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In an Introductory Physics for Life Science (IPLS) course that leverages authentic biological examples, student ideas about entropy as "disorder" or "chaos" come into contact with their ideas about the spontaneous formation of organized…

Representations of quantum computations are almost always based on a tensor product $\otimes$-structure. This coincides with what we are able to execute in our experiments, as well as what we observe in Nature, but it makes certain familiar…

A new understanding of adversarial examples and adversarial robustness is proposed by decoupling the data generator and the label generator (which we call the teacher). In our framework, adversarial robustness is a conditional concept---the…

The process of constructing knowledge is typically taught to students by having them reproduce established results (e.g., homework problems). An alternative pedagogical strategy is to illustrate this process using an open problem, such as…

Covariational reasoning -- reasoning about how changes in one quantity relate to changes in another quantity -- has been examined extensively in mathematics education research. Little research has been done, however, on covariational…

Contribution: We demonstrate that it is feasible to include field specific problems in introductory mathematics courses to motivate engineering students. This is done in a way that still allows large parts of the course to be common to all…

In this paper, we tackle the problem of incrementally learning a classifier, one example at a time, directly on chip. To this end, we propose an efficient hardware implementation of a recently introduced incremental learning procedure that…

Additive regression models have a long history in multivariate nonparametric regression. They provide a model in which each regression function depends only on a single explanatory variable allowing to obtain estimators at the optimal…

Lecture notes used as part of a graduate-level Introduction to Solid State Physics course at Cornell University. I attempt to unify and update the discussion of magnetism and superconductivity relative to standard textbook treatments, and…

Physics education researchers have developed many evidence-based instructional strategies to enhance physics students' conceptual learning. These strategies have historically been tested using assessments such as the Force Concept Inventory…

A general theory of the beam interaction with small discontinuities of the vacuum chamber is developed taking into account the reaction of radiated waves back on the discontinuity. The reactive impedance calculated earlier is reproduced as…

While reinforcement learning has made great improvements, state-of-the-art algorithms can still struggle with seemingly simple set-point feedback control problems. One reason for this is that the learned controller may not be able to excite…

An application design is offered, which students of physics can use when authoring a solver for mechanical systems with constraints. A 'chainlist' concept is introduced to capture a constrained mechanical system configuration and to pass…

This paper introduces two forms of modular inverses and proves their reciprocity formulas respectively. These formulas are then applied to formulate new and generalized algorithm for computing these modular inverses. The same algorithm is…

This study introduces a procedure to obtain general expressions, $y = f(x)$, subject to linear constraints on the function and its derivatives defined at specified values. These constrained expressions can be used describe functions with…

Set up a charged rectangular-plate capacitor in a uniform $\mathbf{B}$-field. Quasi-statically turn off the $\mathbf{B}$-field - what happens? We show that this seemingly simple induction problem (which appears in a famous undergraduate…

The concept of effective resistance, originally introduced in electrical circuit theory, has been extended to the setting of graphs by interpreting each edge as a resistor. In this context, the effective resistance between two vertices…

We present a coinductive framework for defining and reasoning about the infinitary analogues of equational logic and term rewriting in a uniform, coinductive way. The setup captures rewrite sequences of arbitrary ordinal length, but it has…

Some formulas and speculations are presented relative to integrable systems and quantum mechanics.

We extend the notion of memristive systems to capacitive and inductive elements, namely capacitors and inductors whose properties depend on the state and history of the system. All these elements show pinched hysteretic loops in the two…