Algebraic topology and homotopy theory constitute central areas of contemporary mathematics, exploring spaces through algebraic invariants and continuous deformations. Techniques in this field ...

To many in the United States, advanced forms of mathematics are a terrifying maze of numbers, symbols, graphs, and hypotheticals that render our world more complex than simple observations would ...

The Earth's climate system seems to have shifted abruptly between colder and warmer modes in the past. Do we risk the same today from anthropogenic climate change? Frankly, climate models cannot ...

When students are genuinely curious about new concepts and ideas, they develop their own study skills, says Professor Pekka Pankka. Geometry, Algebra, and Topology are pure mathematics and essential ...

Visit NAP.edu/10766 to get more information about this book, to buy it in print, or to download it as a free PDF. §14.2 Algebraic Topology. Topology is generally introduced as I described it in §AG.6, ...

In the computer vision field of object detection, deep learning models are trained to identify objects of interest within an image of a scene. For example, such models can be trained to detect viruses ...

In this course we will consider the structure of (infinite) groups. For this, we will study actions of groups on interesting topological and metric spaces. The geometry of these spaces can be used to ...

Kevin Knudson does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond ...

The Earth's climate system seems to have shifted abruptly between colder and warmer modes in the past. Do we risk the same today from anthropogenic climate change? Frankly, climate models cannot ...