300 Problems in Special and General Relativity

Einstein's theories of special relativity and general relativity form a core part of today's undergraduate (or Masters-level) physics curriculum. This is a supplementary problem book or student's manual, consisting of 150 problems in each of special and general relativity. The problems, which have been developed, tested and refined by the authors over the past two decades, are a mixture of short-form and multi-part extended problems, with hints provided where appropriate. Complete solutions are elaborated for every problem, in a different section of the book; some solutions include brief discussions on their physical or historical significance. Designed as a companion text to complement a main relativity textbook, it does not assume access to any specific textbook. This is a helpful resource for advanced students, for self-study, a source of problems for university teaching assistants, or as inspiration for instructors and examiners constructing problems for their lectures, homework or exams.

Use of the video problem book in preparation of future teachers

The subject of this research is the development of professional competencies of future elementary school teachers in the process of using video problem book (based on the material of math classes). The article discusses different methods of using video materials in preparation of students. An overview of foreign research on the topic is provided. It is noted that currently the methods of using video content are not sufficiently covered in the literature. The questions of which video fragments are better to use, how to include them into the educational process, what particular tasks they pursue, etc. remain unanswered. The article describes the experience of using video problem book as technique of teaching math to students, as well as future elementary school teachers. The author analyzes the work with the video problem book, an essential element of which is the use of “stop motion” technique in a problematic spots of the lesson. The article also presents the results of comparative research of academic performance of the groups of students: an experimental group that used video problem book, and a control group that that did not use video problem book in the educational process. The author picked the following competencies: diagnostic competence of the teacher, ability to make pedagogical decisions, and reflexivity. The implementation of video problem book in the educational process develops in students and future elementary school teacher the skills to make deliberate decisions in different learning situations.

Tiling a Circular Disc with Congruent Pieces

In this note, we prove that any monohedral tiling of the closed circular unit disc with $$k \le 3$$ k ≤ 3 topological discs as tiles has a k-fold rotational symmetry. This result yields the first nontrivial estimate about the minimum number of tiles in a monohedral tiling of the circular disc in which not all tiles contain the center, and the first step towards answering a question of Stein appearing in the problem book of Croft, Falconer, and Guy in 1994.

AUTHOR AND THE CHARACTER: THE IDENTIFICATION PROBLEM (BOOK REVIEW: LEKMANOV O., SVERDLOV M., SIMANOVSKY I. VENEDIKT EROFEEV:THE OUTSIDER)

The edition of «O. Lekmanov, M. Sverdlov and I. Simanovsky for Venedikt Erofeev: The Outsider», which won the Big Book National Literary Award in 2019, is a synthesis of Venedikt Erofeev’s biography (memoirs of the contemporaries, diaries, letters) and a literary analysis of his poem Moskva-Petushki.