Sporadics

Sporadics
Author: Cometan
Publisher: Astral Publishing
Total Pages: 27
Release:
Genre: Religion
ISBN:

Sporadics is the sixteenth instalment in the Little Blue Book Series and comprises of the twenty-eighth discourse of the Monodoxy, which is itself the first disquisition of the founding book of Astronism, titled the Omnidoxy. This publication focuses the nature of the relationship between The Chaos and The Cosmos with the aim of understanding The Chaos, what can be considered as constituting chaotic nature, as well as exploring deeper questions about role of The Chaos in cosmological functions and existentiality. The Little Blue Book Series was created and first published by Cometan himself as a way to simplify and commercialise the immensity of the two million word length of the Omnidoxy into smaller, more bite-size publications. A successful series from its very first published entry, the Little Blue Book Series has gone on to become a symbol of Astronist commercial literature and a way for Cometan’s words to reach readers of all ages and abilities who remain daunted by the beauty and yet the sheer extensiveness of the Omnidoxy as the longest religious text in history.

Sporadic Groups

Sporadic Groups
Author: Michael Aschbacher
Publisher: Cambridge University Press
Total Pages: 336
Release: 1994-03-25
Genre: Mathematics
ISBN: 9780521420495

Sporadic Groups is the first step in a programme to provide a uniform, self-contained treatment of the foundational material on the sporadic finite simple groups. The classification of the finite simple groups is one of the premier achievements of modern mathematics. The classification demonstrates that each finite simple group is either a finite analogue of a simple Lie group or one of 26 pathological sporadic groups. Sporadic Groups provides for the first time a self-contained treatment of the foundations of the theory of sporadic groups accessible to mathematicians with a basic background in finite groups such as in the author's text Finite Group Theory. Introductory material useful for studying the sporadics, such as a discussion of large extraspecial 2-subgroups and Tits' coset geometries, opens the book. A construction of the Mathieu groups as the automorphism groups of Steiner systems follows. The Golay and Todd modules, and the 2-local geometry for M24 are discussed. This is followed by the standard construction of Conway of the Leech lattice and the Conway group. The Monster is constructed as the automorphism group of the Griess algebra using some of the best features of the approaches of Griess, Conway, and Tits, plus a few new wrinkles. Researchers in finite group theory will find this text invaluable. The subjects treated will interest combinatorists, number theorists, and conformal field theorists.

A First Course in the Sporadic SICs

A First Course in the Sporadic SICs
Author: Blake C. Stacey
Publisher: Springer Nature
Total Pages: 119
Release: 2021-05-31
Genre: Science
ISBN: 3030761045

This book focuses on the Symmetric Informationally Complete quantum measurements (SICs) in dimensions 2 and 3, along with one set of SICs in dimension 8. These objects stand out in ways that have earned them the moniker of "sporadic SICs". By some standards, they are more approachable than the other known SICs, while by others they are simply atypical. The author forays into quantum information theory using them as examples, and the author explores their connections with other exceptional objects like the Leech lattice and integral octonions. The sporadic SICs take readers from the classification of finite simple groups to Bell's theorem and the discovery that "hidden variables" cannot explain away quantum uncertainty. While no one department teaches every subject to which the sporadic SICs pertain, the topic is approachable without too much background knowledge. The book includes exercises suitable for an elective at the graduate or advanced undergraduate level.

Nine Mathematical Challenges: An Elucidation

Nine Mathematical Challenges: An Elucidation
Author: A. Kechris
Publisher: American Mathematical Soc.
Total Pages: 221
Release: 2021-09-24
Genre: Education
ISBN: 1470454904

This volume stems from the Linde Hall Inaugural Math Symposium, held from February 22–24, 2019, at California Institute of Technology, Pasadena, California. The content isolates and discusses nine mathematical problems, or sets of problems, in a deep way, but starting from scratch. Included among them are the well-known problems of the classification of finite groups, the Navier-Stokes equations, the Birch and Swinnerton-Dyer conjecture, and the continuum hypothesis. The other five problems, also of substantial importance, concern the Lieb–Thirring inequalities, the equidistribution problems in number theory, surface bundles, ramification in covers and curves, and the gap and type problems in Fourier analysis. The problems are explained succinctly, with a discussion of what is known and an elucidation of the outstanding issues. An attempt is made to appeal to a wide audience, both in terms of the field of expertise and the level of the reader.

The Classification of Finite Simple Groups

The Classification of Finite Simple Groups
Author: Michael Aschbacher
Publisher: American Mathematical Soc.
Total Pages: 362
Release: 2011
Genre: Mathematics
ISBN: 0821853368

Provides an outline and modern overview of the classification of the finite simple groups. It primarily covers the 'even case', where the main groups arising are Lie-type (matrix) groups over a field of characteristic 2. The book thus completes a project begun by Daniel Gorenstein's 1983 book, which outlined the classification of groups of 'noncharacteristic 2 type'.