Mathematics Of Infinity
Download Mathematics Of Infinity PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Mathematics Of Infinity book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
Mathematics of Infinity
""Mathematics of Infinity"" explores the concept of infinity across mathematics and physics, revealing its profound implications and the paradoxes that arise when attempting to define and manipulate it. The book focuses on the mathematical formalization of infinity through set theory, the paradoxes emerging from infinite processes like Zeno's paradox, and infinity's role in modern physics, particularly in cosmology and quantum mechanics. This exploration highlights how infinity challenges our intuition and pushes the boundaries of established scientific thought, revealing its crucial role in interpreting the universe's mysteries. The book traces the historical development of our understanding of infinity, from philosophical debates to groundbreaking mathematical work. It examines how infinity manifests in singularities within general relativity, the infinite degrees of freedom in quantum field theory, and the concept of an infinite universe. By establishing interdisciplinary connections, the book demonstrates how similar mathematical concepts and paradoxes appear across diverse fields, offering a unified perspective on infinity and its applications. Each section builds upon the previous one, culminating in a discussion of the intertwined nature of these concepts and their implications for future research.
The Mathematics of Infinity
Author: Theodore G. Faticoni
language: en
Publisher: John Wiley & Sons
Release Date: 2012-04-17
Praise for the First Edition ". . . an enchanting book for those people in computer science or mathematics who are fascinated by the concept of infinity."—Computing Reviews ". . . a very well written introduction to set theory . . . easy to read and well suited for self-study . . . highly recommended."—Choice The concept of infinity has fascinated and confused mankind for centuries with theories and ideas that cause even seasoned mathematicians to wonder. The Mathematics of Infinity: A Guide to Great Ideas, Second Edition uniquely explores how we can manipulate these ideas when our common sense rebels at the conclusions we are drawing. Continuing to draw from his extensive work on the subject, the author provides a user-friendly presentation that avoids unnecessary, in-depth mathematical rigor. This Second Edition provides important coverage of logic and sets, elements and predicates, cardinals as ordinals, and mathematical physics. Classic arguments and illustrative examples are provided throughout the book and are accompanied by a gradual progression of sophisticated notions designed to stun readers' intuitive view of the world. With an accessible and balanced treatment of both concepts and theory, the book focuses on the following topics: Logic, sets, and functions Prime numbers Counting infinite sets Well ordered sets Infinite cardinals Logic and meta-mathematics Inductions and numbers Presenting an intriguing account of the notions of infinity, The Mathematics of Infinity: A Guide to Great Ideas, Second Edition is an insightful supplement for mathematics courses on set theory at the undergraduate level. The book also serves as a fascinating reference for mathematically inclined individuals who are interested in learning about the world of counterintuitive mathematics.
The Mathematics of Harmony
Author: Alekse? Petrovich Stakhov
language: en
Publisher: World Scientific
Release Date: 2009
Assisted by Scott Olsen (Central Florida Community College, USA) This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the ?Mathematics of Harmony,? a new interdisciplinary direction of modern science. This direction has its origins in ?The Elements? of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the ?golden? algebraic equations, the generalized Binet formulas, Fibonacci and ?golden? matrices), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational radices, Fibonacci computers, ternary mirror-symmetrical arithmetic, a new theory of coding and cryptography based on the Fibonacci and ?golden? matrices).The book is intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.