Related papers: Fun Problems in Geometry and Beyond

Extremal Combinatorics is among the most active topics in Discrete Mathematics, dealing with problems that are often motivated by questions in other areas, including Theoretical Computer Science and Information Theory. This paper contains a…

This paper is about Information Geometry, a relatively new subject within mathematical statistics that attempts to study the problem of inference by using tools from modern differential geometry. This paper provides an overview of some of…

In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information…

We establish fun parallels between coin-weighing puzzles and knights-and-knaves puzzles.

These lecture notes for the course APM 351 at the University of Toronto are aimed at mathematicians and physicists alike. It is not meant as an introductory course to PDEs, but rather gives an overview of how to view and solve differential…

The class of ordinary linear constant coefficient differential equations is naturally embedded into a wider class by associating differential equations to algebraic curves.

We introduce an original approach to geometric calculus in which we define derivatives and integrals on functions which depend on extended bodies in space--that is, paths, surfaces, and volumes etc. Though this theory remains to be fully…

The material of this work is aimed at mathematics educators, as well as math specialists with a keen interest in progressions. In this paper, we study the subject of arithmetic, geometric, mixed, and harmonic progressions or sequences. Some…

Diagram semigroups are interesting algebraic and combinatorial objects, several types of them originating from questions in computer science and in physics. Here we describe diagram semigroups in a general framework and extend our…

This text is a survey of derived algebraic geometry. It covers a variety of general notions and results from the subject with a view on the recent developments at the interface with deformation quantization.

A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.

Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.

We discuss the local and global problems for the equivalence of geometric structures of an arbitrary order and, in later sections, attention is given to what really matters, namely the equivalence with respect to transformations belonging…

We discuss new approaches to fundamental problems of mathematics and mathematical physics such as mathematical foundation of quantum field theory, the Riemann hypothesis, and construction of noncommutative algebraic geometry.

The paper reviews the most illustrative cases of the "peculiar/anomalous" experiences of time (and, to a lesser extent, also space) and discusses a simple algebraic geometrical model accounting for the most pronounced of them.

We distinguish the axiomatic study of proofs in geometry from study about geometry from general axioms for mathematics. We briefly report on an abuse of that distinction and its unfortunate effect on US high school education. We review a…

This is a brief review, in relatively non-technical terms, of recent advances in the theory of random field geometry. These advances have provided a collection of explicit new formulae describing mean values of a variety of geometric…

These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.

We describe algorithms based on invariant theory to solve problems on the geometry of curves, mainly those of genus 2, 3 and 4. New theoretical results building on the first author's PhD thesis are also included.

One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…