In this study, we evaluate an innovative method to improve the teaching of linear algebra. The use of peer instruction in conjunction with a seminar strategy and supported by didactic engineering is proposed as a means to facilitate the mastery of abstract concepts, the undertaking of innovative research in problem solving, and the practical…

Jordan canonical form (JCF) is one of the most important, and useful, concepts in linear algebra. Mathematics, physics, biology, science and engineering undergraduates often find the first application of real JCF in the discipline of differential equations (continuous models) to solving systems of differential equations. In this work, we apply…

This paper presents 'expert opinions' on what should be taught in a first-year linear algebra course at university; the aim is to gain a generic picture and general guiding principles for such a course. Drawing on a Delphi method, 14 university professors--called 'experts' in this study--addressed the following questions: What should be on a…

Linear algebra is a crucial part of mathematical training for engineering students and there are many problems in the application of this subject in engineering, physical, and even mathematical disciplines. In this scope, a study on the sustainability of learning this subject and how it can be improved is considered necessary. This article aims to…

We present the Active Learning tools introduced in basic mathematics courses in the Preparatory Curriculum for Engineering schools at Université Claude Bernard. Additions were introduced in the academic year 2018/2019 in Foundations of Mathematics 2, in the first year of bachelor study program. Its content are Linear Algebra (matrices, vector…

This paper aims to show how through plausible reasoning financial mathematics can be taught at the university level, the work is based on a model designed by García (2019), who created it to teach linear algebra in engineering careers, using technology, of all this model, only the design with methodological procedure is adapted. In this grade The…

The discrete Fourier series is a valuable tool developed and used by mathematicians and engineers alike. One of the most prominent applications is signal processing. Usually, it is important that the signals be transmitted fast, for example, when transmitting images over large distances such as between the moon and the earth or when generating…

We have investigated the temporal patterns of algebra (N = 606) and calculus (N = 507) introductory physics students practicing multiple basic physics topics several times throughout the semester using an online mastery homework application called science, technology, engineering, and mathematics (STEM) fluency aimed at improving basic physics…

In this article we present a didactic proposal for teaching linear algebra based on two compatible theoretical models: emergent models and mathematical modelling. This proposal begins with a problematic situation related to the creation and use of secure passwords, which leads students toward the construction of the concepts of spanning set and…

This article could be of interest to teachers of applied mathematics as well as to people who are interested in applications of linear algebra. We give a comprehensive study of linear systems from an application point of view. Specifically, we give an overview of linear systems and problems that can occur with the computed solution when the…

Beginning algebra is a gatekeeper course into the pipeline to higher mathematics courses required for respected professions in engineering, science, statistics, mathematics, education, and technology. Beginning algebra can also be a perfect storm if the necessary foundational skills are not within a student's grasp. What skills ensure beginning…

This contribution focuses on a scheme developed to characterize the level of difficulty of an examination in the course "Linear Algebra for Engineers" and on the transfer of the underlying idea to a similar scheme for examinations in the course "Analysis I for Engineers". Using these schemes, it is possible to define standards…

A study was conducted at the Technical University Berlin involving students who twice failed the written examination in the first semester course Linear Algebra for Engineers in order to better understand the reasons behind their failure. The study considered student understanding in terms of Bloom's taxonomy and the ways in which students…

This article details the application of an economic theory to the fiscal operation of a small engineering consulting firm. Nobel Prize-winning economist Wassily Leontief developed his general input-output economic theory in the mid-twentieth century to describe the flow of goods and services in the U.S. economy. We use one mathematical model that…

European cooperation is a relevant subject that contributes to building a competitive network of high education institutions. A case of teacher mobility on behalf of the Erasmus programme is presented: it considers some Operations Research topics and the development of the Lego on My Decision module. The module considers eight lecture hours in…