Related papers: A First Course in Linear Algebra: Study Guide for …

This material is a rewriting and expansion of notes for beginning graduate students in seminars in combinatorics (Department of Mathematics, University of California San Diego). Solid skills in linear and multilinear algebra were required…

These are lecture notes for a 1-semester undergraduate course (in computer science, mathematics, physics, engineering, chemistry or biology) in applied categorical meta-language. The only necessary background for comprehensive reading of…

This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…

This Ph.D. thesis contains original contributions to several areas within the disciplines of disordered systems, numerical linear algebra, and scientific computing: (1) Theoretical and numerical study of the errors caused by using certain…

This is a book on elementary mathematics suitable to use in courses for first-year students of science and engineering. Students often find the formal approach to math courses rather discouraging, and demand 'rel-life applications' in order…

The main point of this paper is to present a class of equations over integers that one can check if they have a solution by checking a set of inequalities. The prototype of such equations is the equations appearing in the well-known…

This text is aimed at undergraduates, or anyone else who enjoys thinking about shapes and numbers. The goal is to encourage the student to think deeply about seemingly simple things. The main objects of study are lines, squares, and the…

Flipped classroom pedagogy is widely used in undergraduate mathematics to promote active learning, yet it remains unclear whether students experience it in systematically different ways. In this study, we analyze student perceptions from an…

We give a self-contained exposition of some mathematical aspects of the Mueller-Stokes formalism. In the first part we review some basic notions of linear algebra and establish a proper notation. In the second part we introduce the…

We unify Linear Algebra by proposing a definition of determinants via one equation that implies all known properties of them:\\ 1. Cramer's Rule,\\ 2. Cofactor expansion,\\ 3. Antisymmetry of determinants,\\ 4. Linearity of determinants,\\…

In a previous paper, we have given an algebraic model to the set of intervals. Here, we apply this model in a linear frame. We define a notion of diagonalization of square matrices whose coefficients are intervals. But in this case, with…

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…

This paper outlines our ideas on how to teach linear algebra in a mechanized mathematical environment, and discusses some of our reasons for thinking that this is a better way to teach linear algebra than the ``old fashioned way''. We…

Concise introduction to a relatively new subject of non-linear algebra: literal extension of text-book linear algebra to the case of non-linear equations and maps. This powerful science is based on the notions of discriminant…

This book introduces the mathematical foundations and techniques that lead to the development and analysis of many of the algorithms that are used in machine learning. It starts with an introductory chapter that describes notation used…

This book offers an introduction to vertex algebra based on a new approach. The new approach says that a vertex algebra is an associative algebra such that the underlying Lie algebra is a vertex Lie algebra. In particular, vertex algebras…

This is an introduction to rings and fields, written for a quarter-long undergraduate course. It includes the basic properties of ideals, modules, algebras and polynomials, the constructions of ring extensions and finite fields, some…

The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…

A generalization of the already studied transformations of the linear differential equation into a system of the first order equations is given. The proposed transformation gives possibility to get new forms of the N-dimensional system of…

The present article is an empirical study that investigates the learning situation of linear algebra. Research was performed among 60 science and engineering students from different universities in Zhejiang, Jiangsu, Hubei, and Shandong who…