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We discuss the results of using large language models (LLMs) to conduct original scientific research in an unfamiliar subject area during the Fall 2025 semester. Students in a graduate astronomy and astrophysics course were asked to test whether LLMs could help them complete research tasks faster and at a level of detail and accuracy required for scientific publication. Most students employed LLMs for a total of 5-10 hours. While all students completed a draft paper on an unsolved problem related to galaxies by semester's end, their impressions of the models' value varied. About half thought that the models saved them time. Many noted that LLMs failed to provide appropriately detailed insights or steps to addressing open, niche questions over a several-month timeframe. The LLMs also frequently (about 20% of the time) returned false citations, links, or summaries of papers. The models struggled with generating complex functional code, accessing online packages or Application Programming Interfaces (APIs), and retrieving astronomical datasets from existing archives. In writing code and in chats, the LLMs made implicit, overly simplifying assumptions and often doubled down even after

The content of the following pages was part of a special topics lecture given at the Australian National University during the first semester of 2026. That was a very nice expericence, I really enjoyed giving this 12 weeks (2 hours a week) lecture. It is meant to be self contained, starting with results on Fourier transform and Sobolev spaces. As a toy model, before treating the Navier-Stokes system, we focus on the non linear heat equation where the non linearity is polynomial. Ultimately, we prove existence and uniqueness of mild solutions of the Navier-Stokes equations in critical spaces. This script contains some exercises and the text of the mid-semester exam as well as the final exam.

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 presents both an analytical solution and a numerical approximation to the Falling Astronaut Problem and compares the educational merit of the two approaches. The analytical solution is exact; however, the derivation requires techniques that are more advanced than what is typically seen in an introductory undergraduate physics course. In contrast, the numerical approximation presents a novel application of concepts with which a first-semester undergraduate is likely to be familiar. The paper stresses the pedagogical implications of this problem, specifically the opportunity for introductory undergraduate students to learn the utility of differential equations, numerical approximations, and data spreadsheets. On a more fundamental level, the paper argues that the Falling Astronaut Problem presents an instructional opportunity for physics students to acquire a nuanced and informative lens through which to conceptualize cause and effect in the universe.

With the rapid rise of generative AI in higher education and the unreliability of current AI detection tools, developing policies that encourage student learning and critical thinking has become increasingly important. This study examines student use and perceptions of generative AI across three proof-based undergraduate mathematics courses: a first-semester abstract algebra course, a topology course and a second-semester abstract algebra course. In each case, course policy permitted some use of generative AI. Drawing on survey responses and student interviews, we analyze how students engaged with AI tools, their perceptions of generative AI's usefulness and limitations, and what implications these perceptions hold for teaching proof-based mathematics. We conclude by discussing future considerations for integrating generative AI into proof-based mathematics instruction.

Engaging in meaningful collaborations with peers, both inside and outside the classroom, can greatly enhance students' understanding of physics and other STEM disciplines. We analyzed the characteristics of women and men who typically worked alone versus those who collaborated with peers in a calculus-based introductory physics course comparing pre pandemic traditional in-person classes to Zoom based pandemic classes. We discuss our findings by considering students' prior academic preparation, their physics grades and physics self-efficacy, as well as their perceptions of how effective peer collaboration is for their physics self-efficacy. We also compared our results to the first-semester algebra-based introductory physics course.

Upper-level, undergraduate quantum mechanics (QM) is widely considered a difficult subject with many varied approaches to teaching it and considerable variation in content coverage. For example, two common approaches to undergraduate QM instruction are spins-first, which focuses on the postulates of QM in spin systems before discussing wavefunctions, and wavefunctions-first, which focuses on the Schrödinger equation and its solutions for continuous functions in various potentials before discussing spin. These different approaches, along with the content variability in the textbooks used by instructors, may mean students learn different things in QM classes across the United States (U.S.). In this paper, we offer a characterization of QM courses based on survey responses from instructors at institutions across the U.S. With the responses of 76 instructors teaching QM courses (or sequences), we present results detailing their teaching methodologies, use of pedagogical resources, and coverage of QM topics. We find that the plurality of instructors in our sample are using traditional lecture, but many instructors are using interactive lecture or another non-traditional method. Addition

Enhancing interaction and feedback collection in a first-semester computer science course poses a significant challenge due to students' diverse needs and engagement levels. To address this issue, we created and integrated a command-based chatbot on the course communication server on Discord. The DiscordBot enables students to provide feedback on course activities through short surveys, such as exercises, quizzes, and lectures, facilitating stress-free communication with instructors. It also supports attendance tracking and introduces lectures before they start. The research demonstrates the effectiveness of the DiscordBot as a communication tool. The ongoing feedback allowed course instructors to dynamically adjust and improve the difficulty level of upcoming activities and promote discussion in subsequent tutor sessions. The data collected reveal that students can accurately perceive the activities' difficulty and expected results, providing insights not possible through traditional end-of-semester surveys. Students reported that interaction with the DiscordBot was easy and expressed a desire to continue using it in future semesters. This responsive approach ensures the course me

