相关论文: Elements of Linear and Real Analysis

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…

A short introduction to the mathematical methods and technics of differential algebras and modules adapted to the problems of mathematical and theoretical physics is presented.

This is an introduction to advanced linear algebra, with emphasis on geometric aspects, and with some applications included too. We first review basic linear algebra, notably with the spectral theorem in its general form, and with the…

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 course on Feynman integrals starts from the basics, requiring only knowledge from special relativity and undergraduate mathematics. Topics from quantum field theory and advanced mathematics are introduced as they are needed. The course…

This monograph, written for educational purposes, serves as an introduction to the concept of integrability as it applies to systems of differential equations (both ordinary and partial) as well as to vector-valued fields. The general cases…

Our introductory classes in statistics and data science use too much mathematics. The key causal effect which our students want our classes to have is to improve their future performance and opportunities. The more professional their…

The a priori analysis (APA) is discussed as a tool to assess the reliability of grades in standard curricular courses. This unusual, but striking application is presented when teaching the section on data treatment of a Laboratory Course to…

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 is the first installment of an exposition of an ACL2 formalization of elementary linear algebra, focusing on aspects of the subject that apply to matrices over an arbitrary commutative ring with identity, in anticipation of a future…

This note highlights the key aspects of the Feichtinger algebra $\mathbf{S}_{0}(\mathbb{R})$ on the real line for non-experts.

These lecture notes provide an introduction to the theory and application of symmetry methods for ordinary differential equations, building on minimal prerequisites. Their primary purpose is to enable a quick and self-contained approach for…

Multilayered artificial neural networks are becoming a pervasive tool in a host of application fields. At the heart of this deep learning revolution are familiar concepts from applied and computational mathematics; notably, in calculus,…

Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic…

Data science is an emerging interdisciplinary field that combines elements of mathematics, statistics, computer science, and knowledge in a particular application domain for the purpose of extracting meaningful information from the…

Since the subject of noncommutative geometry is now entering maturity, we felt there is need for presentation of the material at an undergraduate course level. Our review is a zero order approximation to this project. Thus, the present…

This monograph aims at providing an introduction to key concepts, algorithms, and theoretical results in machine learning. The treatment concentrates on probabilistic models for supervised and unsupervised learning problems. It introduces…

This study explores how pre- and post-assessments shape learning outcomes in an Introductory Real Analysis course. Pre-assessments act as learning roadmaps, highlighting prior knowledge and guiding student focus, while post-assessments…

This textbook is an introduction to economic networks, intended for students and researchers in the fields of economics and applied mathematics. The textbook emphasizes quantitative modeling, with the main underlying tools being graph…

This is a brief introduction to the world of Noncommutative Algebra aimed at advanced undergraduate and beginning graduate students.