Related papers: Teaching linear algebra at university
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…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…
The evolution of mathematics is shaped importantly by interestingness: researchers choose which problems to pursue, and students choose which problems to engage with, based on expectations of interest and challenge. As AI systems,…
Lecture notes from the mini-course "Topics in Lorentz Geometry" taught at the University of S\~{a}o Paulo, in March/2019. The text has three parts: (i) an overall view of linear algebra in the pseudo-Euclidean space $\mathbb{R}^n_\nu$, with…
Across scientific domains, a fundamental challenge is to characterize and compute the mappings from underlying physical processes to observed signals and measurements. While nonlinear neural networks have achieved considerable success, they…
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…
Machine learning has a long collaborative tradition with several fields of mathematics, such as statistics, probability and linear algebra. We propose a new direction for machine learning research: $C^*$-algebraic ML $-$ a…
Curriculum Learning - the idea of teaching by gradually exposing the learner to examples in a meaningful order, from easy to hard, has been investigated in the context of machine learning long ago. Although methods based on this concept…
Those of us who teach Mathematics for Liberal Arts (MLA) courses often underestimate the mathematical abilities of the students enrolled in our courses. Despite the fact that many of these students suffer from math anxiety and will admit to…
This book collects the lectures about graph theory and its applications which were given to students of mathematical departments of Moscow State University and Peking University. Graph theory is a very wide field with a lot of applications…
The quality of mathematics education depends largely on the quality of education in general. The main idea may be summarized as follows: in order to educate the younger generation of people to be able to meet adequately the demands of the…
We present here algorithms for efficient computation of linear algebra problems over finite fields.
One of the traditional applications of relation algebras is to provide a setting for infinite-domain constraint satisfaction problems. Complexity classification for these computational problems has been one of the major open research…
This survey describes probabilistic algorithms for linear algebra computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problem instances. The paper…
Both the basic educational contents for students and study programs for science teachers include several topics in physics and astronomy, from the simplest ones to others as advanced as nuclear fusion to explain stellar evolution and…
With the advent of computers, one needs algebraic structures that can simultaneously work with bulk data. One such algebraic structure, namely, n-linear algebras of type I are introduced in this book and its applications to n-Markov chains…
Given an associative, not necessarily commutative, ring R with identity, a formal matrix calculus is introduced and developed for pairs of matrices over R. This calculus subsumes the theory of homogeneous systems of linear equations with…
In this chapter, I discuss teaching mathematical tools specifically tailored for economics students. A typical one-semester course in this area seeks to blend a range of topics: from foundational elements of subjects such as linear algebra…
While there are numerous linear algebra teaching tools, they tend to be focused on the basics, and not handle the more advanced aspects. This project aims to fill that gap, focusing specifically on methods like Strassen's fast matrix…