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At the University of Colorado Boulder, as part of our broader efforts to transform middle- and upper-division physics courses, we research students' difficulties with particular concepts, methods, and tools in classical mechanics,…
In many longitudinal settings, economic theory does not guide practitioners on the type of restrictions that must be imposed to solve the rotational indeterminacy of factor-augmented linear models. We study this problem and offer several…
We consider the problem of learning optimal solutions of a partially known linear optimization problem and recovering its underlying cost function where a set of past decisions and the feasible set are known. We develop a new framework,…
Our preliminary experiment examined a potential pain point with ASSIST, California's database of articulation agreements. That pain point is cross-referencing multiple articulation agreements to manually develop an optimal academic plan.…
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…
This paper presents the preliminary considerations of the application of a software to an experimental work conducted on Digital Storytelling in Mathematics, as part of the project Prin 2015 "Digital Interactive Storytelling in Mathematics:…
The engineering of machine learning systems is still a nascent field; relying on a seemingly daunting collection of quickly evolving tools and best practices. It is our hope that this guidebook will serve as a useful resource for machine…
We propose a methodology, based on machine learning and optimization, for selecting a solver configuration for a given instance. First, we employ a set of solved instances and configurations in order to learn a performance function of the…
Science about optimization methods is rapidly developing today. In machine learning, computer vision, biology, medicine, construction and in many other different areas optimization methods have vast popularity and they appear as important…
Large Language Models (LLMs) have shown remarkable performance in various natural language processing tasks but face challenges in mathematical reasoning, where complex problem-solving requires both linguistic understanding and mathematical…
How can complexity theory and algorithms benefit from practical advances in computing? We give a short overview of some prior work using practical computing to attack problems in computational complexity and algorithms, informally describe…
Here practical aspects of conducting research via computer simulations are discussed. The following issues are addressed: software engineering, object-oriented software development, programming style, macros, make files, scripts, libraries,…
This article introduces the concept of optimization learning, a methodology to design optimization proxies that learn the input/output mapping of parametric optimization problems. These optimization proxies are trustworthy by design: they…
Employing Large Language Models (LLMs) to address mathematical problems is an intriguing research endeavor, considering the abundance of math problems expressed in natural language across numerous science and engineering fields. LLMs, with…
The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…
In this work, a new multiobjective optimization algorithm called multiobjective learner performance-based behavior algorithm is proposed. The proposed algorithm is based on the process of transferring students from high school to college.…
In this paper we discuss how teaching of mathematics for middle school and high school students can be improved dramatically when motivation of concepts and ideas is done through the classical problems and the history of mathematics. This…
Creating impact in real-world settings requires artificial intelligence techniques to span the full pipeline from data, to predictive models, to decisions. These components are typically approached separately: a machine learning model is…
We consider the problem of solving a large-scale system of linear equations in a distributed or federated manner by a taskmaster and a set of machines, each possessing a subset of the equations. We provide a comprehensive comparison of two…
In the first part of this paper, we present a unified framework for analyzing the algorithmic complexity of any optimization problem, whether it be continuous or discrete in nature. This helps to formalize notions like "input", "size" and…