Conceptually driven and visually rich tasks in texts and teaching practice: the case of infinite series

The study we report here examines parts of what Chevallard calls the institutional dimension of the students’ learning experience of a relatively under-researched, yet crucial, concept in Analysis, the concept of infinite series. In particular, we examine how the concept is introduced to students in texts and in teaching practice. To this purpose, we employ Duval's Theory of Registers of Semiotic Representation towards the analysis of 22 texts used in Canada and UK post-compulsory courses. We also draw on interviews with in-service teachers and university lecturers in order to discuss briefly teaching practice and some of their teaching suggestions. Our analysis of the texts highlights that the presentation of the concept is largely a-historical, with few graphical representations, few opportunities to work across different registers (algebraic, graphical, verbal), few applications or intra-mathematical references to the concept's significance and few conceptually driven tasks that go beyond practising with the application of convergence tests and prepare students for the complex topics in which the concept of series is implicated. Our preliminary analysis of the teacher interviews suggests that pedagogical practice often reflects the tendencies in the texts. Furthermore, the interviews with the university lecturers point at the pedagogical potential of: illustrative examples and evocative visual representations in teaching; and, student engagement with systematic guesswork and writing explanatory accounts of their choices and applications of convergence tests

On the use of non-canonical quantum statistics

We develop a method using a coarse graining of the energy fluctuations of an equilibrium quantum system which produces simple parameterizations for the behaviour of the system. As an application, we use these methods to gain more understanding on the standard Boltzmann-Gibbs statistics and on the recently developed Tsallis statistics. We conclude on a discussion of the role of entropy and the maximum entropy principle in thermodynamics.Comment: 29 pages, uses iopart.cls, major revisions of text for better readability, added a discussion about essentially microcanonical ensemble

Transforming a 4th year Modern Optics Course Using a Deliberate Practice Framework

We present a study of active learning pedagogies in an upper division physics course. This work was guided by the principle of deliberate practice for the development of expertise, and this principle was used in the design of the materials and the orchestration of the classroom activities of the students. We present our process for efficiently converting a traditional lecture course based on instructor notes into activities for such a course with active learning methods. Ninety percent of the same material was covered and scores on common exam problems showed a 15 % improvement with an effect size greater than 1 after the transformation. We observe that the improvement and the associated effect size is sustained after handing off the materials to a second instructor. Because the improvement on exam questions was independent of specific problem topics and because the material tested was so mathematically advanced and broad (including linear algebra, Fourier Transforms, partial differential equations, vector calculus), we expect the transformation process could be applied to most upper division physics courses having a similar mathematical base.Comment: 31 page

Teaching control with Basic Maths: Introduction to Process Control course as a novel educational approach for undergraduate engineering programs

In this article, we discuss a novel education approach to control theory in undergraduate engineering programs. In particular, we elaborate on the inclusion of an introductory course on process control during the first years of the program, to appear right after the students undergo basic calculus and physics courses. Our novel teaching proposal comprises debating the basic elements of control theory without requiring any background on advanced mathematical frameworks from the part of the students. The methodology addresses, conceptually, the majority of the steps required for the analysis and design of simple control systems. Herein, we thoroughly detail this educational guideline, as well as tools that can be used in the classroom. Furthermore, we propose a cheap test-bench kit and an open-source numerical simulator that can be used to carry out experiments during the proposed course. Most importantly, we also assess on how the Introduction to process control course has affected the undergraduate program on Control and Automation Engineering at Universidade Federal de Santa Catarina (UFSC, Brazil). Specifically, we debate the outcomes of implementing our education approach at UFSC from 2016 to 2023, considering students' rates of success in other control courses and perspectives on how the chair helped them throughout the course of their program. Based on randomised interviews, we indicate that our educational approach has had good teaching-learning results: students tend to be more motivated for other control-related subjects, while exhibiting higher rates of success.Comment: 55 pages, 13 figures, Screening at the Journal of Control, Automation and Electrical System

When holography meets coherent diffraction imaging

Modern imaging techniques at the molecular scale rely on utilizing novel coherent light sources like X-ray free electron lasers for the ultimate goal of visualizing such objects as individual biomolecules rather than crystals. Here, unlike in the case of crystals where structures can be solved by model building and phase refinement, the phase distribution of the wave scattered by an individual molecule must directly be recovered. There are two well-known solutions to the phase problem: holography and coherent diffraction imaging (CDI). Both techniques have their pros and cons. In holography, the reconstruction of the scattered complex-valued object wave is directly provided by a well-defined reference wave that must cover the entire detector area which often is an experimental challenge. CDI provides the highest possible, only wavelength limited, resolution, but the phase recovery is an iterative process which requires some pre-defined information about the object and whose outcome is not always uniquely-defined. Moreover, the diffraction patterns must be recorded under oversampling conditions, a pre-requisite to be able to solve the phase problem. Here, we report how holography and CDI can be merged into one superior technique: holographic coherent diffraction imaging (HCDI). An inline hologram can be recorded by employing a modified CDI experimental scheme. We demonstrate that the amplitude of the Fourier transform of an inline hologram is related to the complex-valued visibility, thus providing information on both, the amplitude and the phase of the scattered wave in the plane of the diffraction pattern. With the phase information available, the condition of oversampling the diffraction patterns can be relaxed, and the phase problem can be solved in a fast and unambiguous manner.Comment: 22 pages, 7 figure

EXPERIMENTAL MARKETS USING THE ELECTRONIC MARKET PLACE (EMP)

A computer system for implementing electronic markets on networks of personal computers is described. The program allows a researcher or teacher to design market simulations to meet a variety of goals, and records a complete set of market activities for analysis. Illustrations of example markets are provided, and the classroom application of market simulations in teaching agricultural economics is discussed.Computer software, Experimental economics, Simulations, Marketing,