These are the lecture notes based on [dD23] for the (upcoming) lecture "T-systems with a special emphasis on sparse moment problems and sparse Positivstellensätze" in the summer semester 2024 at the University of Konstanz. The main purpose of this lecture is to prove the sparse Positiv- and Nichtnegativstellensätze of Samuel Karlin (1963) and to apply them to the algebraic setting. That means given finitely many monomials, e.g. $1, x^2, x^3, x^6, x^7, x^9,$ how do all linear combinations of these look like which are strictly positive or non-negative on some interval $[a,b]$ or $[0,\infty)$, e.g. describe and even write down all $f(x) = a_0 + a_1 x^2 + a_2 x^3 + a_3 x^6 + a_4 x^7 + a_5 x^9$ with $f(x)>0$ or $f(x)\geq 0$ on $[a,b]$ or $[0,\infty)$, respectively. To do this we introduce the theoretical framework in which this question can be answered: T-systems. We study these T-systems to arrive at Karlin's Positiv- and Nichtnegativstellensatz but we also do not hide the limitations of the T-systems approach. The main limitation is the Curtis$-$Mairhuber$-$Sieklucki Theorem which essentially states that every T-system is only one-dimensional and hence we can only apply these resul

The current dropout rate in physics studies in Germany is about 60\%, with the majority of dropouts occurring in the first year. Consequently, the physics study entry phase poses a significant challenge for many students. Students' stress perceptions can provide more profound insights into the processes and challenges during that period. In a panel study featuring 67 measuring points involving up to 128 participants at each point, we investigated students' stress perceptions with the Perceived Stress Questionnaire (PSQ), identified underlying sources of stress, and assessed self-estimated workloads across two different cohorts. This examination occurred almost every week during the first semester, and for one cohort also in the second semester, yielding a total of 3,241 PSQ data points and 5,823 stressors. The PSQ data indicate a consistent stress trajectory across all three groups studied that is characterized by significant dynamics between measuring points, spanning from $M=20.1, SD=15.9$ to $M=63.6, SD=13.4$ on a scale from 0 to 100. Stress levels rise in the first weeks of the lecture, followed by stable, elevated stress levels until the exams and a relaxation phase afterward

Online teaching has expanded access to education, offering flexibility compared to traditional face-to-face instruction. While early research has explored online teaching, it is important to understand the perspective of instructors who conducted their first online classes during the Covid-19 pandemic. This study focuses on instructors teaching online for the first time, regardless of whether they volunteered. Surveys were conducted when universities transitioned from in-person to online instruction in April 2020, with a follow-up survey after their first online teaching semester. The study investigated instructors' expectations of class success before their first online teaching experience. Using Bayesian modeling, we analyzed how these expectations varied based on instructors' characteristics (self-efficacy in online teaching, technological proficiency, and acceptance of technology) and course attributes (subject area, class size, and instructional design). Results showed that instructors' self-efficacy significantly impacted their expectations of success, while smaller class sizes were associated with lower expectations. Interestingly, factors like prior use of technology platfo

ChatGPT is a groundbreaking ``chatbot"--an AI interface built on a large language model that was trained on an enormous corpus of human text to emulate human conversation. Beyond its ability to converse in a plausible way, it has attracted attention for its ability to competently answer questions from the bar exam and from MBA coursework, and to provide useful assistance in writing computer code. These apparent abilities have prompted discussion of ChatGPT as both a threat to the integrity of higher education and conversely as a powerful teaching tool. In this work we present a preliminary analysis of how two versions of ChatGPT (ChatGPT3.5 and ChatGPT4) fare in the field of first-semester university physics, using a modified version of the Force Concept Inventory (FCI) to assess whether it can give correct responses to conceptual physics questions about kinematics and Newtonian dynamics. We demonstrate that, by some measures, ChatGPT3.5 can match or exceed the median performance of a university student who has completed one semester of college physics, though its performance is notably uneven and the results are nuanced. By these same measures, we find that ChatGPT4's performance

Recent studies provide evidence that social constructivist pedagogical methods such as active learning, interactive engagement, and inquiry-based learning, while pedagogically more effective, can enable inequities in the classroom. By conducting a quantitative empirical examination of gender-inequitable group dynamics in two inquiry-based physics labs, we extend results of previous work. Using a survey on group work preferences and video recordings of lab sessions, we find similar patterns of gendered role-taking noted in prior studies. These results are not reducible to differences in students' preferences. We find that an intervention which employed partner agreement forms, with the goal of reducing inequities, had a positive impact on students' engagement with equipment during a first-semester lab course. Our work will inform implementation of more effective interventions in the future and emphasizes challenges faced by instructors who are dedicated to both research-based pedagogical practices and efforts to promote diversity, equity, and inclusion in their classrooms.

