Square Matrices Associated to Mixing Problems ODE Systems

In this chapter, mixing problems are considered since they always lead to linear ordinary differential equation (ODE) systems, and the corresponding associated matrices have different structures that deserve to be studied deeply. This structure depends on whether or not there is recirculation of fluids and if the system is open or closed, among other characteristics such as the number of tanks and their internal connections. Several statements about the matrix eigenvalues are analyzed for different structures, and also some questions and conjectures are posed. Finally, qualitative remarks about the differential equation system solutions and their stability or asymptotical stability are included

Data Simulation and Trend Removal Optimization Applied to Electrochemical Noise

A well-known technique, electrochemical noise analysis (ENA), measures the potential fluctuations produced by kinetic variations along the electrochemical corrosion process. This practice requires the application of diverse signal processing methods. Therefore, in order to propose and evaluate new methodologies, it is absolutely necessary to simulate signals by computer data generation using different algorithms. In the first approach, data were simulated by superimposing Gaussian noise to nontrivial trend lines. Then, several methods were assessed by using this set of computer-simulated data. These results indicate that a new methodology based on medians of moving intervals and cubic splines interpolation show the best performance. Nevertheless, relative errors are acceptable for the trend but not for noise. In the second approach, we used artificial intelligence for trend removal, combining an interval signal processing with backpropagation neural networks. Finally, a non-Gaussian noise function that simulates non-stationary pits was proposed and all detrending methods were re-evaluated, resulting that when increasing difference between trend and noise, the accuracy of the artificial neural networks (ANNs) was reduced. In addition, when polynomial fitting, moving average removal (MAR) and moving median removal (MMR) were evaluated, MMR yielded best results, though it is not a definitive solution

Teaching and Learning of Calculus

Mathematics Education; Learning & Instructio

Inverse Modeling Problems in Task Enrichment for STEM Courses

Problem solving is considered as one of the most important topics in STEM (science, technology, engineering, and mathematics) education, and this is especially relevant when problems require modeling skills in order to be solved. Also, it should be noted that in many branches of science and technology, typical problems are posed in an inverse form. Then, combining both characteristics, the so-called inverse modeling problems deserve to be studied deeply, particularly in their potential for task enrichment. For those reasons, since 2016, a research project was carried out, by using inverse modeling problems to develop prospective teacher’s task enrichment skills. The results of this experience that took place in 2017 showed nine different groups of proposals where only few participants were very creative, whereas many others posed trivial problems or simply imitated examples analyzed previously. After that, a new research design was proposed during 2018 and implemented during the first months of 2019, with the aim of avoiding—or at least attenuating—those difficulties observed in the previous fieldwork. The new results showed interesting differences and few similarities when compared with the other experience. In this chapter, both experiences are analyzed, and lastly, findings and final conclusions are reported

Teaching and Learning of Calculus

Mathematics Education; Learning & Instructio

About the Notion of Inverse Problem in STEM Education

Inverse problems play an important role in STEM disciplines; although this concept is not well-defined in STEM education. For instance, Mason considers inversion as ‘undoing’, whereas Keller observes that if two problems are inverses of one another, then one of them has been studied extensively, while the other is newer and the former is called ‘direct’, while the latter is called ‘inverse’. Groetsch observes that if y is the effect of a given cause x when a mathematical model K is posited (Kx=y), then, two inverse problems arise: causation (given K and y, determine x) and model identification or specification (given x and y, determine K). This last view is an adaptation of the IPO-model, taught in Computer Science. During the last 5 years, we designed and put in practice and experience based-on inverse problems and their utilization in teachers training courses. This area is strongly connected with active learning, since as Kaur observed, an effective mathematics instruction begins when the instructors take the role of designers with the aim of facilitate active learning activities. In this chapter, we reflect on these experiences to construct a wider theoretical framework for inverse problems in STEM education

The 13th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics

Ngā mihi aroha ki ngā tangata katoa and warm greetings to you all. Welcome to Herenga Delta 2021, the Thirteenth Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics. It has been ten years since the Volcanic Delta Conference in Rotorua, and we are excited to have the Delta community return to Aotearoa New Zealand, if not in person, then by virtual means. Although the limits imposed by the pandemic mean that most of this year’s 2021 participants are unable to set foot in Tāmaki Makaurau Auckland, this has certainly not stopped interest in this event. Participants have been invited to draw on the concept of herenga, in Te Reo Māori usually a mooring place where people from afar come to share their knowledge and experiences. Although many of the participants are still some distance away, the submissions that have been sent in will continue to stimulate discussion on mathematics and statistics undergraduate education in the Delta tradition. The conference invited papers, abstracts and posters, working within the initial themes of Values and Variables. The range of submissions is diverse, and will provide participants with many opportunities to engage, discuss, and network with colleagues across the Delta community. The publications for this thirteenth Delta Conference include publications in the International Journal of Mathematical Education in Science and Technology, iJMEST, (available at https://www.tandfonline.com/journals/tmes20/collections/Herenga-Delta-2021), the Conference Proceedings, and the Programme (which has created some interesting challenges around time-zones), by the Local Organizing Committee. Papers in the iJMEST issue and the Proceedings were peer reviewed by at least two reviewers per paper. Of the ten submissions to the Proceedings, three were accepted. We are pleased to now be at the business end of the conference and hope that this event will carry on the special atmosphere of the many Deltas which have preceded this one. We hope that you will enjoy this conference, the virtual and social experiences that accompany it, and take the opportunity to contribute to further enhancing mathematics and statistics undergraduate education. Ngā manaakitanga, Phil Kane (The University of Auckland | Waipapa Taumata Rau) on behalf of the Local Organising Committ

Mathematical models for chemistry and biochemistry service courses

International audienceIn this paper, applications and modelling problems for chemistry and or biochemistry courses are analysed. They obtain better results than others, in order to motivate students of chemical careers towards mathematical problem solving, since these problems are specially tailored for their needs. A teaching experience, carried out during two decades is analysed and a particular example is exposed with further details. The results of this experience led us to several conclusions that are included in the last section of the article