Course of linear algebra and multidimensional geometry

Course of analytical geometry

This book is a regular textbook of analytical geometry covering vector algebra and its applications to describing straight lines, planes, and quadrics in two and three dimensions. The stress is made on vector algebra by using skew-angular coordinates and by introducing some notations and prerequisites for understanding tensors. The book is addressed to students specializing in mathematics, physics, engineering, and technologies and to students of other specialities where educational standards require learning this subject.

Course of differential geometry

This book is a textbook for the basic course of differential geometry. It is recommended as an introductory material for this subject.

Theory Building in Geometry Education: Designing and implementing a course for 12-15 year old students

If we want mathematics education to be valuable to everybody, including those who do not pursue mathematics-related careers, we need to use mathematics as a training ground for certain ways of thinking. This dissertation focuses on one aspect of mathematical thinking, namely theory building. It has three parts - unpacking what constitutes theory building, the development of a course aimed at theory building, and a qualitative description of an implementation of that course with 12 to 15-year-old students in two schools in Pune, India. The description aims to understand some of how students eng…

Principles of Differential Geometry

The present text is a collection of notes about differential geometry prepared to some extent as part of tutorials about topics and applications related to tensor calculus. They can be regarded as continuation to the previous notes on tensor calculus as they are based on the materials and conventions given in those documents. They can be used as a reference for a first course on the subject or as part of a course on tensor calculus.

Fun Problems in Geometry and Beyond

We discuss fun problems, vaguely related to notions and theorems of a course in differential geometry. This paper can be regarded as a weekend "treasure chest" supplementing the course weekday lecture notes. The problems and solutions are not original, while their relation to the course might be so.

张量代数与分析短程教程，及其在微分几何中的应用

A short course on Tensor algebra and analysis, with applications to differential geometry

本文面向研究生编写张量代数与分析短程教程，以笛卡尔坐标为起点并扩展至曲线坐标及协变、逆变形式，进而服务于曲线曲面微分几何与连续介质力学应用。