Students' beliefs about the extent to which meaningful others, including their peers, recognize them as a strong science student are correlated with their persistence in science courses and careers. Yet, prior work has found a gender bias in peer recognition, in which student nominations of strong peers disproportionately favor men over women, in some instructional contexts. Researchers have hypothesized that such a gender bias diminishes over time, as determined by students' academic year: studies have found a gender bias in science courses aimed at first-year students, but not in science courses aimed at beyond first-year students. This hypothesis that patterns of peer recognition change over time, however, has yet to be tested with longitudinal data--previous studies only examine snapshots of different students in different science courses. In this study, we isolate the effect of time on peer recognition by analyzing student nominations of strong peers across a two-semester introductory physics course sequence, containing the same set of students and the same instructor in both semesters, at a mostly-women institution. Using a combination of social network analysis and qualitati

Course load analytics (CLA) inferred from LMS and enrollment features can offer a more accurate representation of course workload to students than credit hours and potentially aid in their course selection decisions. In this study, we produce and evaluate the first machine-learned predictions of student course load ratings and generalize our model to the full 10,000 course catalog of a large public university. We then retrospectively analyze longitudinal differences in the semester load of student course selections throughout their degree. CLA by semester shows that a student's first semester at the university is among their highest load semesters, as opposed to a credit hour-based analysis, which would indicate it is among their lowest. Investigating what role predicted course load may play in program retention, we find that students who maintain a semester load that is low as measured by credit hours but high as measured by CLA are more likely to leave their program of study. This discrepancy in course load is particularly pertinent in STEM and associated with high prerequisite courses. Our findings have implications for academic advising, institutional handling of the freshman e

Workplaces of the future require advanced competence profiles from employees, not least due to new options for teleworking and new complex digital tools. The acquisition of advanced competence profiles is to be addressed by formal education. For example, the method of Building Information Modeling (BIM) aims at digitizing the design, construction, and operation of structures and as such requires advanced competence profiles. In this study, two educational scenarios based on teleworking and complex digital tools are compared, each with one cohort and consisting of two learning activities. The first cohort initially completes as first learning activity a semester-long course that aims at BIM domain competences. The semester-long course of the second cohort fosters meta competences, such as communication, collaboration, and digital literacy. At the end of the semester, both cohorts solve in a second learning activity a BIM practice task. Research questions are: (1) Do the two educational scenarios promote the competences to be addressed? And related: (2) What is the impact of the initial course that fosters domain competences or meta competences? Methodologically, the learning outcome

The cyclic format of the undergraduate physics curriculum depends on students' ability to recall and utilize material covered in prior courses in order to reliably build on that knowledge in later courses. However, there is evidence to suggest that people often do not retain all, or even most, of what they learned previously. How much information is retained appears to be dependent both on the individuals' approach to learning as well as the style of instruction. In particular, there is evidence to suggest that active engagement techniques in the classroom can improve students' retention of the material over time. Here, we report the findings of a longitudinal investigation of students' retention of conceptual understanding as measured by the Force and Motion Conceptual Evaluation (FMCE) following a first-semester, calculus-based introductory physics course, which features significant active engagement in both lecture and recitation. By administering the FMCE at the end of a first-semester physics course and again at the beginning of the subsequent second-semester physics course, we examine students' knowledge retention over time periods ranging from 1-15 months. We find that the s

MAROON-X is a fiber-fed, optical EPRV spectrograph at the 8-m Gemini North Telescope on Mauna Kea, Hawai'i. MAROON-X was commissioned as a visiting instrument in December 2019 and is in regular use since May 2020. Originally designed for RV observations of M-dwarfs, the instrument is used for a broad range of exoplanet and stellar science cases and has transitioned to be the second-most requested instrument on Gemini North over a number of semesters. We report here on the first two years of operations and radial velocity observations. MAROON-X regularly achieves sub-m/s RV performance on sky with a short-term instrumental noise floor at the 30 cm/s level. We will discuss various technical aspects in achieving this level of precision and how to further improve long-term performance

We present a model for competency-based grading for calculus-based introductory physics that encourages students to obtain proficiency with all course content. By allowing students to continually improve their proficiency with skills and content throughout the semester, this formative grading system is designed to create a more flexible learning environment that better accommodates the varying schedules and needs of students. While all students show improvement in their performance following the implementation of this grading system, the largest gains were found for women and first generation students, both of whom often pose a retention risk in science and engineering degree programs.