This concise book reviews methods used for gluing space-time manifolds together. It is therefore relevant to theorists working on branes, walls, domain walls, concepts frequently used in theoretical cosmology, astrophysics, and gravity theory. Nowadays, applications are also in theoretical condensed matter physics where Riemannian geometry appears. The book also reviews the history of matching conditions between two space-time manifolds from the early times of general relativity up to now.
Exploring common themes in modern art, mathematics, and science, including the concept of space, the notion of randomness, and the shape of the cosmos. This is a book about art—and a book about mathematics and physics. In Lumen Naturae (the title refers to a purely immanent, non-supernatural form of enlightenment), mathematical physicist Matilde Marcolli explores common themes in modern art and modern science—the concept of space, the notion of randomness, the shape of the cosmos, and other puzzles of the universe—while mapping convergences with the work of such artists as Paul Cezanne, Mark Rothko, Sol LeWitt, and Lee Krasner. Her account, focusing on questions she has investigated in her own scientific work, is illustrated by more than two hundred color images of artworks by modern and contemporary artists. Thus Marcolli finds in still life paintings broad and deep philosophical reflections on space and time, and connects notions of space in mathematics to works by Paul Klee, Salvador Dalí, and others. She considers the relation of entropy and art and how notions of entropy have been expressed by such artists as Hans Arp and Fernand Léger; and traces the evolution of randomness as a mode of artistic expression. She analyzes the relation between graphical illustration and scientific text, and offers her own watercolor-decorated mathematical notebooks. Throughout, she balances discussions of science with explorations of art, using one to inform the other. (She employs some formal notation, which can easily be skipped by general readers.) Marcolli is not simply explaining art to scientists and science to artists; she charts unexpected interdependencies that illuminate the universe.
Groups and Manifolds is an introductory, yet a complete self-contained course on mathematics of symmetry: group theory and differential geometry of symmetric spaces, with a variety of examples for physicists, touching briefly also on super-symmetric field theories. The core of the course is focused on the construction of simple Lie algebras, emphasizing the double interpretation of the ADE classification as applied to finite rotation groups and to simply laced simple Lie algebras. Unique features of this book are the full-fledged treatment of the exceptional Lie algebras and a rich collection of MATHEMATICA Notebooks implementing various group theoretical constructions.
About the Book Ever since the creation of science fiction, readers the world over have been fascinated with concepts and technology far beyond current comprehension. But what if the science in science fiction could be explained and understood? With the progression of physics, the theories and mathematical equations behind mind-blowing concepts can become a bit easier to grasp. In The Split-Second Interval, William Holland begins by introducing the very basic history of physics, including the necessary mathematical concepts to understand the movement of an object in space-time, and progresses to the transition of three-dimensional logic to the time-based four-dimensional logic while describing Hypercube and four-dimensional movement. From there, a whole new world of universal understanding opens up, propelling the reader on a journey through anywhere and anywhen. Included in his work is a short story based on the principles discussed through the earlier pages, putting all the knowledge gained into one neat and wonderous tale, now with the foundation to understand the science behind the fiction. About the Author William Holland currently resides in Phoenix. He enjoys playing his keyboard, chess, cooking, and flying his Phantom ultralight aircraft. Holland volunteers in his community by making pancakes at local pancake breakfasts and serving ice cream at events.
In a self contained and exhaustive work the author covers Group Theory in its multifaceted aspects, treating its conceptual foundations in a proper logical order. First discrete and finite group theory, that includes the entire chemical-physical field of crystallography is developed self consistently, followed by the structural theory of Lie Algebras with a complete exposition of the roots and Dynkin diagrams lore. A primary on Fibre-Bundles, Connections and Gauge fields, Riemannian Geometry and the theory of Homogeneous Spaces G/H is also included and systematically developed.
Math and Art: An Introduction to Visual Mathematics explores the potential of mathematics to generate visually appealing objects and reveals some of the beauty of mathematics. With downloadable resources and a 16-page full-color insert, it includes numerous illustrations, computer-generated graphics, photographs, and art reproductions to demonstrate how mathematics can inspire art. Basic Math Topics and Their Visual Aspects Focusing on accessible, visually interesting, and mathematically relevant topics, the text unifies mathematics subjects through their visual and conceptual beauty. Sequentially organized according to mathematical maturity level, each chapter covers a cross section of mathematics, from fundamental Euclidean geometry, tilings, and fractals to hyperbolic geometry, platonic solids, and topology. For art students, the book stresses an understanding of the mathematical background of relatively complicated yet intriguing visual objects. For science students, it presents various elegant mathematical theories and notions. Comprehensive Material for a Math in Art Course Providing all of the material for a complete one-semester course on mathematics in art, this self-contained text shows how artistic practice with mathematics and a comprehension of mathematical concepts are needed to logically and creatively appreciate the field of mathematics.
Time is an exceptional dimension that is common to many application domains such as medicine, engineering, business, or science. Due to the distinct characteristics of time, appropriate visual and analytical methods are required to explore and analyze them. This book starts with an introduction to visualization and historical examples of visual representations. At its core, the book presents and discusses a systematic view of the visualization of time-oriented data along three key questions: what is being visualized (data), why something is visualized (user tasks), and how it is presented (visual representation). To support visual exploration, interaction techniques and analytical methods are required that are discussed in separate chapters. A large part of this book is devoted to a structured survey of 101 different visualization techniques as a reference for scientists conducting related research as well as for practitioners seeking information on how their time-oriented data can best be visualized.
