Related papers: Blending Mathematical and Physical Negative-ness
Computer experiments refer to the study of real systems using complex simulation models. They have been widely used as alternatives to physical experiments. Design and analysis of computer experiments have attracted great attention in past…
Trying to be effective (no matter who exactly and in what field) a person face the problem which inevitably destroys all our attempts to easily get to a desired goal. The problem is the existence of some insuperable barriers for our mind,…
Student learning of sound waves can be helped through the creation of group-learning classroom materials whose development and design rely on explicit investigations into student understanding. We describe reasoning in terms of sets of…
In the mentor-student communication process, students often struggle to receive prompt and clear guidance from their mentors, making it challenging to determine their next steps. When mentors don't respond promptly, it can lead to student…
This article seeks to encourage a mathematical dialog regarding a possible solution to Beals Conjecture. It breaks down one of the worlds most difficult math problems into laymans terms and encourages people to question some of the most…
Machine-learning methods are gradually being adopted in a wide variety of social, economic, and scientific contexts, yet they are notorious for struggling with exact mathematics. A typical example is computer algebra, which includes tasks…
As dynamic and control systems become more complex, relying purely on numerical computations for systems analysis and design might become extremely expensive or totally infeasible. Computer algebra can act as an enabler for analysis and…
Computation is intertwined with essentially all aspects of physics research and is invaluable for physicists' careers. Despite its disciplinary importance, integration of computation into physics education remains a challenge and, moreover,…
We develop objective linear algebra in a new setting with a cardinality functor that can take negative values. The signs arise as little homotopies, as ratios between orientations. To illustrate the workings of the theory we give an…
Mathematical reasoning recently has been shown as a hard challenge for neural systems. Abilities including expression translation, logical reasoning, and mathematics knowledge acquiring appear to be essential to overcome the challenge. This…
We give an overview of our philosophy of pictures in mathematics. We emphasize a bi-directional process between picture language and mathematical concepts: abstraction and simulation. This motivates a program to understand different…
While proof is a central component of postsecondary mathematical study, proof construction has historically posed significant difficulties for students who intend to earn mathematics degrees at the undergraduate level. This work is…
Computation, the use of a computer to solve, simulate, or visualize a physical problem, has revolutionized how physics research is done. Computation is used widely to model systems, to simulate experiments, and to analyze data. Yet, in most…
Field theory is an area in physics with a deceptively compact notation. Although general purpose computer algebra systems, built around generic list-based data structures, can be used to represent and manipulate field-theory expressions,…
In this work, we address the question of how to enhance signal-agnostic searches by leveraging multiple testing strategies. Specifically, we consider hypothesis tests relying on machine learning, where model selection can introduce a bias…
Assessments are usually thought of as ways for instructors to get information from students. In this work, we flip this perspective and explore how assessments communicate information to students. Specifically, we consider how assessments…
Algebraic effects are computational effects that can be described with a set of basic operations and equations between them. As many interesting effect handlers do not respect these equations, most approaches assume a trivial theory,…
Traditionally, scholars in physics education research pay attention to students solving well-structured learning activities, which provide restricted room for collaboration and idea-generation due to their close-ended nature. In order to…
Models of physical systems are used to explain and predict experimental results and observations. When students encounter discrepancies between the actual and expected behavior of a system, they revise their models to include the newly…
We propose neural-symbolic integration for abstract concept explanation and interactive learning. Neural-symbolic integration and explanation allow users and domain-experts to learn about the data-driven decision making process of large…