
J. OShaughnessy – PRIMUS, 2024
The Mathematical Sciences Department at Shenandoah University focused on increasing the participation of women in the mathematics program by fostering a welcoming learning community and promoting double majors. Data from the past decade is presented. During this time, the program saw an increase in women undergraduate mathematics majors from 11%…
Descriptors: Females, Mathematics Education, Communities of Practice, Majors (Students)
David Faitelson; Shai Gul; Michal Arieli – PRIMUS, 2024
Exercise is essential for mastering mathematics, but it faces two major hurdles. First, students are often not motivated to do their homework. Second, checking traditional homework is a manual and labor-intensive process that becomes harder to support as the number of students increases. We argue that computer games could alleviate both problems.…
Descriptors: Mathematics Instruction, College Mathematics, Homework, Computer Games
Andriunas, R.; Boyle, B.; Lazowski, A. – PRIMUS, 2022
This paper discusses a project for linear algebra instructors interested in a concrete, geometric application of matrix diagonalization. The project provides a theorem concerning a nested sequence of tetrahedrons and scaffolded questions for students to work through a proof. Along the way students learn content from three-dimensional geometry and…
Descriptors: Algebra, Geometry, Matrices, Mathematics Instruction
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