Related papers: A case for teaching about parameters in calculus c…
These Course Notes provide an introduction to mathematical proofs for undergraduate students transitioning from computational calculus to abstract mathematics. Topics include propositional logic, proof techniques, mathematical induction,…
Convenient parameterizations of matrices in terms of vectors transform (certain classes of) matrix equations into covariant (hence rotation-invariant) vector equations. Certain recently introduced such parameterizations are tersely…
This paper frames calculus as a global, centuries-long development rather than a subject that began only with Newton and Leibniz. Drawing on ideas from Greek, Indian, Islamic, and later European mathematics, it highlights how concepts like…
University students taking introductory physics are generally successful executing mathematical procedures in context, but often struggle with the use of mathematical concepts for sense making. Physics instructors note that their students…
This article discusses how to make statistical graphics a more prominent element of the undergraduate statistics curricula. The focus is on several different types of assignments that exemplify how to incorporate graphics into a course in a…
Monte Carlo is a versatile and frequently used tool in statistical physics and beyond. Correspondingly, the number of algorithms and variants reported in the literature is vast, and an overview is not easy to achieve. In this pedagogical…
Probabilistic Circuits (PCs) have emerged as an efficient framework for representing and learning complex probability distributions. Nevertheless, the existing body of research on PCs predominantly concentrates on data-driven parameter…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
We show how any dataset of any modality (time-series, images, sound...) can be approximated by a well-behaved (continuous, differentiable...) scalar function with a single real-valued parameter. Building upon elementary concepts from chaos…
Regular expressions in an Automata Theory and Formal Languages course are mostly treated as a theoretical topic. That is, to some degree their mathematical properties and their role to describe languages is discussed. This approach fails to…
Algorithms typically come with tunable parameters that have a considerable impact on the computational resources they consume. Too often, practitioners must hand-tune the parameters, a tedious and error-prone task. A recent line of research…
Measurement uncertainty is a non trivial aspect of the laboratory component of most undergraduate physics courses. Confusion about the application of statistical tools calls for the elaboration of guidelines and the elimination of…
We discuss several ways of illustrating fundamental concepts in statistical and thermal physics by considering various models and algorithms. We emphasize the importance of replacing students' incomplete mental images by models that are…
The sequent calculus is a formalism for proving validity of statements formulated in First-Order Logic. It is routinely used in computer science modules on mathematical logic. Formal proofs in the sequent calculus are finite trees obtained…
In problem solving, understanding the problem that one seeks to solve is an essential initial step. In this paper, we propose computational methods for facilitating problem understanding through the task of recognizing the unknown in…
Uncertainty in machine learning is not generally taught as general knowledge in Machine Learning course curricula. In this paper we propose a short curriculum for a course about uncertainty in machine learning, and complement the course…
"Math is not a spectator sport." "Lecturing is educational malpractice." Slogans like these rally some mathematicians to teach classes that feature "active learning", where lecturing is eschewed for student participation. Yet as much as I…
The intention of these notes is to give a mathematical account of how I believe students could be taught to think about functional programming languages and to explain how such languages work.
In recent years, neural networks (NNs) have driven significant advances in machine learning. However, as tasks grow more complex, NNs often require large numbers of trainable parameters, which increases computational and energy demands.…
This book is an attempt to help students transform all of the concepts of quantum mechanics into concrete computer representations, which can be constructed, evaluated, analyzed, and hopefully understood at a deeper level than what is…