Related papers: Course of analytical geometry
This text is a support for different courses of the master of Mechanics of the University Paris-Saclay. The content of this text is an introduction, for graduate students, to tensor algebra and analysis. Far from being exhaustive, the text…
An introductory overview of vector spaces, algebras, and linear geometries over an arbitrary commutative field is given. Quotient spaces are emphasized and used in constructing the exterior and the symmetric algebras of a vector space.…
Vector algebra is a powerful and needful tool for Physics but unfortunately, due to lack of mathematical skills, it becomes misleading for first undergraduate courses of science and engineering studies. Standard vector identities are…
This book is a textbook for the basic course of differential geometry. It is recommended as an introductory material for this subject.
This book is a textbook for the course of foundations of geometry. It is addressed to mathematics students in Universities and to High School students for deeper learning the elementary geometry. It can also be used in mathematics coteries…
These are lecture notes for a course on the theory of Clifford algebras, with special emphasis on their wide range of applications in mathematics and physics. Clifford algebra is introduced both through a conventional tensor algebra…
The book is designed for a semester-long course in Foundations of Geometry and meant to be rigorous, conservative, elementary and minimalist. List of topics: Euclidean geometry: The Axioms / Half-planes / Congruent triangles / Perpendicular…
Mostly aimed at an audience with backgrounds in geometry and homological algebra, these notes offer an introduction to derived geometry based on a lecture course given by the second author. The focus is on derived algebraic geometry, mainly…
This is the first paper in a series of eight where in the first three we develop a systematic approach to the geometric algebras of multivectors and extensors, followed by five papers where those algebraic concepts are used in a novel…
The article presents a new approach to euclidean plane geometry based on projective geometric algebra (PGA). It is designed for anyone with an interest in plane geometry, or who wishes to familiarize themselves with PGA. After a brief…
The traditional study of plane and space algebraic curves by looking at their tangent vectors, curvatures and torsions provides geometric, but unfortunately not sufficient information about individual curves in order to be able to…
This is a draft of a textbook on differential forms. The primary target audience is sophmore level undergraduates enrolled in what would traditionally be a course in vector calculus. Later chapters will be of interest to advaced…
We review some recent applications of machine learning to algebraic geometry and physics. Since problems in algebraic geometry can typically be reformulated as mappings between tensors, this makes them particularly amenable to supervised…
In this book, there are five chapters: Systems of Linear Equations, Vector Spaces, Homogeneous Systems, Characteristic Equation of Matrix, and Matrix Dot Product. It has also exercises at the end of each chapter above to let students…
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…
Linear Geometry studies geometric properties which can be expressed via the notion of a line. All information about lines is encoded in a ternary relation called a line relation. A set endowed with a line relation is called a liner. So,…
This is a survey article on real algebra and geometry, and in particular on its recent applications in optimization and convexity. We first introduce basic notions and results from the classical theory. We then explain how these relate to…
The purpose of this book is to build up the fundament of an Arakelov theory over adelic curves in order to provide a unified framework for the researches of arithmetic geometry in several directions.
In this article, we briefly describe various tools and approaches that algebraic geometry has to offer to straighten bent objects. Throughout this article we will consider a specific example of a bent or curved piece of paper which in our…
We present a geometrical interpretation of linear regression based on vectors in n dimensions (n the number of data points). This is to be used as a didactic tool for teachers when presenting that topic.