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Two vectors in $\BZ^3$ are called \emph{twins} if they are orthogonal and have the same length. The paper describes twin pairs using cubic lattices, and counts the number of twin pairs with a given length. Integers $M$ with the property…
An important step in learning to use math in science is learning to see physics equations as not just calculational tools, but as ways of expressing fundamental relationships among physical quantities, of coding conceptual information, and…
Student performance of virtual introductory physics class (calculus-based mechanics) is analyzed. A fully web-enhanced class was done synchronously. The analysis is done in two categories, averaging all mid-exams (or chapter exams) and…
Traditionally, Electromagnetism is taught following the chronological development of the matter. The final product of this path is a presentation of Electromagnetism realized by adding one layer over another with the risk of transferring…
Without the use of cameras to record 2D motion and an appropriate analysis tool, creating a laboratory activity for students to experience the vector nature of momentum can be challenging. Even with appropriate measurement tools, it is…
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…
Students' difficulties in quantum mechanics may be the result of unproductive framing rather than a fundamental inability to solve the problems or misconceptions about physics content. Using the theoretical lens of epistemological framing,…
Symbolic equations are one of the many representations used in physics. Understanding these representations is important for students because they are how students access knowledge in physics. In this paper I build off of the work by Redish…
Weak measurements have an increasing number of applications in contemporary quantum mechanics. They were originally described as a weak interaction that slightly entangled the translational degrees of freedom of a particle to its spin,…
We analyze the problem solving strategies of physics professors in a case where their physical intuition fails. A non-intuitive introductory-level problem was identified and posed to twenty physics professors. The problem placed the…
We examine the relationship between homework completion and exam performance for students having different physics aptitudes for five different semesters of an introductory electricity and magnetism course. In our analysis, we plot exam…
We describe student difficulties in applying the superposition principle in combination with Gauss's law. We addressed these difficulties by developing a tutorial that uses guided inquiry. Students who used this tutorial following…
This study investigates how Learning Assistants (LAs) and related course features are associated with inequities in student learning in introductory university physics courses. 2,868 physics students' paired pre- and post-test scores on…
This paper is a modern exposition of old ideas. The setting is a Euclidian space $E$ of dimension $n$ with associated vector space $V$ of dimension $n$. A (non-zero) sliding vector is a vector in $V$ that is free to move, but only within a…
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…
We discuss the categorization of 20 quantum mechanics problems by physics professors and undergraduate students from two honors-level quantum mechanics courses. Professors and students were asked to categorize the problems based upon…
Helping students learn to think like a physicist is an important goal of many introductory physics courses. One characteristic distinguishing more experienced physicists from novice students is that they make better use of problem solving…
In this contribution three-loop QCD corrections to current correlators are considered. The application of the large momentum procedure, which provides a systematic expansion in $(m^2/q^2)^n$, allows the computation of terms up to $n=6$ for…
Interest has focussed recently on low energy implications of a nontrivial scale invariant sector of an effective field theory with an IR fixed point, manifest in terms of ``unparticles'' with peculiar properties. If unparticle stuff exists…
Motivated by a model in quantum computation we study orthogonal sets of integral vectors of the same norm that can be extended with new vectors keeping the norm and the orthogonality. Our approach involves some arithmetic properties of the…