Related papers: Designing Problems for Improved Instruction and Le…
Curriculum learning is a class of training strategies that organizes the data being exposed to a model by difficulty, gradually from simpler to more complex examples. This research explores a reverse curriculum generation approach that…
In this article we describe special type of mathematical problems that may help develop teaching methods that motivate students to explore patterns, formulate conjectures and find solutions without only memorizing formulas and procedures.…
The area of inverse problems in mathematics is highly interdisciplinary. In various fields of science, engineering, medicine, and industry, there arises a need to reconstruct information about unknown entities that cannot be directly…
Transformers can learn to perform numerical computations from examples only. I study nine problems of linear algebra, from basic matrix operations to eigenvalue decomposition and inversion, and introduce and discuss four encoding schemes to…
Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
Curriculum learning (CL) - ordering training data from easy to hard - has become a popular strategy for improving reasoning in large language models (LLMs). Yet prior work employs disparate difficulty metrics and training setups, leaving…
This dissertation focuses on the design and the implementation of domain-specific compilers for linear algebra matrix equations. The development of efficient libraries for such equations, which lie at the heart of most software for…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
In this paper, we tackle the problem of automatically generating algorithms for linear algebra operations by taking advantage of problem-specific knowledge. In most situations, users possess much more information about the problem at hand…
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…
Linear systems are the bedrock of virtually all numerical computation. Machine learning poses specific challenges for the solution of such systems due to their scale, characteristic structure, stochasticity and the central role of…
Making new methods for quantum problems often relies on using basic operations in linear algebra. Often these routines are hidden behind well-known libraries that have been optimized over decades. Attempting to improve on those basic…
We assess the situation of our elementary Linear Algebra classes in the US holistically and through personal history recollections. Possible remedies for our elementary Linear Algebra's teaching problems are discussed and a change from…
This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…
This material provides thorough tutorials on some optimization techniques frequently used in various engineering disciplines, including convex optimization, linearization techniques and mixed-integer linear programming, robust optimization,…
The linear inverse problem is fundamental to the development of various scientific areas. Innumerable attempts have been carried out to solve different variants of the linear inverse problem in different applications. Nowadays, the rapid…
A pedagogical approach of problem-based learning with embedded librarianship in several undergraduate mathematics courses is implemented in this educational research. The students are assigned to work on several projects on various…
Due to the remarkable language understanding and generation abilities of large language models (LLMs), their use in educational applications has been explored. However, little work has been done on investigating the pedagogical ability of…
This document presents a series of open questions arising in matrix computations, i.e., the numerical solution of linear algebra problems. It is a result of working groups at the workshop Linear Systems and Eigenvalue Problems, which was…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…