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Computing has revolutionised the study of complex nonlinear systems, both by allowing us to solve previously intractable models and through the ability to visualise solutions in different ways. Using ubiquitous computing infrastructure, we…
Partial differential equations (PDEs) are widely used across the physical and computational sciences. Decades of research and engineering went into designing fast iterative solution methods. Existing solvers are general purpose, but may be…
We propose the first learning scheme for functional differential equations (FDEs). FDEs play a fundamental role in physics, mathematics, and optimal control. However, the numerical analysis of FDEs has faced challenges due to its…
"AI for Science" aims to solve fundamental scientific problems using AI techniques. As most physical phenomena can be described as Partial Differential Equations (PDEs) , approximating their solutions using neural networks has evolved as a…
This chapter narrates the journey of developing and integrating computing into the physics curriculum through three consecutive courses, each tailored to the learners' level. It starts with the entry-level "Physics Playground in Python" for…
We present the Deep Picard Iteration (DPI) method, a new deep learning approach for solving high-dimensional partial differential equations (PDEs). The core innovation of DPI lies in its use of Picard iteration to reformulate the typically…
We describe a course designed to help future educators build an integrated understanding of the different elements of physics education research (PER), including: research into student learning, content knowledge from the perspective of how…
This study examines the adaptation of the problem-solving studio to computer science education by combining it with pair programming. Pair programming is a software engineering practice in industry, but has seen mixed results in the…
We designed three color-coding schemes to identify related information across representations and to differentiate distinct information within a representation in slide-based instruction for calculus-based introductory mechanics. We found…
Many STEM concepts pose significant learning challenges to students due to their inherent complexity and abstract nature. Visualizing complex problems through animations can significantly enhance learning outcomes. However, the creation of…
Partial differential equations (PDEs) are used, with huge success, to model phenomena arising across all scientific and engineering disciplines. However, across an equally wide swath, there exist situations in which PDE models fail to…
Partial differential equations (PDEs) on surfaces are fundamental to scientific computing and geometry processing. A popular approach to solving PDEs on surfaces is the finite element method (FEM), where the surface is divided into discrete…
The physics informed neural network (PINN) is a promising method for solving time-evolution partial differential equations (PDEs). However, the standard PINN method may fail to solve the PDEs with strongly nonlinear characteristics or those…
Drawing appropriate diagrams is a useful problem solving heuristic that can transform a problem into a representation that is easier to exploit for solving the problem. A major focus while helping introductory physics students learn problem…
Course-based undergraduate research experiences (CUREs) increase students' access to research. This lesson plan describes an interdisciplinary CURE developed to be able to involve over 60 students per semester in original research using…
The objectives of physics laboratory courses include fostering conceptual understanding and development of several important cognitive, psycho-motor, attitudinal and affective abilities. In most of the Indian colleges and universities (and…
Pseudocode is extensively used in introductory programming courses to instruct computer science students in algorithm design, utilizing natural language to define algorithmic behaviors. This learning approach enables students to convert…
Novice programmers often struggle with problem solving due to the high cognitive loads they face. Furthermore, many introductory programming courses do not explicitly teach it, assuming that problem solving skills are acquired along the…
Large Language Models (LLMs) have shown strong performance on programming tasks, but can they generate student-like code like real students - imperfect, iterative, and stylistically diverse? We present ParaStudent, a systematic study of…
Deep learning approaches for partial differential equations (PDEs) have received much attention in recent years due to their mesh-freeness and computational efficiency. However, most of the works so far have concentrated on time-dependent…