Related papers: Mechanics and special relativity: tutorial problem…
We introduce EXAMS-V, a new challenging multi-discipline multimodal multilingual exam benchmark for evaluating vision language models. It consists of 20,932 multiple-choice questions across 20 school disciplines covering natural science,…
This is lecture notes on the course "Stochastic Processes". In this format, the course was taught in the spring semesters 2017 and 2018 for third-year bachelor students of the Department of Control and Applied Mathematics, School of Applied…
Problem Roulette (PR) is a web-based study service at the University of Michigan that offers random-within-topic access to a large library of past exam problems in introductory physics courses. Built on public-private cloud computing…
Navigating the complexities of physics reasoning has long been a difficult task for Large Language Models (LLMs), requiring a synthesis of profound conceptual understanding and adept problem-solving techniques. In this study, we investigate…
Apart from an account of classical preliminaries, this volume contains a systematic introduction to Sobolev spaces and functions of bounded variation with selected applications. This is installment III of a four part discussion of certain…
During the last decade we have witnessed an impressive development in so-called interpreted languages and computational environments such as Maple, Mathematica, IDL, Matlab etc. Problems which until recently were typically solved on…
A primary goal of science and engineering (S & E) education is to produce good problem solvers, but how to best teach and measure the quality of problem-solving remains unclear. The process is complex, multifaceted, and not fully…
In the first Lecture, the Big Bang and the Standard Model of particle physics are introduced, as well as the structure of the latter and open issues beyond it. Neutrino physics is discussed in the second Lecture, with emphasis on models for…
When education researchers describe newly developed curricular materials, they typically concentrate on the research base behind their design, and the efficacy of the final products, but do not highlight the initial stages of creating the…
The research presented in this thesis was motivated by the need to improve introductory physics courses. Introductory physics courses are generally the first courses in which students learn to create models to solve complex problems.…
Machine learning techniques have emerged as powerful tools to tackle various challenges. The integration of machine learning methods with Physics has led to innovative approaches in understanding, controlling, and simulating physical…
This paper outlines a deceptively complex problem in classical mechanics which the paper names the "Falling Astronaut Problem," and it explores a method for teachers to implement this problem in an undergraduate classroom. The paper…
A survey was developed to probe student understanding of quantum mechanics at the beginning of graduate instruction. The survey was administered to 202 physics graduate students enrolled in first-year quantum mechanics courses from seven…
Large Language Models (LLMs) have achieved remarkable progress on advanced reasoning tasks such as mathematics and coding competitions. Meanwhile, physics, despite being both reasoning-intensive and essential to real-world understanding,…
This is an extended version of a talk on October 4, 2004 at the research seminar ``Differential geometry and applications'' (headed by Academician A. T. Fomenko) at Moscow State University. The paper contains an overview of available (but…
Most students struggle when faced with complex and ill-structured tasks because the strategies taught in schools and universities simply require finding and applying the correct formulae or strategy to answer well-structured, algorithmic…
Several N-body problems in ordinary (3-dimensional) space are introduced which are characterized by Newtonian equations of motion (``acceleration equal force;'' in most cases, the forces are velocity-dependent) and are amenable to exact…
This paper is a tutorial for eigenvalue and generalized eigenvalue problems. We first introduce eigenvalue problem, eigen-decomposition (spectral decomposition), and generalized eigenvalue problem. Then, we mention the optimization problems…
Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…
We describe how graduate students categorize introductory mechanics problems based on the similarity of their solutions. Graduate students were asked at the end of a teaching assistant training class to categorize problems from their own…