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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…

Educators and policy-makers have advocated for reform of undergraduate biology education, calling for greater integration of mathematics and physics in the biology curriculum. While these calls reflect the increasingly interdisciplinary…

Computational models are invaluable in capturing the complexities of real-world biological processes. Yet, the selection of appropriate algorithms for inference tasks, especially when dealing with real-world observational data, remains a…

In this paper we describe our experience in developing curriculum courses aimed at graduate students in emerging computational fields, including biology and medical science. We focus primarily on computational data analysis and statistical…

The past decade has seen an increasing body of literature devoted to the estimation of causal effects in network-dependent data. However, the validity of many classical statistical methods in such data is often questioned. There is an…

Think-aloud interviews have been a valuable but underused tool in statistics education research. Think-alouds, in which students narrate their reasoning in real time while solving problems, differ in important ways from other types of…

While intelligent tutoring systems (ITSs) can use information from past students to personalize instruction, each new student is unique. Moreover, the education problem is inherently difficult because the learning process is only partially…

Stochastic models are highly relevant tools in science, engineering, and society. Recent work suggests emerging quantum computing technologies can substantially decrease the memory requirements for simulating stochastic models. Here we show…

Hierarchically-organized data arise naturally in many psychology and neuroscience studies. As the standard assumption of independent and identically distributed samples does not hold for such data, two important problems are to accurately…

Incremental computation aims to compute more efficiently on changed input by reusing previously computed results. We give a high-level overview of works on incremental computation, and highlight the essence underlying all of them, which we…

We introduce computational causal inference as an interdisciplinary field across causal inference, algorithms design and numerical computing. The field aims to develop software specializing in causal inference that can analyze massive…

Mathematicians have traditionally been a select group of academics that produce high-impact ideas allowing substantial results in several fields of science. Throughout the past 35 years, undergraduates enrolling in mathematics or statistics…

In recent years, the integration of gamification into educational settings has garnered significant attention as a means to enhance student engagement and learning outcomes. By leveraging gamified elements such as points and leaderboards,…

Many problems in science and engineering require making predictions based on few observations. To build a robust predictive model, these sparse data may need to be augmented with simulated data, especially when the design space is…

Quantitative methods and mathematical modeling are playing an increasingly important role across disciplines. As a result, interdisciplinary mathematics courses are increasing in popularity. However, teaching such courses at an advanced…

Counterfactual inference considers a hypothetical intervention in a parallel world that shares some evidence with the factual world. If the evidence specifies a conditional distribution on a manifold, counterfactuals may be analytically…

The original "Seven Motifs" set forth a roadmap of essential methods for the field of scientific computing, where a motif is an algorithmic method that captures a pattern of computation and data movement. We present the "Nine Motifs of…

Mathematical software systems are becoming more and more important in pure and applied mathematics in order to deal with the complexity and scalability issues inherent in mathematics. In the last decades we have seen a cambric explosion of…

Statistical science (as opposed to mathematical statistics) involves far more than probability theory, for it requires realistic causal models of data generators - even for purely descriptive goals. Statistical decision theory requires more…

Numeric simulations based on the Huygens-Fresnel method allow one to develop intuition about the behavior of coherent light in diffraction and interference experiments. They give an opportunity to numerically observe and appreciate a number…