An interactive approach for illustrating a proof of the sampling theorem using MATHEMATICA

Abstract

Learning methods in engineering education should evolve to take advantage of the progress of technology. Despite being one of the most important theorems of engineering, at undergraduate level the foundations of sampling theorem are usually oversimplified, whereas at graduate level its proof is frequently presented in the context of a rigorous mathematical framework. This paper presents an interactive approach to illustrate an amenable proof of the sampling theorem through example. Apart from its practical value as a learning tool, the proof captures some mathematical subtleties that can help to understand some more advanced concepts. The goal of this work is to show that learning the sampling theorem through an interactive example of its mathematical proof can be an enjoyable and insightful experience.

A Mathcad‐based educational experience to address the design of nonisothermal plug flow reactors

“…Over the last few years, the pedagogy of teaching engineering courses is continually advancing through the implementation of mathematical software packages, since they minimize the mathematical difficulties for students and allow teachers to devote more time addressing other engineering issues, making the course more student-friendly [4,8]. In this context, a significant number of computer-aided educational experiences by using mathematical software packages like Polymath [14,25,26], Mathcad [5,6,9,22], MATLAB [12,13,19], Maple [11,20], MATHEMATICA [2,10,15], or Excel [3,16,18,27] are found in the engineering field. Even though engineering competencies can be well acquired using any of this software, it is important to select one that does not involve an additional complexity given the limited time that can be dedicated to learning it in class [4].…”

Prospective elementary teachers’ informal mathematical proof using GeoGebra: The case of 3D shapes

“…Furthermore, a study conducted by Nyaumwe and Buzuzi (2007) focused on teachers' attitudes towards proofs in the secondary school mathematics curriculum, and the findings demonstrated that teachers expressed neutral attitudes toward technology as a method of proof. Conversely, proof using technology captures certain mathematical details that can aid in understanding some more sophisticated notions (Guerrero, 2018), but there are still limited studies focused on the use of technology in supporting students' and teachers' understanding of mathematical proofs.…”