Simple groups, Lie groups, and the search for symmetry II | Math History | NJ Wildberger скачать в хорошем качестве

Simple groups, Lie groups, and the search for symmetry II | Math History | NJ Wildberger

This is the second video in this lecture on simple groups, Lie groups and manifestations of symmetry. During the 19th century, the role of groups shifted from its origin in number theory and the theory of equations to its role in describing symmetry in geometry. In this video we talk about the history of the search for simple groups, the role of symmetry in tesselations, both Euclidean, spherical and hyperbolic, and the introduction of continuous groups, or Lie groups, by Sophus Lie. Along the way we meet briefly many remarkable mathematical objects, such as the Golay code whose symmetries explain partially the Mathieu groups, the exceptional Lie groups discovered by Killing, and some of the other sporadic simple groups, culminating with the Monster group of Fisher and Greiss. The classification of finite simple groups is a high point of 20th century mathematics and the cumulative efforts of many mathematicians. ************************ Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary. My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/... My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things. Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects! If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at   / njwildberger   Your support would be much appreciated. Here are the Insights into Mathematics Playlists:    • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist   Here are the Wild Egg Maths Playlists (some available only to Members!)    • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist      • Playlist   ************************